Whole numbers
Example: Which of the following shows the number 56,000,010,500 in words?
1) Fifty six million, one thousand five hundred 2) Fifty six million, ten thousand five hundred 3) Fifty six billion, one thousand five hundred 4) Fifty six billion, ten thousand five hundred
Answer: Fifty six billion, ten thousand five hundred

Example: Upon logging into MSN Messenger, Natalie found 15,146,562 people online at that time. Which of the following shows the number of people online at that time in words?
1) Fifteen million, one thousand forty six hundred, five sixty two 2) Fifteen million, one hundred forty six thousand, five sixty two 3) Fifteen million, one forty six thousand, five hundred sixty two 4) Fifteen million, one hundred forty six thousand, five hundred sixty two
Answer: Fifteen million, one hundred forty six thousand, five hundred sixty two

Example: Which of the following is the standard form of the number 'seven million, two hundred five thousand, seventeen'?
1) 7,200,517 2) 7,205,017 3) 7,205,170 4) 7,200,005,017
Answer: 7,205,017

Example: When an inch of rain falls, a one square mile area receives about seventeen million, three hundred eighty thousand gallons of water. Which of the following shows that number in standard form?
1) 17,380 2) 17,000,380 3) 17,380,000 4) 17,300,800,000
Answer: 17,380,000

Example: Which digit is in the ten million’s place in the number 14,567,890?
1) 1 2) 4 3) 9 4) 14
Answer: 1

Example: What is the place value of digit 3 in the number 34,412?
1) 34,412 2) 30,000 3) 3,000 4) 3
Answer: 30,000

Example: Which of the following is the expanded form of the number 50,000,967,605?
1) 50,000,000 + 900,000 + 67,000 + 600 + 10 + 5 2) 50,000,000 + 900,000 + 60,000 + 7,000 + 600 + 5 3) 50,000,000,000 + 900,000 + 60,000 + 7,000 + 600 + 5 4) 50,000,000,000 + 900,000 + 67,000 + 600 + 5
Answer: 50,000,000,000 + 900,000 + 60,000 + 7,000 + 600 + 5

Example: What is the value of 10 + 9,000,000,000 + 9?
1) 900,019 2) 9,000,019 3) 9,000,000,019 4) 9,000,000,109
Answer: 9,000,000,019

Example: Without repeating digits, write the smallest 6 digit number in standard form using digits 4, 6, 9, 1, 3, 7.
Answer: 134,679

Example: Without repeating digits, write the largest 6 digit number in standard form using digits 6, 2, 8, 9, 5, 4.
Answer: 986,542

Example: Which of the following is not correct?
1) 45,768 < 45,678 2) 45,768 > 45,678 3) 45,867 > 45,678 4) 45,787 < 45,878
Answer: 45,768 < 45,678

Example: Select the smallest number
1) 100,101,110 2) 101,101,110 3) 110,101,110 4) 100,101,101
Answer: 100,101,101

Example: Which of the following options shows the given numbers arranged from greatest to least. 279,632; 89,263; 101,991; 110,099
1) 279,632; 110,099; 101,991; 89,263 2) 89,263; 101,991; 110,099; 279,632 3) 279,632; 101,991; 110,099; 89,263 4) 279,632; 89,263; 101,991; 110,099
Answer: 279,632; 110,099; 101,991; 89,263

Example: A city has a population of 378,765. What will be the result when you round off this number to the nearest ten thousand?
1) 379,000 2) 370,000 3) 400,000 4) 380,000
Answer: 380,000


Properties of whole numbers and order of operation
Example: Which of the following property is used in the expression given below? 12 + 4 = 4 + 12
1) Commutative property 2) Associative property 3) Distributive property 4) None of the above
Answer: Commutative property

Example: Write the missing number to make the following a true statement. 87 + 45 + 13 = 87 +  + 45
Answer: 13

Example: Which of the following property is used in the expression given below? (13 X 2) X 5 = 13 X (2 X 5)
1) Commutative property 2) Associative property 3) Commutative property and Associative property 4) Distributive property
Answer: Associative property

Example: Write the missing number to make the following a true statement. 875 + (947 + 125) = 947 + (875 + ______)
Answer: 125

Example: Solve by using commutative and associative property. 12 + 9 + 5 + 8 + 15 + 11
1) 40 2) 50 3) 60 4) 70
Answer: 60

Example: Evaluate 5 X 32 X 4
1) 310 2) 320 3) 630 4) 640
Answer: 640

Example: Which of the following property is used in the expression given below? 6 X (20 – 4) = (6 X 20)  (6 X 4)
1) Commutative property 2) Associative property 3) Commutative and Associative property 4) Distributive property
Answer: Distributive property

Example: Write the missing number to make the following a true statement. (15 X 28) + (15 X 12 ) = 15 X ____
Answer: 40

Example: Solve 54 X 25 + 54 X 75
1) 5,400 2) 5,986 3) 7,500 4) 2,500
Answer: 5,400

Example: Danielle purchased 5 chairs and 5 tables for her office. If the cost of each chair is $35 and the cost of each table is $65, find the total amount she paid for the 5 chairs and 5 tables.
1) $450 2) $500 3) $550 4) $600
Answer: $500

Example: The sum of three whole numbers is 74. If the first two whole numbers are 20 and 14, what is the third number?
1) 74 – (20 – 14) 2) 74 – 20 + 14 3) 74 – (20 + 14) 4) 74 + 20 + 14
Answer: 74 – (20 + 14)

Example: Alexis went to a shop and purchased two tshirts that cost $10 each and a cap that costs $6. She gave $30 to the cashier. How much money will the cashier return to Alexis?
1) $30  $10 + $6 2) $30 – (2 X $10 + $6) 3) $30  2 X ($10 + $6) 4) None of the above
Answer: $30 – (2 X $10 + $6)

Example: The table below shows the cost of some items.
1) $(2x5 + 6 + 3x10 + 20) 2) $(2x5 + 2x6 + 10 + 20) 3) $(2x5 + 3x6 + 1x10 + 1x30) 4) $(2x5 + 3x6 + 1x10 + 1x20)
Answer: $(2x5 + 3x6 + 1x10 + 1x20)

Example: Solve using the correct order of operations. 56  8 ÷ 4 X 3 = ?
1) 24 2) 36 3) 50 4) 162
Answer: 50

Example: Which of the following expression has the value of 20?
1) 40 ÷ (8 – 4) X 4 – 2 2) (40 ÷ 8) + 4 X 2  4 3) 40 ÷ (8 – 4) X (4 – 2) 4) 40 ÷ (8 – 4) X 4  4
Answer: 40 ÷ (8 – 4) X (4 – 2)

Example: Steven is a college student and lives in his college dorm. Last week he traveled to his parents' house on Friday afternoon. It took him 6 hours to get home and when he got home he realized that his average speed was only 24 miles per hour. Last month when he traveled to his parents house on a Saturday morning it took him only 4 hours to cover the same distance. At what average speed did he travel last month when visiting his parents' house?
1) 46 miles per hour 2) 36 miles per hour 3) 32 miles per hour 4) 24 miles per hour
Answer: 36 miles per hour

Example: Compare and select the missing sign. 16 ÷ 4 X 4 + 2 ____ (16 ÷ 4) X (4 + 2)
1) < 2) > 3) =
Answer: <

Example: Write the missing number. ____ ÷ 5 + 2 X 4 = 12
Answer: 20


Estimating with whole numbers
Example: Estimate the following by first rounding off each number to the nearest ten thousand. 51,561 + 27,382
1) 80,000 2) 79,000 3) 78,000 4) 70,000
Answer: 80,000

Example: In a Holiday & Home Expo a manufacturer sells $45,789 worth of home accessories in the first day, $50,899 worth of home accessories in the second day and $44,105 worth of home accessories in the third day. Which of the following option best represents the approximate total sales for the manufacturer in the three days?
1) $150,000 2) $143,000 3) $140,000 4) $138,000
Answer: $140,000

Example: Estimate the following by first rounding off each number to the nearest ten. thousand. 91,272  69,567
1) 2,000 2) 20,000 3) 21,000 4) 30,000
Answer: 20,000

Example: Daniel works in an Auto Transporting Company as an interstate walkin truck driver. As per the company’s rule he has to report the mileage reading of the truck before and after each trip. If his records for a trip shows the reading 15,811 in the beginning and 18,997 at the end, approximately how many miles (to the nearest hundred) did he travel during that trip?
1) 2,200 2) 3,000 3) 3,200 4) 3,500
Answer: 3,200

Example: Estimate the following by first rounding off the numbers to the nearest hundreds. 128 X 897
1) 8,000 2) 9,000 3) 10,800 4) 90,000
Answer: 90,000

Example: A group of 68 students of the Naval Academy in Houston, Texas plans to visit some famous attractions such as The Georgia Aquarium, The CNN Center and The World of Coke in Atlanta. If a bus ticket from Houston to Atlanta cost around $112, approximately how much money would they pay as bus fare to reach Atlanta?
1) $7,070 2) $7,200 3) $7,700 4) $7,800
Answer: $7,700

Example: Estimate the following by first rounding off the numbers to the nearest tens. 661 ÷ 59
1) 11 2) 60 3) 110 4) 660
Answer: 11

Example: Mrs. Harris baked 782 cookies for a sale. She wants to pack the cookies in the 59 decorative packets that she has. About how many cookies would Mrs. Harris be able to pack in each packet?
Answer: 13

Example: Estimate the following by first rounding off the numbers to the nearest thousands. 3,416 + 7,341 – 1,976
1) 10,000 2) 9,000 3) 8,700 4) 8,000
Answer: 8,000

Example: Below is a table with historical and predicted population figures in millions.
1) 1999 2) 2008 3) 2050 4) None of the above
Answer: 1999


Number Theory
Example: 2 is the only even prime number. All other even numbers are composite.
1) True 2) False
Answer: True

Example: Which of the following is not correct?
1) If x is divisible by 3, it must be divisible by 9. 2) If x is divisible by 9, it must be divisible by 3. 3) If x is divisible by 6, it must be divisible by 3. 4) If x is divisible by 6, it must be divisible by 2.
Answer: If x is divisible by 3, it must be divisible by 9.

Example: Which of the following is divisible by 8?
1) 32,446 2) 32,442 3) 23,424 4) 23,422
Answer: 23,424

Example: Which of the following is divisible by both 4 and 5?
1) 5,520 2) 5,530 3) 5,550 4) 5,554
Answer: 5,520

Example: Select the missing digit. The number 1,_37 is divisible by 9.
1) 9 2) 8 3) 7 4) 6
Answer: 7

Example: A jeweler has 2,664 diamonds. These diamonds are to be fixed in rings such that no diamonds are left and each ring has equal number of diamonds. Which of the following could be the number of diamonds in each ring?
1) 4 2) 6 3) 9 4) All of the above
Answer: All of the above

Example: Which group shows all the factors of 32?
1) 1, 2, 4, 12, 16, 32 2) 1, 2, 4, 8, 12, 32 3) 1, 2, 4, 8, 16, 32 4) 2, 4, 8, 16, 32
Answer: 1, 2, 4, 8, 16, 32

Example: Some of the 6th grade students of St. Paul Middle School are helping their teacher arrange a total of 48 decorated pots in equal groups for a craft exhibition. The students wrote all the possible choices by listing the factors of 48 as follows: 1, 2, 3, 4, 6, 12, 16, 24, 48 When the students showed their list to the teacher, the teacher told them that there was one more choice. What number did the students miss in listing the factors of 48?
1) 7 2) 8 3) 14 4) 18
Answer: 8

Example: Which of the following shows all the common factors of 12, 18 and 20?
1) 1, 2 2) 1, 3, 4 3) 1, 3, 5 4) 1, 2, 3, 4, 5
Answer: 1, 2

Example: Which of the following is the prime factorization of the number 90?
1) 2³ X 3 X 5 2) 2 x 3³ x 5 3) 2 x 3² x 5 4) 2³ x 3³ x 5
Answer: 2 x 3² x 5

Example: Find the Greatest Common Factor (GCF) of the following set of numbers 16, 24 and 80
1) 2 2) 4 3) 6 4) 8
Answer: 8

Example: Steven is packing 20 cookies, 15 candies and 10 burgers for a campout trip with his friends. He wants to pack these snacks into packets such that each pack has the same number of cookies (say a), the same number of candies (say b) and the same number of burgers (say c)in each packet after leaving 4 cookies, 3 candies and 2 burgers for himself. Which of the following could be the greatest number of packets that he can make?
1) 2 2) 4 3) 6 4) 8
Answer: 4

Example: Which of the following is a group of multiples of 25?
1) 1, 5, 25 2) 1, 25, 625 3) 25, 45, 55 4) 25, 50, 75
Answer: 25, 50, 75

Example: Which of the following is the group of the first two common multiples of 7 and 21?
1) 1 and 7 2) 14 and 21 3) 21 and 42 4) 42 and 56
Answer: 21 and 42

Example: Find the LCM of 6, 10 and 12.
1) 34 2) 26 3) 60 4) 80
Answer: 60

Example: What is the least common multiple of 3, 5 and 7?
1) 21 2) 35 3) 90 4) 105
Answer: 105

Example: Matthew is buying water bottles and lunch boxes for his shop. Water bottles are available in packages of 10 and lunch boxes are available in packages of 12. What is the smallest number of water bottles and lunch boxes he should buy to have an equal number of each?
1) 120 2) 100 3) 90 4) 60
Answer: 60

Example: Select the least common denominator (LCD) for the following pair of fraction.
1) 4 2) 5 3) 20 4) 30
Answer: 20


Algebra – Expressions
Example: Which of the following pair contains like terms?
1) 14x, 43y 2) 5x², 2y² 3) 6x²y, 4yx² 4) 8x²y², 9y²x
Answer: 6x²y, 4yx²

Example: Select the coefficient of x in the following expression. 3z + 2xy + 2
1) 3z + 2 2) 2y 3) 3 4) 2
Answer: 2y

Example: Which of the following options does not represent the given algebraic expression in words? x + 15
1) The sum of x and 15 2) 15 more than x 3) 15 added to x 4) 15 times x
Answer: 15 times x

Example: Select the algebraic expression for the phrase given below. '2 less than quotient of x and y'
Answer:

Example: If 3 is added to two times of p, it becomes q. Which of the following represents q?
1) 3p + 2 2) 2q + 3 3) 2p + 3 4) 3 + p
Answer: 2p + 3

Example: Elizabeth, Madison and Lauren bought a wristwatch for x dollars as a gift for their Mom's 40th birthday. Elizabeth spent one fourth of the money, Madison spent 12 dollar more than Elizabeth did and Lauren spent the rest of the money for the wristwatch. How much money did Lauren spend on the wristwatch?
Answer:

Example: Review the table below,
1) 8a 2) 9a 3) 7a + 4 4) 8a + 1
Answer: 8a + 1

Example: Evaluate the following algebraic expression by substituting the given value of the variable. 6n² + 1, n = 3
1) 19 2) 37 3) 55 4) 70
Answer: 55

Example: If x = 1 and y = 2 then write the value of the following expression. 3 + (x + y)²
Answer: 12

Example: Select the missing number for the table given below.
1) 45 2) 44 3) 40 4) 39
Answer: 44

Example: Simplify 6r²– 2r + 2r² + 6r
Answer:

Example: Add a + b + c and 5a + 5b + 5c
1) a + b + c 2) 6a + 6b + 6c 3) 5a² + 5b² + 5c² 4) 6a³ + 6b³ + 6c³
Answer: 6a + 6b + 6c

Example: Subtract 2x from 3 + 9x.
1) 11 x + 3 2)  3  7x 3) 7x + 3 4) 7x + 1
Answer: 7x + 3

Example: A rectangular frame is (3x + 1) cm long and 2x cm wide. Which of the following expression represents the perimeter (in cm) of the rectangular frame?
1) 5x ² + 2x 2) 6x² + 2x 3) 6x + 1 4) 10x + 2
Answer: 10x + 2


Algebra – Equation with one variable
Example: Which equation represents the statement given below? 'A number x increased by 5 is equal to 15'.
1) x + 5 = 15 2) x  5 = 15 3) x + 15 = 5 4) 5x = 15
Answer: x + 5 = 15

Example: 8 students are working on a science project. The number of girls working on that project is 2 more than the number of boys. If x boys are working on that project then which of the following equation can be used to find the number of boys working on the project.
1) x + 2 = 8 2) x  2 = 8 3) x + 8 = 2 4) x + x + 2 = 8
Answer: x + x + 2 = 8

Example: An equation is shown below, 9x = 81 Which of the following method could be used to solve the above equation?
1) Multiply 9x by 9 and multiply 81 by 9 2) Divide 9x by 9 and divide 81 by 9 3) Multiply 9x by 9 and multiply 81 by 81 4) Divide 9x by 9 and divide 81 by 81
Answer: Divide 9x by 9 and divide 81 by 9

Example: Select the value of x for the given equation. 3x  24 = 0
1) 72 2) 27 3) 21 4) 8
Answer: 8

Example: Determine whether the given value of the variable is a solution of the equation. 1 = k + 1, k= 1
1) Yes 2) No
Answer: No

Example: Which of the following equation does not have the solution n = 8?
Answer:

Example: Solve x + 11 = 55.
1) x = 4 2) x = 5 3) x = 44 4) x = 66
Answer: x = 44

Example: Solve
Answer:

Example: Solve the following equation. 5 x = 90
1) x = 18 2) x = 85 3) x = 95 4) x = 450
Answer: x = 18

Example: Solve
Answer:

Example: Hannah spends 2 hours every day in a coaching institute to study math. This is one sixth of her daily study hours (in school, home and coaching institute). How many hours a day does Hannah study in all?
1) 12 2) 6 3) 3 4) 2
Answer: 12

Example: Solve the following equation. 5 + 7x = 40
1) x = 4 2) x = 5 3) x = 6 4) x = 35
Answer: x = 5

Example: Elijah had $20 and Luke had $30. They bought a football together. Elijah paid one third of the football cost and Luke paid two third of the football cost. Then Elijah and Luke had equal amount of money left. What was the cost of the football?
1) $40 2) $30 3) $10 4) $8
Answer: $30
 

Understanding integers
Example: Select true or false. ‘Zero is less than every negative integer and greater than every positive integer.’
1) True 2) False
Answer: False

Example: Which of the following is not an integer between 7 and 9?
1) 0 2) 8 3) 4 4) 5
Answer: 8

Example: Which of the following option correctly represents the integers 3, 4 and 4 on a number line?
Answer:

Example: Write an integer for the given situations. 'A deposit of $350'
1) + 350 2)  350
Answer: + 350

Example: Which of the situation does not match the given integer? 40
1) A loss of $40 2) 40 m below sea level 3) A salary increase of $40 4) Losing a weight of 40 lbs
Answer: A salary increase of $40

Example: Eric tries bungee jumping during his visit to his cousin’s place in Colorado. He jumps from a crane fixed on a bridge over a river. The initial jumping point is 97 feet above the bridge. After jumping, Eric slightly touches the water which is at a same distance under the bridge as the initial jumping point was over the bridge. If the bridge represents 0, and the initial jumping point represents +97, what integer would best describe Eric’s lowest position after jumping?
Answer: 97

Example: Write the additive inverse of the integer +78.
Answer: 78

Example: What is the absolute value of 9?
1) 0 2) 1 3) 9 4) 9
Answer: 9

Example: Maria deposited $560 in her bank account in the first week of April. After two weeks she withdrew $370 to purchase a mountain bike to gift her son on his birthday. Write an integer expression to represent the balance amount in Maria’s account at the end of April, if there was already $4,575 in her account at the beginning of April.
Answer: $4,575 + $560  $370

Example: Compare (15)  (12)
1) < 2) > 3) =
Answer: <

Example: The climate data for the American AmundsenScott station at the South Pole shows that the average daily minimum temperature in degree Celsius from January to December is as follows:
1) January 2) July 3) August 4) December
Answer: July

Example: Which of the following option represents the given integers from greatest to the lowest? 8, 5, 0, 12, 1, 9, 15
1) 0, 1, 5, 8, 9, 12, 15 2) 12, 9, 8, 0, 1, 5, 15 3) 15, 12, 9, 8, 5, 1, 0 4) 15, 5, 1, 0, 8, 9, 12
Answer: 15, 5, 1, 0, 8, 9, 12

Example: The following table shows the depths of 5 trenches in different seas and oceans in the world in meters. Arrange the trenches from the shallowest to the deepest?
Answer: Litke deep, Sandwich trench, Java trench, Milwaukee trench, Mariana trench
 

Addition and subtraction of integers
Example: Write an addition expression shown on the given number line.
1) (3) + 7 = 4 2) (3) + (4) = 7 3) 4 + (7) = 3 4) 4 + (3) = 1
Answer: 4 + (7) = 3

Example: Which of the following integer comes after 17?
1)  18 2)  16 3) 16 4) 18
Answer:  16

Example: Add (18) + (16) = .
1) 34 2) 2 3) 2 4) 34
Answer: 34

Example: Add 37 + (82) = .
1) 55 2) 45 3) 55 4) 119
Answer: 45

Example: Add (9) + 17 + (21) = .
1) 47 2) 29 3) 13 4) 13
Answer: 13

Example: Add (987) + 57 + (257) + 100 + 487
Answer: 600

Example: Mr. Allen deposited $450 in his bank account in the month of June, and withdrew $625 from his account in the month of July to purchase a guitar for his brother. If there was $2,450 in his account in the beginning of June, find the balance in Mr. Allen’s account after the withdrawal in the month of July.
Answer: $2,275

Example: Write a subtraction expression shown on the given number line.
1) (6)  1 = 7 2) (7) – (1) = 6 3) (6) – (7) = 1 4) (7) – (6) = 1
Answer: (6) – (7) = 1

Example: Subtract (27) – (35)
1) 62 2) 8 3) 8 4) 62
Answer: 8

Example: Subtract 29 – (28) = .
1) 47 2) 1 3) 1 4) 57
Answer: 57

Example: In golf, the scores are expressed as integer numbers that signifies whether a golfer is over par, at par, or under par. ‘Par’ is the number of strokes a skilled golfer takes to finish that hole. The player with the lowest score wins the game. At a golf tournament, Brandon scored +2 and Alexander scored 12. Who won the game and with how many points?
1) Brandon, 10 2) Alexander, 14 3) Alexander, 10 4) Brandon, 14
Answer: Alexander, 14

Example: Compare (6) + (9) ____ (6) – (9).
1) < 2) > 3) =
Answer: <

Example: Mrs. Garcia conducted a quiz competition for her sixth graders by dividing her class into two groups A and B. There were 3 rounds in the competition. The contestants received +5 points for every correct answer and 4 points for every wrong answer. If team A scored (2), 16 and (11) in the 3 rounds and team B scored 7, (2) and 7 in the 3 rounds, which team won the quiz competition?
1) Team A 2) Team B
Answer: Team B

Example: Find the missing term in ___ + (9) = 6
Answer: 15

Example: Evaluate the expression x – (19) when x = (13).
1) 6 2) 6 3) 22 4) 32
Answer: 6

Example: Subtract the sum of (250) and 138 from the difference of 136 and (272).
1) 24 2) 20 3) 296 4) 520
Answer: 520

Example: In a two hour fire sale, a store manager gains $36 and $28 by selling a dozen bed sheets and some home décor items respectively. He also suffers losses of $14, $19 and $18 by selling 3 art pieces during the two hour sale. What would be his total profit or loss in the 2 hour sale?
1) Profit, $27 2) Profit, $13 3) Loss, $13 4) No profit, no loss
Answer: Profit, $13
 

Multiplication and division of integers
Example: Find the product (6) x (12) = .
1) 72 2) 84 3) 72 4) 84
Answer: 72

Example: 19 x (6) = .
1) 114 2) 104 3) 104 4) 114
Answer: 114

Example: Alexis took an online math test that had a total of 30 questions. Each right answer on the test is worth +10 points and each wrong answer is worth 8 points. If Alexis attempted all the questions on the test but got 13 of them wrong, how much did she score on the test?
1) 66 2) 104 3) 130 4) 170
Answer: 66

Example: Solve (5) x 23 + (17) x 5 = .
Answer: 200

Example: Divide (108) ÷ (6) = .
1) 18 2) 16 3) 16 4) 18
Answer: 18

Example: Divide 225 ÷ (25) = .
1) 11 2) 9 3) 9 4) 11
Answer: 9

Example: Abigail works in an underground coal mine in West Virginia. The elevator she uses descends into the mine at a rate of 8 meters per minute. If she starts to descend in the elevator from a floor 20 meters above the ground level, how much time will it take Abigail to reach 380 meters?
1) 50 sec 2) 400 sec 3) 50 min 4) 1 hour
Answer: 50 min

Example: Find the missing term  ÷ (3) = 15
Answer: 45

Example: Simplify (5) – (48) ÷ (16) + (2) x 6
1) 4 2) 10 3) 14 4) 20
Answer: 20

Example: Mr. Moore, a wholesale dealer, earns a profit of $3 by selling a flour bag and suffers a loss of $5 by selling a rice bag when clearing his old stock. In a particular month, he sold 2,500 flour bags and an unknown number of rice bags to clear his old stock. If he had a total loss of $500 in clearing his old stock during that month, how many rice bags did Mr. Moore sell during this period?
1) 2,400 2) 1,600 3) 1,500 4) 1,400
Answer: 1,600

Example: Evaluate (y) ÷ (3) when y = 18.
1) 54 2) 6 3) 6 4) 54
Answer: 6
 

Coordinate plane and functions
Example: Select True or False. The horizontal axis in a coordinate plane is called yaxis.
1) True 2) False
Answer: False

Example: In the coordinate plane below, name the quadrant where the point F is located.
1) Quadrant I 2) Quadrant II 3) Quadrant III 4) Quadrant IV
Answer: Quadrant IV

Example: In the coordinate plane below, what are the coordinates of point D?
1) (1,3) 2) (1,3) 3) (3,1) 4) (3,1)
Answer: (3,1)

Example: Name the quadrant where the given ordered pair is located. (10,6.5)
1) Quadrant I 2) Quadrant II 3) Quadrant III 4) Quadrant IV
Answer: Quadrant III

Example: Which of the following is an equation for the function that results in the values shown in the table below?
1) y = x + 1 2) y = x + 3 3) y = 2x + 1 4) y = 3x + 1
Answer: y = 3x + 1

Example: Which of the following equation represents the situation below? ‘The number of girls (g) is 7 less than twice the boys (b).’
1) g = 7b – 2 2) g = 2b – 7 3) b = 7g – 2 4) b = 2g – 7
Answer: g = 2b – 7

Example: Grace and her mom go for a daily morning walk. Each day Grace’s mother walks 4 km more than two times the distance Grace walks. Which of the following option represents an equation for the given situation where the distance covered by Grace is represented by ‘p’ and the distance covered by her mother is represented by ‘q’?
1) q = 2p + 4 2) q = 2p – 4 3) p = 2q + 4 4) p = 2q – 4
Answer: q = 2p + 4

Example: Find the missing value in the given function table.
1) 1 2) 0 3) 1 4) 3
Answer: 3

Example: Which of the following ordered pair is not a solution of y = 3x + 8?
1) (0,8) 2) (1,5) 3) (2,1) 4) (3,1)
Answer: (2,1)

Example: Which of the following option represents an equation for the given group of ordered pairs? (1,13), (0,9), (1,5), (2,1), (2, 17)
1) y = 2x + 9 2) y = 4x + 5 3) y = 4x + 9 4) y = 5x + 8
Answer: y = 4x + 9

Example: Which of the following function is not an example of a linear function?
1) y = 4x + 3 2) y = x (x – 1) 3) y = 2x + 5x 4) y = 1 + x
Answer: y = x (x – 1)

Example: Which of the following graph represents the function described by the equation y = x + 2?
Answer:

Example: Use the given graph of a linear function to find the value of ‘y’ when x = 2.
1) 2 2) 1 3) 0 4) 2
Answer: 2
 

Comparing and ordering fractions

Example: Mr. Lewis had some money in his wallet. He gave one fourth of the money to Caleb, one third of the money to Jordan, five twelfth of the money to Gabriel and one sixth of the money to Eric. Who got the most amount of money from the Mr. Lewis?
1) Caleb 2) Gabriel 3) Jordan 4) Eric
Answer: Gabriel

Example: Matthew made two models shown below. Which of the following comparison is correct for the models?
Answer:

Example: Which of the following is correct?
Answer:

Example:
1) Mr. Lopez 2) Mr. Nelson
Answer: Mr. Lopez

Example: Which of the following shows the fractions arranged from greatest to least?
Answer:


Example: Which of the following is correct?
Answer:

Example: Which of the following shows the mixed numbers arranged from greatest to least?
Answer:

Example:
1) Math, Science, Art, Language 2) Art, Language, Math, Science 3) Math, Science, Language, Art 4) Math, Art, Language, Science
Answer: Math, Art, Language, Science


Example: A model is given below. Which of the following is represented by the model?
Answer:


Example: Write the missing number.
Answer: 6



 

Multiplication and Division of Fractions



Example:
1) 6 2) 8 3) 12 4) 24
Answer: 6

Example:
Answer:

Example: Estimate the following by first rounding the numbers to the nearest whole numbers and then solving.
1) 5 2) 6 3) 9 4) 10
Answer: 9

Example: Select the reciprocal of the following.
1) 2) 3) 4)
Answer:




Example:
1) 8 2) 9 3) 10 4) 11
Answer: 9

Example:
Answer: 20

Example:
Answer:

Example: Estimate the following by first rounding the fraction to zero, half or one then solving.
1) 2) 3) 1 4) 2
Answer: 1

Example: Which of the following is not equal to 1?
Answer:

Example: Find the number whose two fifth is 80.
1) 240 2) 200 3) 150 4) 120
Answer: 200

Example:
1) 50 2) 80 3) 100 4) 125
Answer: 80
 

Comparing and ordering decimals
Example:
1) 0.221 2) 2.210 3) 22.10 4) 220.1
Answer: 2.210

Example:
1) 0.0002 2) 0.012 3) 0.002 4) 0.02
Answer: 0.002

Example: Which of the following shows the number 824.020 in words?
1) Eight hundred twenty four and twenty thousands 2) Eight hundred twenty four and twenty hundredths 3) Eight hundred twenty four and twenty thousandths 4) Eight twenty four hundred and twenty thousandths
Answer: Eight hundred twenty four and twenty thousandths

Example: Which of the following shows the number “two thousand thirty two and four thousandths” in standard form?
1) 232.004 2) 2,032.004 3) 232.0004 4) 2,032.0004
Answer: 2,032.004

Example: Sara kept some of her word documents in a folder on a computer desktop. The folder’s size is one and sixty three hundredths GB. Which of the following shows the size of the folder in standard form?
1) 163 GB 2) 1.63 GB 3) 1.063 GB 4) 1.0063 GB
Answer: 1.63 GB

Example: Which of the following shows expanded form of the decimal 41.342?
1) 40 + 0.3 + 0.04 + 0.002 2) 40 + 1 + 0.03 + 0.04 + 0.002 3) 40 + 1 + 0.3 + 0.04 + 0.002 4) 40 + 1 + 0.3 + 0.4 + 0.002
Answer: 40 + 1 + 0.3 + 0.04 + 0.002

Example: What is the place value of 2 in 0.124?
1) Two 2) Twenty 3) Two hundred 4) Two hundredths
Answer: Two hundredths

Example: Which of the following is correct?
1) 0.03 < 0.008 2) 0.04 > 0.004 3) 0.083 > 0.38 4) 0.38 > 0.4
Answer: 0.04 > 0.004

Example: Which of the following is greater than 422.031?
1) 421.831 2) 422.103 3) 422.0031 4) 421.301
Answer: 422.103

Example: In which of the following, the decimals are arranged from greatest to least?
1) 2.041, 2.14, 2.41, 21.04 2) 2.14, 2.41, 2.041, 21.04 3) 21.04, 2.41, 2.14, 2.041 4) 21.04, 2.14, 2.41, 2.041
Answer: 21.04, 2.41, 2.14, 2.041

Example: The approximate value of π (pie) is 3.141592654. What would be the value of π rounded to the nearest thousandth.
1) 3.15 2) 3.142 3) 3.141 4) 3.14
Answer: 3.142


Example: Convert into decimals.
1) 0.00375 2) 0.0375 3) 0.375 4) 0.385
Answer: 0.0375

Example: Convert the mixed number given below to decimal.
1) 1.578 2) 1.675 3) 1.785 4) 1.875
Answer: 1.875


Example: Select the correct sign.
1) < 2) > 3) =
Answer: >


Addition and subtraction of decimals
Example: Find the sum 3.7 + 21.11
1) 21.81 2) 21.48 3) 24.18 4) 24.81
Answer: 24.81

Example: Grace wants to purchase some gifts for her cousins whom she plans to visit on Christmas. She selected a doll that costs $15.09 and a soft toy that costs $6.29 more than the doll from a nearby toy shop. How much money should she pay for the doll and the soft toy in all?
1) $21.28 2) $21.38 3) $36.47 4) $36.57
Answer: $36.47

Example: Estimate the following by first rounding the numbers to the nearest hundredth and then solving. 3.9235 + 8.038
1) 12.034 2) 11.961 3) 11.96 4) 11.95
Answer: 11.96

Example: Andrea bought a story book that cost $7.15, a puzzle game that cost $8.99 and a water bottle that cost $11.10. Which of the following is the best estimate for the total cost of the story book, puzzle game and the water bottle?
1) $25 2) $26 3) $27 4) $28
Answer: $27

Example: Subtract 7 – 0.11
1) 6.89 2) 6.9 3) 6.99 4) 7.89
Answer: 6.89

Example: Joshua wants to buy a toy robot that cost $63.99, but he has only $50.75. How much more money does he need to buy that toy robot?
1) $12.15 2) $12.24 3) $13.24 4) $13.25
Answer: $13.24

Example: Estimate the following by first rounding the numbers to the nearest tenth and then solving. 12.087  2.038
1) 10 2) 10.04 3) 10.05 4) 10.01
Answer: 10.01

Example: William wants to buy a binocular that costs $34.89. He has about three fifth of the cost of the binocular. Which of the following is the best estimate of the additional money that he needs to buy the binocular?
1) $7 2) $14 3) $15 4) $21
Answer: $14

Example: Solve 17.38 – 12.99 + 22.62
1) 26.01 2) 26.11 3) 27.01 4) 27.11
Answer: 27.01

Example: Jack saved a total of $45.5 from his weekly allowance. On his graduation day, he wanted to go out with his friends for a movie and a dinner and so his Mom gave him another $50. On the graduation evening, he spent $35.65 for dinner, $9.45 for movie tickets, and $12.20 for popcorns and soft drinks. How much money was left with Jack after the movie and dinner?
1) 36.2 2) 37.2 3) 37.4 4) 38.2
Answer: 38.2

Example: Estimate the following by first rounding the numbers to the nearest whole numbers and then solving. 4.792 + 45.72 – 5.821
1) 43 2) 44 3) 45 4) 46
Answer: 45
 

Multiplication and division of decimals
Example: Multiply 0.004 X 0.4
1) 0.00016 2) 0.0016 3) 0.016 4) 0.16
Answer: 0.0016

Example: On a Saturday morning, Steven and Cody drove to visit their grandparents about 300 miles away in Lancing, Michigan from their home town in Ohio. They drove the car for 4 hours at an average speed of 25.5 miles per hour and then stopped for an half hour break. After the break they drove at an average speed of 40 miles per hour and reached their destination in 5 hours. How many miles did Steven and Cody cover before the break?
1) 94 miles 2) 102 miles 3) 178.5 miles 4) 196 miles
Answer: 102 miles

Example: Estimate the following by first rounding the numbers to the nearest whole numbers and then solving. 2.679 X 15.04321
1) 3 2) 4.5 3) 30 4) 45
Answer: 45

Example: Sophia wants to buy a 1.96 feet long metal bar to build a project. If a feet of the bar costs $16.25, which of the following is closest to the amount of money that Sophia would have to pay to get the desired length of the metal bar?
1) $18 2) $24 3) $32 4) $34
Answer: $32

Example: Which of the following is the scientific notation for the number 460,234?
Answer:

Example:
1) 532,000,000 2) 5,320,000 3) 532,000 4) 532
Answer: 5,320,000

Example: Divide 1.21 ÷ 1.1
1) 11 2) 1.1 3) 0.11 4) 0.011
Answer: 1.1

Example: Gabriel bought a packet of pens that contains 15 equally priced pens. If the cost of the packet was $25.95, what is the cost of each pen?
1) $1.5 2) $1.6 3) $1.73 4) $1.79
Answer: $1.73

Example: Estimate the following by first rounding the numbers to the nearest whole numbers and then solving. 174.982 ÷ 25.1209
1) 7 2) 6 3) 6.5 4) 6.9
Answer: 7

Example: Andy burns about 402.25 calories while walking on his treadmill for around 39.30 minutes every day. About how many calories per minute on average does he burn every day using his treadmill?
Answer: 10 calories

Example: Solve 0.64 x 0.25 + 6.35 ÷ 0.5
1) 12.46 2) 12.78 3) 12.86 4) 14.30
Answer: 12.86

Example: Julia has a glass slide of dimensions as shown in the first figure and Jessica has a glass slide of dimensions as shown in the second figure. What is the difference between the areas of Julia’s and Jessica’s glass slides?
1) 0.02 cm ² 2) 0.20 cm ² 3) 1.02 cm ² 4) 2 cm ²
Answer: 0.20 cm ²


Solving fraction and decimal equations

Example:
Answer:

Example: Gabriel has 5 videogame CDs. This is two third of the total number of CDs that he has. Which of the following is not a way to find the total number of CDs that Gabriel has?
Answer:

Example:
1) Yes 2) No
Answer: No




Example:
Answer:

Example: Solve the following for n = 0.1 n³ + 17
1) 17.0003 2) 17.0001 3) 17.001 4) 17.3
Answer: 17.001

Example: Determine whether s = 0.08 is a solution of the equation. s ÷ 0.02 = 0.04
1) Yes 2) No
Answer: No

Example: Solve the equation x + 4.02 = 11.6
1) x = 6.4 2) x = 7.4 3) x = 7.58 4) x = 14.62
Answer: x = 7.58

Example: Solve the equation 6.25 = x – 12.002
1) x = 6.23 2) x = 6.248 3) x = 18.252 4) x = 18.27
Answer: x = 18.252

Example: Solve the equation 3.5x = 7
1) x = 0.2 2) x = 0.5 3) x = 2 4) x = 5
Answer: x = 2

Example:
1) x = 0.4 2) x = 0.20 3) x = 0.25 4) x = 4
Answer: x = 0.25

Example: Jacob and Michael took a vacation together in Hawaii. Their total expense for hotels, airfare and meals was $5796.60. The expense for hotels and meals was double that of the expense for airfare. If they contributed equally for these expenses, how much money did each of them pay for airfare?
1) $3,864.40 2) $1,932.20 3) $966.10 4) $483.05
Answer: $966.10
 

Sequence and Pattern
Example: Write the common difference in the given arithmetic sequence.
1, 13, 25, 37, 49 …
Answer: 12

Example: Cameron saw the following sequence in a Math book:
5, 15, 10, 20, 15, 25, 20, 30, ___,
Which of the following rule would Cameron use to find the next number in this sequence?
1) Add 5 2) Subtract 5 3) Add 10 4) Subtract 10
Answer: Subtract 5

Example:
1) 3 X number of squares in (n1)th figure 2) 3(n1) 3) 3n 4) n³
Answer: 3 X number of squares in (n1)th figure

Example: Which of the below sequence follows the rule: Start with 640, then subtract 30 from each number to get the next number.
1) 640, 670, 700, 730, 760 2) 640, 610, 580, 550, 520 3) 640, 610, 580, 540, 500 4) 640, 600, 560, 520, 480
Answer: 640, 610, 580, 550, 520

Example: Write the next term in the sequence given below.
7, 18, 29, 40, ___,
Answer: 51

Example:
Answer:


Example:
1) 32 2) 22 3) 16 4) 15
Answer: 16

Example: Write the value of the missing term in the sequence given in the table below.
Answer: 49

Example: Find the next three terms in the sequence given below.
1, 2, 4, 8, 16, 32, 64, 128, ___, ___,___,
1) 256, 512, 1,024 2) 192, 384, 768 3) 256, 384, 512 4) 192, 320, 512
Answer: 256, 512, 1,024

Example: Find the wrong number in the given sequence.
52, 51, 48, 43, 34, 27, 16
1) 43 2) 34 3) 27 4) 16
Answer: 34

Example: Sara's teacher asked Sara to write a sequence that starts with 8 and follows the rule ‘Add 12’. She wrote the sequence given below. On checking Sara’s work, her teacher found that one number in the sequence is not correct. Which is the incorrect number in the sequence?
8, 20, 32, 44, 56, 68, 78, 92, 104,
1) 68 2) 78 3) 92 4) 104
Answer: 78

Example: Find the 8th term of the following sequence.
50, 56, 62, 68…
1) 92 2) 88 3) 86 4) 74
Answer: 92

Example: In a game, 80 contestants participate at the start of the game. 6 of them are eliminated in each round of the game. How many participants will be left at the beginning of the fourth round of the game?
1) 56 2) 62 3) 68 4) 74
Answer: 62

Example: Which term of the sequence 1, 6, 11, 16, 21… is 41?
1) 8th 2) 9th 3) 10th 4) 11th
Answer: 9th

Example: In a TV reality show, if the value of first question in a game is $x, then the value gets doubled in the next question i.e. $2x in the second question, $4x in the third question and so on. If the first question of the game starts with a value of $250, which question will have the value $4,000?
1) 4th 2) 5th 3) 12th 4) 16th
Answer: 5th


Ratio and proportion
Example: In the pattern shown below, what is the ratio of the number of violet triangles to the number of green triangles?
1) 2:3 2) 3:2 3) 3:5 4) 5:3
Answer: 5:3

Example: Convert the following ratio in the simplest form. 28:68
1) 2:6 2) 4:17 3) 7:17 4) 14:34
Answer: 7:17

Example: Which of the following represents an equivalent ratio to the given ratio? 6:15
1) 2:3 2) 10:30 3) 14:35 4) 18:40
Answer: 14:35

Example: Which ratio is larger in the following?
16:18 or 25:30
1) 16:18 2) 25:30 3) Both are equal
Answer: 16:18

Example: Which of the following is the missing number in the table of equivalent ratios below?
1) 42 2) 46 3) 52 4) 54
Answer: 52

Example: Select true or false. The ratios a:b and b:a are equal
1) True 2) False
Answer: False

Example: Find the ratio of the following in the simplest form. 8 kg to 400 grams
1) 1:2 2) 1:50 3) 2:1 4) 20:1
Answer: 20:1

Example: William and his mom were making two separate soil beds for planting some tomatoes and potatoes in their backyard garden. William made a 4 m by 2.5 m soil bed for potatoes, and his mom made a 5 m by 3.2 m soil bed for tomatoes. What would be the ratio of the areas of soil beds made by William and his mother?
1) 2:3 2) 4:1 3) 5:8 4) 8:5
Answer: 5:8

Example: Which of the following pair of numbers best represent the number 135 divided in the ratio 4:5?
1) 40, 95 2) 60, 75 3) 75, 60 4) 80, 55
Answer: 60, 75

Example: Jennifer bought 10 comic books from a book exhibition for her kids, Justin and Grace, and distributed the books to them in the ratio of their ages. If Justin is 9 years old and Grace is 6 years old, how many comic books did each of them get?
Answer: Justin – 6 and Grace  4

Example: The greater part when a number is divided in the ratio 2:7 is 273. Find the number.
1) 341 2) 351 3) 361 4) 451
Answer: 351

Example: Mr. Hall works as an Aircraft Maintenance Manager in Boston, Massachusetts. The ratio of his monthly expenses to his monthly savings is 11:4. What would be his income if he saves $9,200 each month?
1) $16,100 2) $24,300 3) $25,300 4) $34,500
Answer: $34,500


Example:
1) Yes 2) No
Answer: No

Example: A florist arranges 144 tulips to make 9 bouquets for a valentine day sale. Which proportion could be solved to find x  the expected number of tulips arranged in 30 such bouquets?
Answer:


Example: Find the value of ‘n’ in the given proportion.
1) 6 2) 16 3) 24 4) 27
Answer: 24

Example: Mr. Martin and Mr. Harris are the two candidates for an upcoming general election. A survey, conducted by a daily newspaper, among the 600 registered voters shows that 320 people would vote for Mr. Martin. If 75,000 people are expected to vote in the election, how many votes would Mr. Harris get according to the survey?
Answer: 35,000


Rates
Example: Find the unit rate of gasoline if the cost of 5 gallons of gasoline is $17.
1) $2.04 2) $3.04 3) $3.20 4) $3.40
Answer: $3.40

Example:
1) $3.15 2) $3.25 3) $4.15 4) $8.50
Answer: $4.15

Example: Assuming that you need to buy a total of 6 liters of coke, which is a better deal for you  2 liter bottles of coke that costs $3.75 each or 1.5 liter bottles of coke that costs $2.95 each?
Answer: 2 liter bottles of coke

Example: Alexis and Sarah learn music lessons from two different instructors Mr. Brown and Mrs. Taylor. Mr. Brown charges $35 for 3 hours and Mrs. Taylor charges $50 for 4 hours. Which instructor offers a cheaper rate?
Answer: Mr. Brown

Example: What is the average speed of a bus that travels 200 miles in 5 hours?
1) 20 miles/hour 2) 40 miles/hour 3) 45 miles/hour 4) 50 miles/hour
Answer: 40 miles/hour

Example: Two brothers, Nicolas and Andrew, traveled by car to visit their common friend Daniel who lives 240 km away from their home. They took 4 hours to reach Daniel’s house. If they want to travel back to their home in 3 hours, how much faster should they drive?
1) 10 km/hour 2) 20 km/hour 3) 60 km/hour 4) 80 km/hour
Answer: 20 km/hour


Percentages
Example: What percent is not shaded in the following figure?
1) 40% 2) 45% 3) 50% 4) 55%
Answer: 45%

Example: Write the following fraction as a percent.
1) 30% 2) 60% 3) 65% 4) 75%
Answer:75%


Example: Compare the two fractions and choose the right sign:
1) < 2) > 3) =
Answer: <

Example: Write the following decimal as a percent.
0.125
1) 1.25% 2) 12.5% 3) 25% 4) 125%
Answer: 12.5%

Example: Convert the following percent to a decimal.
52.6%
1) 526 2) 5.26 3) 0.526 4) 0.0526
Answer: 0.526

Example: Compare:
1) < 2) > 3) =
Answer: =

Example: Order the following numbers from greatest to least.
Answer:

Example:
1) 36 2) 75 3) 90 4) 150
Answer: 75

Example: Compare the two numbers below and choose the right sign:
50% of 450  45% of 500
1) < 2) > 3) =
Answer: =

Example: Ryan and David went to a pizza restaurant for lunch on a Sunday afternoon. If the total bill at the restaurant was $38.50 and David paid 60% of the bill, how much did Ryan pay?
1) $23.10 2) $22.40 3) $15.40 4) $14.40
Answer: $15.40

Example: What percent of 3 days is 18 hours?
1) 75% 2) 42% 3) 30% 4) 25%
Answer: 25%

Example:
1) 10% 2) 25% 3) 45% 4) 54%
Answer: 45%

Example: If 12% of a number equals 54, what is that number?
1) 450 2) 540 3) 620 4) 800
Answer: 450

Example:
Answer: 200
 

Percent Problems in every day shopping and banking
Example: About how much would a customer pay for a DVD with a sticker price of $13.95 after a 20% discount?
1) $2.80 2) $10.25 3) $11.15 4) $11.75
Answer: $11.15

Example: Robert wants to gift a beaded jewelry set to his sister on her coming birthday. The jewelry set he selected is marked 15% off the original price. About how much would Robert pay for the jewelry set, if the original price of the set was $24.99?
1) $19.75 2) $21.25 3) $22.50 4) $23.75
Answer: $21.25

Example: Find the discount if marked price = $36 and discount = 40%.
1) $14.40 2) $14.80 3) $15 4) $15.40
Answer: $14.40

Example: Julia went to buy two T–shirts to gift her cousins on Christmas. The store was giving a discount of 12% on each item purchased and a 15% discount on every second item if two items were purchased together. How much would Julia pay for the two Tshirts if each of the Tshirt costs $25?
1) $47 2) $46.25 3) $43.25 4) $42.5
Answer: $43.25

Example: Cameron and his five friends visited the Kachemak Bay Shorebird festival in Alaska. On their way back they had their dinner at a restaurant in Homer. About how much did Cameron and his friends spend in the restaurant if the bill was $80.10 and they left a 15% tip?
1) $85 2) $90 3) $92 4) $100
Answer: $92

Example: Calculate the sales tax for an item that costs $85 if the sales tax rate is 8%?
1) $5.8 2) $6.8 3) $7.2 4) $7.8
Answer: $6.8

Example: Nicole wants to purchase a 22 CDROM collection of the eleventh edition of Encyclopedia Britannica for her school library. How much total amount would she pay, if the item costs $50 and the sales tax rate is 8%?
Answer: $54

Example: Which is a better deal: a 20% discount on an item that costs $95 or a $10 off on the same item with a list price of $85?
1) 20% discount on $95 2) $10 off on $85
Answer: $10 off on $85

Example: Benjamin buys a computer from a shop for 12% off the original price of $599. Nathan buys the same computer from another store for 15% off the original price of $625. Who paid more for the computer?
1) Benjamin 2) Nathan
Answer: Nathan

Example: Find the amount a customer would pay after two successive discounts of 10% and 5% on an item whose original cost was $120.
1) $97.2 2) $102 3) $102.6 4) $108
Answer: $102.6

Example: Jennifer purchased a bike from a sale for her son. The original price of the bike was $125 but the sale offered a 16% discount on the bike. If Jennifer should pay 7% sales tax, how much money would she pay for the bike?
1) $105 2) $112.35 3) $113.75 4) $117.65
Answer: $112.35

Example:
1) $15 2) $30 3) $45 4) $60
Answer: $30

Example: Robert is saving money to buy a new car. He put $6600 in a savings account at a simple interest rate of 6% per year. If he wants to withdraw the money after 20 months to buy the car, how much money would he get on withdrawal?
1) $6,830 2) $6,860 3) $6,930 4) $7,260
Answer: $7,260

Example: Find the principal amount when interest rate is 6%, time is 4 years and the simple interest is $96.
1) $240 2) $300 3) $400 4) $420
Answer: $400

Example: In how many years will $450 become $540 at a simple interest rate of 5%?
1) 4 years 2) 5 years 3) 6 years 4) 24 years
Answer: 4 years

Example: If a sum of $200 earns a simple interest of $200 in 8 years, what is the rate of interest?
1) 10% 2) 12% 3) 12.5% 4) 25%
Answer: 12.5%


Similar figures
Example: In the two similar figures shown below, which of the following is not a pair of corresponding sides?
1) AB and CD 2) CD and PQ 3) BC and SP 4) AD and QR
Answer: AB and CD

Example: In the two similar figures shown below, which of the following is a pair of corresponding angles?
1) Angle KLM and CBA 2) Angle LMN and DCB 3) Angle MNK and CDA 4) Angle NKL and BCD
Answer: Angle NKL and BCD

Example: Which of the following pair of figures are similar?
Answer:

Example: Find the missing length if the given figures are similar.
1) 4 cm 2) 5 cm 3) 8 cm 4) 20 cm
Answer: 5 cm

Example: Find the missing measure of angle P for the given pair of similar figures.
1) 45° 2) 90° 3) 135° 4) 145°
Answer: 135°

Example: Brandon works as a painter in a billboard advertising company. He needs to paint a rectangular billboard that is similar to a 3 inch long and 2 inch wide photo frame. If the width of the billboard is 36 feet, what would be the length of the billboard Brandon needs to paint?
1) 24 feet 2) 42 feet 3) 52 feet 4) 54 feet
Answer: 54 feet

Example: Are the triangles given below similar?
1) Yes 2) No
Answer: Yes

Example: The triangles shown below are similar. Find the missing side ‘p’.
1) 4 cm 2) 6 cm 3) 7.5 cm 4) 8 cm
Answer: 7.5 cm

Example: Use the similar triangles to find the height of the in the figure below.
1) 18 ft 2) 22 ft 3) 24.5 ft 4) 40.5 ft
Answer: 18 ft
 

Geometry – Lines and Angles
Example: Which of the following shows line segment AB?
Answer:

Example: Which of the following is not correct?
1) An unlimited number of lines can be drawn through a given point. 2) A line segment is a part of a line. 3) Line AB is the same as line BA. 4) Ray PQ is the same as ray QP.
Answer:Ray PQ is the same as ray QP.

Example: Find the measure of the angle ABC.
1) 55° 2) 65° 3) 125° 4) 135°
Answer: 125°

Example: Select the type of angle shown in the figure given below.
1) Acute 2) Right 3) Obtuse 4) Reflex
Answer: Acute

Example: Select the type of angle pairs shown in the figure given below.
1) Vertical angles 2) Complementary angles 3) Adjacent angles 4) Supplementary angles
Answer: Adjacent angles

Example: Which of the following statement is correct?
1) Two obtuse angles can be supplementary. 2) The sum of two adjacent angles is always 180°. 3) A pair of vertically opposite angles is always equal. 4) If the sum of two adjacent angles is 180°, then the angles are called vertical angles.
Answer: A pair of vertically opposite angles is always equal.

Example: In the given figure, if angle 1 = 2x and angle 2 = 3x + 20, find the measure of angle 4.
1) 32° 2) 64° 3) 96° 4) 116°
Answer: 116°

Example: Find the complement of an angle with measure 67°.
1) 23° 2) 33° 3) 123° 4) 133°
Answer: 23°

Example: Find the supplement of an angle that has a complement of 58°.
1) 32° 2) 42° 3) 122° 4) 148°
Answer: 148°

Example: Which of the following represents a pair of skew lines?
Answer:

Example: Which of the following option represents all the lines parallel to line GH?
1) AB, CD, AE 2) AB, DH, EF 3) AB, CD, EF 4) EG, FH, CG
Answer: AB, CD, EF

Example: Select true or false. ‘Skew lines are neither parallel nor intersecting and they lie in different planes.'
1) True 2) False
Answer: True

Example: Name the pair of angles that are colored yellow in the given diagram.
1) Alternate interior angles 2) Alternate exterior angles 3) Vertical angles 4) Corresponding angles
Answer: Corresponding angles

Example: Choose the correct option: The measures of a pair of alternate interior angles formed by a transversal passing through two parallel lines are .
1) Equal 2) Unequal 3) Complementary 4) Supplementary
Answer: Equal

Example: Find the measure of angle ‘f’ if the measure of angle ‘a’ is equal to 75°.
1) 115° 2) 105° 3) 95° 4) 75°
Answer: 105°
 

Geometry – Polygons
Example: Find the number of triangles in the given figure.
1) 4 2) 6 3) 8 4) 12
Answer: 8

Example: Identify the side opposite to angle ABC in the given triangle ABC
1) AB 2) BC 3) AC
Answer: AC

Example: Which of the following option best represents the type of triangle in the given figure?
1) Obtuse triangle 2) Right triangle 3) Acute triangle 4) Equilateral triangle
Answer: Acute triangle

Example: Which of the following option best represents the type of triangle in the given figure?
1) Equilateral triangle 2) Isosceles triangle 3) Scalene triangle 4) Right angled triangle
Answer: Isosceles triangle

Example: Select true or false. A right triangle can also be an isosceles triangle.
1) True 2) False
Answer: True

Example: Which of the following option can possibly be the three angles of a triangle?
1) 59°, 72°, 61° 2) 30°, 20°, 125° 3) 45°, 61°, 73° 4) 63°, 37°, 80°
Answer: 63°, 37°, 80°

Example: State whether the measures 2 cm, 10 cm and 15 cm could possibly be the lengths of the 3 sides of a triangle.
1) Yes 2) No
Answer: No

Example: Use the given diagram to find the measure of angle BAC.
1) 40° 2) 55° 3) 65° 4) 115°
Answer: 65°

Example: Which of the following figure shows a quadrilateral?
Answer:

Example: Which of the following option represents a pair of opposite sides in the given quadrilateral?
1) PQ and QR 2) PS and QR 3) PS and SR 4) SR and RQ
Answer: PS and QR

Example: Which of the following represents the shape of the table top in the picture shown below?
1) Square 2) Rectangle 3) Trapezoid 4) Parallelogram
Answer: Trapezoid

Example:
1) Rhombus 2) Rectangle 3) Square 4) Trapezoid
Answer: Square

Example: Determine whether the given statement is true or false. All squares are rhombuses and also rectangles.
1) True 2) False
Answer: True

Example: Use the given diagram to find the measure of angle NML.
1) 45° 2) 65° 3) 75° 4) 80°
Answer: 65°

Example: Which of the following option represents a polygon?
Answer:

Example: Identify the irregular polygon from the given options.
Answer:

Example: Alyssa was playing with some blocks of different colors. She tried to make a flower using the blocks. What is the shape of each block Alyssa used to make the flower?
Answer: Hexagon

Example: What is the sum of the interior angle measures in an octagon?
1) 540° 2) 720° 3) 900° 4) 1,080°
Answer: 1,080°

Example: Elizabeth wants to cut a thick cardboard in the shape of a regular hexagon to make a sign for her room. First she plans to make a regular hexagon on a sheet of paper. What would be the measure of each angle that she needs to draw to make the regular hexagon?
1) 60° 2) 90° 3) 120° 4) 135°
Answer: 120°

Example: How many diagonals can be drawn in a pentagon?
1) 8 2) 5 3) 4 4) 3
Answer: 5


Measurement and geometric figures
Example: Find the measure of the angle SPQ of the given quadrilateral PQRS.
1) 75° 2) 85° 3) 105° 4) 115°
Answer: 105°

Example: Find the perimeter of the following figure.
1) 12 cm 2) 16 cm 3) 18 cm 4) 20 cm
Answer: 20 cm

Example: Find the perimeter of the following polygon.
1) 11.5 cm 2) 10.5 cm 3) 10.0 cm 4) 9.5 cm
Answer: 10.5 cm

Example: Find the perimeter of the given rectangle.
1) 14.5 cm 2) 24.5 cm 3) 28.5 cm 4) 29.0 cm
Answer: 29.0 cm

Example: Logan, a carpenter, wants to make a wooden frame for the rectangular glass top of a table he made. If the glass top is 8 m long and 5 m wide, what would be the length of the wooden frame Logan needs?
1) 13 m 2) 15 m 3) 26 m 4) 40 m
Answer: 26 m

Example: Find the missing length ‘p’ of the given square if its perimeter is 30 cm.
1) 7.5 cm 2) 10 cm 3) 120 cm 4) 900 cm
Answer: 7.5 cm

Example: Find the perimeter of a regular octagon with 4.5 cm side length.
1) 18 cm 2) 27 cm 3) 36 cm 4) 45 cm
Answer: 36 cm

Example: If the perimeter of a regular hexagonal sign board is 49.5 cm, find the length of its side.
Answer: 8.25 cm

Example: Madison wanted to make a painting for an upcoming craft exhibition. Her mother gave her a square velvet cloth of 25 cm sides for painting. To make the cloth into a rectangle with desirable dimensions, Madison cut off a 3 cm long piece from one side of the square cloth and painted a scenery on the rest of the cloth. If she wants to decorate the painting with a designer lace, what would be the length of the lace she needs?
1) 100 cm 2) 94 cm 3) 90 cm 4) 88 cm
Answer: 94 cm

Example: Find the circumference of a circle with radius 4.2 cm.
Answer: 26.4 cm

Example: Courtney, a gardener, made a circular flower bed with 13 feet radius in the middle of a large rectangular park. She planted different types of flowering plants in the flower bed. Now she wants to plant some evergreen shrubs a foot outside and around the flower bed. If Courtney wants the shrubs 6 inches apart, about how many evergreen shrubs would she need for the fence?
1) 14 2) 90 3) 150 4) 180
Answer: 180

Example: Find the radius of a circle with circumference 66 km.
1) 105 km 2) 21 km 3) 10.5 km 4) 7 km
Answer: 10.5 km

Example: Alexander plans to build a stone border along the outer circumference of the circular pond in his farm house. If Alexander calculates a total cost of $528 at $2 per meter for the stone border, what is the outer diameter of the pond in his farm house?
1) 42 m 2) 63 m 3) 84 m 4) 168 m
Answer: 84 m

Example:
1) 47 cm 2) 54 cm 3) 124 cm 4) 131 cm
Answer: 47 cm

Example:
1) 1.457 km 2) 1.757 km 3) 3.731 km 4) 4.371 km
Answer: 4.371 km
 

Statistics – Mean, median, mode
Example: What is the mean of the data set given below? 4, 8, 5, 3, 9, 10, 2 and 7
Answer: 6

Example: The sum of 20 numbers is 160. What is the mean of the numbers?
1) 3,200 2) 80 3) 54 4) 8
Answer: 8

Example: What will be the mean of 5 numbers, if the mean of 3 of them is 30 nd the mean of the remaining 2 is 20?
1) 24 2) 25 3) 26 4) 28
Answer: 26

Example: Yesterday, Sophia solved 3 math worksheets in the morning and 2 worksheets in the evening. The average time she took for the 3 worksheets in the morning was 20 minutes and the average time she took for the 2 worksheets in the evening was 25 minutes. Which of the following is the average time she took for all 5 worksheets?
1) 24 minutes 2) 23 minutes 3) 22 minutes 4) 21 minutes
Answer: 22 minutes

Example: Find the missing number in the data set: 50, 50, ___, 150, 200, 250, 500, 300, when the mean of the data set = 200
1) 100 2) 150 3) 200 4) 250
Answer: 100

Example:
1) 160 cm 2) 165 cm 3) 168 cm 4) 170 cm
Answer: 160 cm

Example: What is the median of the data set given below? 15, 18, 27, 27, 35, 35, 40, 47, 47, 47, 52
1) 27 2) 35 3) 40 4) 45
Answer: 35

Example: Find the missing number in the data set: 11, 12, 14, 16, ___, 18, 19, 19, when the median of the data set = 17
1) 15 2) 16 3) 17 4) 18
Answer: 18

Example:
1) 58 2) 59 3) 59.5 4) 60
Answer:60

Example: What is the mode of the data given below? 45, 99, 78, 93, 93, 99, 56, 99, 43, 56, 78, 99, 56
Answer: 99

Example: Find the missing number in the data set: 56, 52, 51, 51, ___, 56, 53, 51, 56, when the mode of the data set = 56
1) 4 2) 51 3) 53 4) 56
Answer: 56

Example:
1) 12 years 2) 11 years 3) 10 years 4) 9 years
Answer: 11 years

Example: The graph below shows the expenses incurred by Mrs. Miller for her 5 project reports. Study the graph and find the average amount Mrs. Miller spent on a project report.
1) $20 2) $38 3) $40 4) $190
Answer: $38

Example:
1) 3 2) 66 3) 68 4) 72
Answer: 68

Example: The stemandleaf plot shown below represents the weights (in lbs) of 20 cartons loaded in a truck. Study the stemandleaf plot and find the mode of the data.
1) 5 2) 8 3) 54 4) 68
Answer: 68
 

Statistics – Displaying and interpreting data
Example: The high temperatures recorded in Phoenix, Arizona during 5 consecutive weekdays in the month of July is as follows: Monday  100°F, Tuesday  102°F, Wednesday  105°F, Thursday  104°F, and Friday  105°F. Which of the following table shows the data accurately?
Answer:

Example: Mrs. Davis a sixth grade teacher took a surprise science test in her class. The table below shows the test scores of the 40 sixth grade students in her class. Read the frequency table and answer the question below.
1) 6 2) 10 3) 11 4) 16
Answer: 16

Example: Jessica and Alyssa were playing a dice game. The following data shows the scores Jessica obtained while throwing the dice 25 times. 1 5 2 4 3 6 1 4 2 5 1 6 2 6 3 5 4 1 3 2 3 6 1 5 2 Which of the following options best represents the data in a frequency table?
Answer:

Example: The graph below shows the number of times the listed countries won the FIFA world cup in football from 1930 to 2010. Study the graph and answer the question below.
Answer: 3

Example: Mrs. Miller wants to give her friends their favorite flowers on Valentine’s Day. She knows that 10 of her friends like roses, 8 like tulips and 12 like orchids. Which of the following option represents the data in a pictograph?
Answer:

Example: The graph below shows the points scored by six girls in a Science test. Study the graph, and answer the question given below.
1) Olivia 2) Emma 3) Grace 4) Victoria
Answer: Victoria

Example: The table below shows the maximum life span of some of the birds according to a Nature Bulletin published on March 24, 1973 by the Forest Preserve District of Cook County (Illinois).
Answer:

Example: Michael and Matthew work in the same organization. The following graph shows their monthly budget.
1) True 2) False
Answer: False

Example: The following table shows the medals won by the sixth grade students of St. Jude Middle School in an inter school athletic meet.
Answer:

Example: The line plot below shows the weights of all members of a fitness club. Study the plot and answer the question given below.
1) 12 2) 26 3) 27 4) 77
Answer: 27

Example: Mr. Lewis, a sports instructor, was preparing a group of 15 students for a trekking expedition. He recorded the ages of his students, as shown below, to order some trekking clothes for them. Later he made a line plot for the data to easily communicate the ages of the students to the clothes supplier. 8 12 13 15 9 11 9 12 11 10 12 13 15 12 10 Which of the following best represents the line plot made by Mr. Lewis?
Answer:

Example: The stemandleaf plot shown below represents the time taken in minutes by some students to solve an online Math worksheet. Study the table and answer the question given below.
1) 3 2) 6 3) 7 4) 14
Answer: 6

Example: The table below shows the time taken by 20 students to complete their math home work in minutes.
Answer:

Example: The histogram below shows the hours spend watching television by some 6th grade students each day during their holidays. Study the graph and answer the following question.
1) 4 2) 7 3) 11 4) 25
Answer: 11

Example: The table below shows the ages of 50 people who attended Kayla’s birthday party.
Answer:

Example: The line graph below shows the annual sales of a book by a store. Study the graph and answer the question given below.
1) 2004 2) 2005 3) 2006 4) 2007
Answer: 2007

Example: The annual sales of two companies’ bikes for the years 2003 to 2007 are as shown in the graph below. Study the graph and answer the question given below.
1) 4 2) 19 3) 4,000 4) 19,000
Answer: 4,000

Example: Every month Alexis saves a part of her allowances. The following table shows her savings from the month of January 2010 till June 2010.
Answer:

Example: The pie chart below shows the monthly budget of Mr. Williams. Study the chart, and the answer the question below.
1) $201 2) $1,010 3) $2,010 4) $2,100
Answer: $2,010

Example: The pie chart below shows the percent of employees in different age groups in a company. Which of the following table correctly represents the data given in the pie chart?
Answer:

Example: Which of the following graphs would be more appropriate to show the temperature recorded at every 30 minutes of a day?
1) Pie chart 2) Stem and leaf plot 3) Bar graph 4) Line graph
Answer: Line graph

Example: The bar graph below shows the daily sales of refrigerators during a week in Andrew’s store. Study the graph, and answer the question below.
1) The vertical axis is not labeled. 2) The horizontal axis is not labeled. 3) It is not possible to sell 30 refrigerators on Monday. 4) The vertical axis scale does not have equal intervals.
Answer: The vertical axis scale does not have equal intervals.

Example:
1) (8, 6), (12, 6) 2) (12, 6), (12, 10) 3) (8, 10), (12, 6) 4) (8, 10), (8, 6)
Answer: (8, 10), (12, 6)
 

Geometry – Polygon Relationships
Example: Which of the following options represents a pair of congruent figures?
Answer:

Example: Which of the following is correct about the figures?
1) The figures are congruent since they are quadrilaterals 2) The figures are similar since they have the same shape 3) The figures are both similar and congruent 4) The figures are neither similar nor congruent
Answer: The figures are similar since they have the same shape

Example: Select true or false. ‘Two circles are congruent if they have the same radii.’
1) True 2) False
Answer: True

Example: Which of the following lines is a line of symmetry to the given diagram?
1) Line p 2) Line q 3) Line r 4) Line s
Answer: Line r

Example: How many lines of symmetry does the figure below have?
1) 0 2) 2 3) 4 4) 8
Answer: 0

Example: The figure below shows half part of a designed paper and a dotted line. The dotted line is a line of symmetry for the whole paper. Which of the following represents the other half part?
Answer:

Example: Does the figure below have rotational symmetry?
1) Yes 2) No
Answer: No

Example: The figure shown below has rotational symmetry. What is the angle of each rotationally symmetrical turn?
Answer:

Example: Which of the following transformation is translation?
Answer:

Example: Which of the following is a reflection for the given figure?
Answer:

Example: What combination of transformation is used for getting to position 4 from position 1 in the diagram below?
1) Rotation, then translation and finally reflection 2) Reflection, then translation and finally rotation 3) Rotation, then reflection and finally translation 4) Translation, then reflection and finally rotation
Answer: Rotation, then translation and finally reflection

Example: A figure, a point of rotation and a line of reflection is shown below. Which of the following will you get if you reflect the figure about the line, and then rotate that figure 135 degrees anticlockwise?
Answer:

Example: Each Sunday evening Aaron and his friends gather at a particular place. Last Sunday Aaron reached the place a bit early and stopped his car in front of the building. If the figure below shows the sign board of the building as seen from the review mirror of his car, what is the place where Aaron and his friends meet each Sunday evening?
Answer: LIBRARY
 

Measurement – Area of polygons and circles
Example: Estimate the area of the leaf shown in the square grid in which the area of each small square is 1 square cm.
1) 35 square cm 2) 38 square cm 3) 40 square cm 4) 45 square cm
Answer: 45 square cm

Example: Find the area of the given rectangle in square cm.
1) 3,400 cm² 2) 340 cm² 3) 34 cm² 4) 0.34 cm²
Answer: 34 cm²

Example: Daniel wants new carpeting for his office room. His office room measures 20 feet by 18 feet. If the carpeting costs $22 per 5 square feet and he needs to cover his entire office room, how much money does he need for carpeting?
1) $360 2) $1,584 3) $1,800 4) $7,920
Answer: $1,584

Example: Mrs. Smith, the principal of St. Antony’s Middle school, wants to upgrade her school’s prayer hall floor with new Italian tiles. If the school’s prayer hall is 16 m long and 10 m wide, how many square tiles of 40 cm sides does Mrs. Smith need for covering the prayer hall floor?
Answer: 1,000

Example: Find the area of the given triangle.
1) 126 cm² 2) 63 cm² 3) 31.5 cm² 4) 21 cm²
Answer: 31.5 cm²

Example: Hannah made triangular flower beds in all the four corners of her rectangular backyard. The flower beds are in the shape of right triangles with sides 6 m, 8 m and 10 m. If one bag of mulch can cover 8 m2, how many bags of mulch does Hannah need to cover all the four flower beds?
1) 6 2) 10 3) 12 4) 24
Answer: 12

Example: Find the area of the given parallelogram.
Answer: 28 cm²

Example: To protect his plants from the harsh winter, Eric wants to make a garden green house by attaching five parallelogram shaped fabrics with equal measures. If each fabric would have a base length of 5.5 m and width of 4 m, what would be the total area of the fabric Eric needs to make the garden green house?
1) 22 m² 2) 44 m² 3) 88 m² 4) 110 m²
Answer: 110 m²

Example: Find the area of the trapezoid given below.
1) 24 square inches 2) 33 square inches 3) 42 square inches 4) 66 square inches
Answer: 33 square inches

Example: Kayla wants to stitch a wrap skirt for her daughter. She purchased a 60 inch wide plane cloth and painted it with fabric colors. Then she cut the entire cloth into 3 trapezoids of same dimensions to stitch the skirt. If the parallel sides of each piece measures 16 inch and 34 inch, what would be the area of the cloth she is going to use for the skirt?
1) 1,500 square inches 2) 2,500 square inches 3) 4,500 square inches 4) 7,500 square inches
Answer: 4,500 square inches

Example: Find the base of a triangle with area 98 cm² and height 7 cm.
1) 7 cm 2) 10.5 cm 3) 14 cm 4) 28 cm
Answer: 28 cm

Example: James has a trapezoid shaped field of 14,400 m ² in area. The field is located exactly between a road and a canal that are parallel to each other. If the two sides of James’s field that are attached to the road and the canal measure 90 m and 150 m respectively, what would be the distance between the road and the canal attached to his field?
1) 360 m 2) 240 m 3) 120 m 4) 60 m
Answer: 120 m

Example: Ashley made a design as shown below for her art class assignment. Use the square grid to find its area.
1) 14 square units 2) 15 square units 3) 25 square units 4) 36 square units
Answer: 15 square units

Example: Find the area of the shape given in the figure below.
1) 55 cm² 2) 61 cm² 3) 67 cm² 4) 85 cm²
Answer: 55 cm²

Example: Michael wants to enlarge his grandfather’s photo to display it on his room wall. If the actual photo measures 3.5 inches by 4 inches and he wants the enlarged copy to measure 10.5 inch by 12 inch, what will be the change in the area of the photo after enlarging?
1) The area will increase by 2 times 2) The area will increase by 3 times 3) The area will increase by 6 times 4) The area will increase by 9 times
Answer: The area will increase by 9 times

Example:
1) 15,400 cm² 2) 3,850 cm² 3) 440 cm² 4) 220 cm²
Answer: 3,850 cm²

Example: Madison is making a multi colored circular carpet for a restaurant as shown in the figure below. If Madison made the inner circular design with 28 feet diameter and the outer blue band with a width 7 feet all around, what is the area of the blue band in the carpet?
Answer: 770 square feet

Example: Jasmine is making a circular display board for the school elections. She decorated the board by pasting an 88 cm long velvet lace all around the board. Then she hung the board on the wall next to the library. Find the area of the wall covered by the display board.
1) 14 cm² 2) 154 cm² 3) 616 cm² 4) 1,232 cm²
Answer: 616 cm²

Example: Mr. Williams, the principal of St. Paul middle school, wants to make a garden with some flower beds and turf grass on the rectangular school yard that measures 10 m by 8 m. He wants to make 4 circular flower beds in the area and cover the remaining area with turf grass. If each of the flowerbed measures 3.5 m in diameter, how much area (in square m) of the school yard will be covered with turf grass?
Answer: 41.5
 

Volumes of Prisms and Cylinders
Example: Find the volume of the rectangular prism given below.
1) 4,320 square inches 2) 4,320 cubic inches 3) 3,240 cubic inches 4) 2,160 square inches
Answer: 4,320 cubic inches

Example: Find the volume of the triangular prism given below.
1) 0.35 m³ 2) 3.5 m³ 3) 35 m³ 4) 350 m³
Answer: 35 m³

Example: Emily has a rectangular tank that measures 3 m x 2 m x 5 m in her backyard. If she fills the tank with water to a height of 4.25 m, what would be the volume of the water in the tank?
1) 63.75 m³ 2) 42.5 m³ 3) 30 m³ 4) 25.5 m³
Answer: 25.5 m³

Example: Find the missing measurement of a rectangular prism when, V = 4,800 m³ h = 12 m and w = 25 m.
1) 18 m 2) 16 m 3) 12 m 4) 8 m
Answer: 16 m

Example: Jacob dug 2 ponds, each measuring 42 feet long and 15 feet wide, in his farm house for fish farming. Then with the mud dug out from the ponds, he made a 2 feet thick vegetable bed 126 feet long and 60 feet wide. If both the ponds have the same depth, what would be the depth of the ponds in Jacob’s farm?
1) 24 feet 2) 18 feet 3) 12 feet 4) 6 feet
Answer: 12 feet

Example: Compare the volumes of the given prisms and find which of these have a greater volume.
1) Box 1 2) Box 2
Answer: Box 2

Example: A certain tea manufacturer supplies tea leaves in two different types of rectangular packets in the market. The smaller packet measures 6 cm x 5 cm x 7 cm and the larger packet measures 8 cm x 6.5 cm x 10 cm. How much more tea leaves does the larger packet contain than the smaller packet?
1) 170 cm³ 2) 210 cm³ 3) 310 cm³ 4) 520 cm³
Answer: 310 cm³

Example: Find the volume of the cylinder given below. (Use π = 22/7)
1) 0.001848 m³ 2) 0.1848 m³ 3) 18.48 m³ 4) 1,848 m³
Answer: 0.001848 m³

Example: In a craft competition, the 6th grade students St. Xavier’s middle school were asked to make and decorate cylindrical penholders. The school provided each participant a 14 cm wide rectangular craft paper and some decorative items. Hanna rolled the craft paper along its width and made a penholder that has a base radius of 15 cm. What would be the volume of the pen holder she made? (Use π = 22/7) [Hint: The width of the rectangular paper becomes the height of the cylinder]
1) 2,310 cm³ 2) 2,475 cm³ 3) 9,240 cm³ 4) 9,900 cm³
Answer: 9,900 cm³

Example: Find the height of a cylinder with volume 2,512 cm ³ and radius 10 cm. (Use π = 3.14)
1) 3 cm 2) 5 cm 3) 8 cm 4) 13 cm
Answer: 8 cm

Example: A group of villagers plans to construct a cylindrical water tank in their neighborhood for irrigation of their farms during summer. If they want a 20 m high tank with 6,930 m³ capacity, what would be the diameter of the tank? (Use π = 22/7)
1) 7 m 2) 10.5 m 3) 14 m 4) 21 m
Answer: 21 m

Example: Compare the volumes of the given cylinders and find the cylinder with the greater volume.
1) Cylinder (A) 2) Cylinder (B)
Answer: Cylinder (B)

Example: An energy drink company decided to launch its new flavor of energy drink in two different cylindrical cans. One of the cans, Can W, has 7 cm base radius and 9 cm height and the other can, Can H, has 5 cm base radius and 21 cm height. Which can has a lesser capacity and by how much? (Use π = 22/7)
1) Can H by 1,650 cm³ 2) Can W by 1,386 cm³ 3) Can W by 264 cm³ 4) Can H by 264 cm³
Answer: Can W by 264 cm³

Example: Michael wants to build a boundary wall 9 m long, 1.5 m high, and 24 cm thick in the backyard of his house. He plans to build the wall using bricks. How many bricks would he need if each brick measures 30 cm long, 15 cm wide and 8 cm thick?
1) 300 2) 900 3) 1,500 4) 3,000
Answer: 900


Surface area of Prisms, Pyramids and Cylinders
Example: Find the surface area of the cube given below.
1) 18 cm² 2) 27 cm² 3) 54 cm² 4) 81 cm²
Answer: 54 cm²

Example: Find the surface area of the rectangular prism given below.
1) 47 m² 2) 60 m² 3) 94 m² 4) 188 m²
Answer: 94 m²

Example: Madison and her friends plan to display a variety of solid models in their school’s math lab. Madison made 4 rectangular prisms, each measuring 8 inch x 3 inch x 12 inch and now she wants to cover all the 4 prisms with green velvet paper. What would be the length of the velvet paper Madison needs, if the width of the velvet paper is 12 inches and for all the overlaps she needs an extra 10 inch long velvet sheet?
1) 24 inches 2) 96 inches 3) 104 inches 4) 114 inches
Answer: 114 inches

Example: Find the surface area of the square pyramid given below.
1) 45 square feet 2) 65 square feet 3) 105 square feet 4) 200 square feet
Answer: 105 square feet

Example: Matthew, a trekking trainer, decided to make a Range tent with natural canvas. He purchased 500 square feet of natural canvas from a nearby shop and cut one 10 feet square and four congruent triangles of height 12 feet for making the tent. If each of the triangular piece he cut has a base length equal to the side of the square piece, how much canvas is left with Matthew?
1) 140 square feet 2) 160 square feet 3) 240 square feet 4) 340 square feet
Answer: 160 square feet

Example: Find the surface area of the cylinder given below.
1) 2,002 cm² 2) 1,144 cm² 3) 880 cm² 4) 572 cm²
Answer: 880 cm²

Example: Joshua made a gazebo in his backyard with 10 congruent circular pillars similar to the model shown below that he had seen in a magazine. Now he wants to paint the pillars with enamel paint and decorate the surrounding area with flowering plants. How much would Joshua pay to paint the 3 m high pillars with base diameter 84 cm if the paint costs $10 per square meter? (Use π = 22/7) [Hint: Joshua only needs to paint the curved surface of the pillars]
1) $396 2) $792 3) $903 4) $1,584
Answer: $792
 

Addition and Subtraction of Fractions



Example:
Answer:


Example:
Answer:

Example: Estimate the following by first rounding the fraction to zero, half or one and then adding.
Answer:





Example:
Answer:

Example:
Answer:

Example: Estimate the following by first rounding the fraction to zero, half or one and then subtracting.
Answer:




Customary Measurement
Example: Convert: 5,880 yards = ____ miles ____ yards
1) 1 miles 600 yards 2) 2 miles 600 yards 3) 3 miles 600 yards 4) 4 miles 600 yards
Answer: 3 miles 600 yards

Example: Convert 176 ounces to pounds
1) 9 pounds 2) 11 pounds 3) 18 pounds 4) 22 pounds
Answer: 11 pounds

Example: 100 cups = ____ gallon(s) ____ quart(s)
1) 6 gallons 1 quart 2) 6 gallons 4 quarts 3) 12 gallons 4 quarts 4) 16 gallons 1 quart
Answer: 6 gallons 1 quart

Example: Christopher cut down a eucalyptus tree in his farm house since he felt that it could have fallen down in the upcoming thunderstorms and caused damage to the nearby cattle shed. After cutting the eucalyptus tree, he measured the tree trunk and found it to be 18 yards long. If Christopher can get $10 per foot by selling the tree trunk in a nearby marketplace, how much money will he get for the entire tree trunk?
1) $180 2) $360 3) $510 4) $540
Answer: $540

Example: Which of the following is correct?
1) 17 feet < 5 yards 2 feet 2) 22 feet > 8 yards 2 feet 3) 72 inches < 5 feet 10 inches 4) 5,500 feet = 1 mile 220 feet
Answer: 5,500 feet = 1 mile 220 feet

Example: Compare: 26 pounds ____ 326 ounces
1) < 2) > 3) =
Answer: >

Example: Which of the following is greater than 11 gallons?
1) 175 cups 2) 43 quarts 3 cups 3) 89 pints 4) 1,280 fluid ounces
Answer: 89 pints

Example: Add 9 yards 2 feet 7 inches + 29 feet 5 inches
1) 19 yards 1 foot 2) 19 yards 2 feet 3) 20 yards 4) 20 yards 1 foot
Answer: 19 yards 2 feet

Example: Brandon, a computer professional, lives in Beaumont but works in an office 85 miles away in downtown Houston. If he drives to the office only 3 days a week and works from home the other days, how many miles in total does he drive to work and back each week?
1) 255 miles 2) 510 miles 3) 520 miles 4) 1,120 miles
Answer: 510 miles

Example: Subtract 17 lbs 15 ounces from 22 lbs 14 ounces.
1) 5 lbs 9 ounce 2) 5 lbs 1 ounce 3) 4 lbs 15 ounces 4) 4 lbs 9 ounces
Answer: 4 lbs 15 ounces

Example: Jasmine wants to make several cakes for a school charity event. She has a 10 pound flour bag with her and she wants to use all of it to bake the cakes. If she plans to make 8 similar cakes for the charity event, how much flour could she use to make each cake?
1) 10 ounces 2) 1 pound 3) 1 pound 2 ounces 4) 1 pound 4 ounces
Answer: 1 pound 4 ounces

Example: Divide: 61 gallons 2 quarts ÷ 6 = _____.
1) 10 gallons 1 quarts 2) 10 gallons 2 quarts 3) 11 gallons 1 quart 4) 11 gallons 2 quarts
Answer: 10 gallons 1 quarts

Example: A traditional Italian Pasta Fasul soup contains the following ingredients: 11 fl oz dry borlotti beans, 1 quart water, 2 fl oz finely chopped pancetta, 2 cups broth, 5 fl oz broken spaghetti, 1 fl oz finely chopped onion, 1 fl oz finely diced stick celery and 4 fl oz finely chopped carrot. What could be the measure of the total ingredients of the above Pasta Fasul soup recipe?
1) 1 quart 1 cup 2) 2 quarts 1 cup 3) 3 quarts 4) 4 quarts 1 cup
Answer: 2 quarts 1 cup
 

Metric Measurement
Example: Convert: 2,540 mm = ____ m ____ cm
1) 1 m 54 cm 2) 1 m 540 cm 3) 2 m 54 cm 4) 2 m 540 cm
Answer: 2 m 54 cm

Example: Convert: 35 kg 7 grams = _______ grams
1) 35,700 grams 2) 35,007 grams 3) 3,570 grams 4) 357 grams
Answer: 35,007 grams

Example: Convert: 25,025 ml = ____ l ____ ml
1) 250 l 250 ml 2) 25 l 250 ml 3) 25 l 25 ml 4) 2.5 l 25 ml
Answer: 25 l 25 ml

Example: Kaitlin purchased a 75 cm long designer satin cloth for $18 to make a table cover. She liked the cloth so much that she now wants to purchase more of the same cloth to make matching window curtains and pillow covers. How much money would it cost Kaitlin, if she needs to buy 17 more meters of the same designer satin cloth to make window curtains and pillow covers?
Answer: $408

Example: Which of the following is not correct?
1) 3 km 7 m < 3,700 m 2) 1 km = 1,000,000 mm 3) 4 m + 525 cm = 925 cm 4) 1,000 mm = 10 m
Answer: 1,000 mm = 10 m

Example: Which of the following is heavier?
Answer:

Example: Compare: 3.5 l ____ 6,000 ml.
1) < 2) > 3) =
Answer: <

Example: Subtract 27.345 km – 17,876 meters
1) 9.469 km 2) 9.579 km 3) 10.531 km 4) 10.579 km
Answer: 9.469 km

Example: Each member of the two cheerleading groups at St. Paul Middle School needs 2 m 50 cm ribbons of 5 different colors each for an upcoming interschool sports meet. If there are 16 members in each group, how many meters of ribbons should the school purchase in all?
1) 48 m 2) 80 m 3) 200 m 4) 400 m
Answer: 400 m

Example: Add 1.75 kg + 825 g + 11.50 kg
1) 13.40 kg 2) 14.075 kg 3) 14.40 kg 4) 15.075 kg
Answer: 14.075 kg

Example: Mrs. Martin works in a bakery store. She made 23.5 kg of chocolate chunk cookies for Christmas sale. Now she needs to pack the cookies in decorated gift boxes for the sale. How many gift boxes would Mrs. Martin use to pack the cookies, if each gift box needs to have 500 grams of cookies?
Answer: 47

Example: How many 700 ml glasses can be filled with 28 liters of milk?
1) 4 glasses 2) 40 glasses 3) 400 glasses 4) 4,000 glasses
Answer: 40 glasses

Example: Mrs. Collins, a fifth grade teacher, brought two completely filled lemonade coolers with capacity 7.5 liters and 9.5 liters respectively to the class picnic. During the picnic each child had two glasses of lemonade. How many liters of lemonade did the class use if each of the coolers had 750 ml of lemonade left?
1) 14.25 liters 2) 14.50 liters 3) 15.25 liters 4) 15.50 liters
Answer: 15.50 liters
 

Probability
Example: Complete the sentence below: The set of all possible outcomes for an experiment is called _____.
1) Complement events 2) Favorable outcomes 3) Desired events 4) Sample space
Answer: Sample space

Example: Ethan has a 1 dollar (D) coin, a quarter (Q) coin, and a nickel (N) coin in his pocket. Which of the following option represents the sample space if Ethan takes two coins out of his pocket one after another?
1) {DQ, QN, ND} 2) {DQ, QD, QN, ND} 3) {DQ, DN, QD, QN, ND, NQ} 4) {DQ, DN, QD, QN, ND, NQ, DQN}
Answer: {DQ, DN, QD, QN, ND, NQ}

Example: A flower vase contains 5 yellow flowers, 6 red flowers and 14 violet flowers in it. If a person picks a flower at random from this vase, what is the probability of him choosing a violet flower?
1) Certain 2) Likely 3) Unlikely 4) Impossible
Answer: Likely

Example: In a group of 100 people, 40 people have the blood group O positive, 37 have the blood group A positive, 13 have the blood group B positive, and 10 have the blood group O negative. What is the probability of picking a person from this group who can receive blood from any of the other 99 group members?
1) Certain 2) Likely 3) Unlikely 4) Impossible
Answer: Impossible



Example: Jasmine has a collection of 12 headbands in her dresser, out of which only 3 are pink color headbands. If she picks a headband from her drawer without looking, what would be the probability (in decimal) of selecting a pink headband?
1) 0.25 2) 0.50 3) 0.75 4) 1
Answer: 0.25

Example: For a lottery drawing, numbers from 1 to 100 are written on cards and dropped into a box. Find the percent chance of getting a multiple of 4 when a card is chosen at random from the box.
1) 50% 2) 25% 3) 20% 4) 12%
Answer: 25%

Example:
1) Team A 2) Team B 3) Team C 4) Team D
Answer: Team C

Example: What is the probability that the spinner will land on green?
Answer:


Example: Samantha tossed three coins simultaneously 200 times with the following frequencies of different outcomes.
1) No head 2) One head 3) Two head 4) Three head
Answer: Three head

Example: Lauren wants to wrap the birthday gift she bought for her friend Olivia. She visited a grocery store and saw violet, silver, and gold wrapping papers for packing, and green and pink ribbons for decorating available in the grocery store. If Lauren wants to buy one wrapping paper and one ribbon, how many different combinations of a paper and a ribbon can she choose from?
Answer: 6

Example: Which of the following option is not an example of an experiment with equally likely outcomes?
1) Tossing a coin 2) Rolling a number cube 3) Randomly choosing a vowel from a, e, i, o, u 4) Selecting an ace from a deck of cards
Answer: Selecting an ace from a deck of cards

Example: Dylan is participating in the triple jump event in his school’s annual athletic meet. There is an 84% chance of him winning the event. What is the probability that he will not win the event?
1) 0.84 2) 0.26 3) 0.16 4) 21/25
Answer: 0.16

Example: In a sample survey of 1000 random people in a city, 680 people said they were insured with the "Big National Insurance" company. If the city has 2 million people, how many people in the city are most likely insured with the "Big National Insurance" company?
1) 680,000 2) 1,320,000 3) 1,360,000 4) 1,460,000
Answer: 1,360,000

Example: If you roll a numbered cube 198 times, how many times would you expect to roll a number that is a multiple of 3?
1) 99 2) 66 3) 33 4) 22
Answer: 66

Example: Mr. Clark is a concert hall manager. Based on previous records of attendance, he estimates that only 92% of people who purchase a ticket will attend the concert. If the concert hall has a capacity of 575 seats and Mr. Clark wants to have a 100% attendance for the upcoming music concert, how many tickets should he sell?
1) 529 2) 575 3) 625 4) 650
Answer: 625


Example: Which of the following option represents independent events?
1) Choosing a red ball from a box containing red, green, and blue balls, and rolling a five on a numbered cube. 2) Picking a red marble and a blue marble in succession from a bag that contains 2 red marbles, 3 blue marbles, and 1 white marble. 3) Drawing a slip with number 5 and another slip with number 11, one after the other without replacement from a group of slips numbered from 1 to 20. 4) Choosing a King and without keeping it back choosing a Queen one after another from a deck of cards.
Answer: Choosing a red ball from a box containing red, green, and blue balls, and rolling a five on a numbered cube.

Example: Which of the following option represents a dependent event?
1) Getting a head in a coin toss and rolling a 3 on a numbered cube roll 2) First choosing an ace from a deck of cards and after replacement choosing a 10 as the second card 3) Choosing a red marble from a jar that contains 5 red marbles and 3 blue marbles, and rolling a 5 on a numbered cube 4) Drawing a red marble and then without replacement drawing a blue marble from a bag that contains 5 red marbles and 3 blue marbles
Answer: Drawing a red marble and then without replacement drawing a blue marble from a bag that contains 5 red marbles and 3 blue marbles




 

Measurement – Time & temperature
Example: Convert 285 minutes = ___ hrs ___ min
1) 4 hours 15 min 2) 4 hours 45 min 3) 5 hours 15 min 4) 5 hours 45 min
Answer: 4 hours 45 min

Example: 7 weeks 6 days = ____ days
1) 13 days 2) 41 days 3) 45 days 4) 55 days
Answer: 55 days

Example: Compare 7.5 days _____ 180 hours
1) < 2) > 3) =
Answer: =

Example: Find the start time of an activity that is 9 hours 36 minutes long and ends at 4:25 A.M.
1) 6:49 A.M. 2) 6:51 A.M. 3) 6:49 P.M. 4) 6:51 P.M.
Answer: 6:49 P.M.

Example: Find the end time of an activity that is 12 hours 45 minutes long and starts at 10:40 P.M.
1) 10:25 P.M. 2) 11:25 A.M. 3) 10:25 A.M. 4) 9:25 A.M.
Answer: 11:25 A.M.

Example: Find the time taken to complete a task that starts at 11:35 A.M. and ends at 2:09 P.M.
Answer: 2 hours 34 minutes

Example: Daniel and Taylor work in the same multinational company and are supposed to work for a fixed time each day. Today Taylor reached the office at the usual time of 9:30 A.M. and Daniel reached the office at 10:20 A.M. due to a traffic jam. Till what time should Daniel work today if Taylor completed his workday at 6.30 P.M?
1) 7:00 P.M. 2) 7:20 P.M. 3) 7:30 P.M. 4) 7:40 P.M.
Answer: 7:20 P.M.

Example: Convert 149 °F to °C
1) 56 °C 2) 65 °C 3) 76 °C 4) 117 °C
Answer: 65 °C

Example: Convert 35 °C to °F
1) 85 °F 2) 95 °F 3) 100 °F 4) 105 °F
Answer: 95 °F

Example: According to a weather report, the average high temperature in Santiago during December over the last 21 years has been 68 °F and the highest recorded temperature in Santiago in the last 21 years is 104 °F. Find the difference between the highest recorded temperature and the average temperature over the last 21 years in Santiago to the nearest degree Celsius.
Answer: 20 °C

