Number formats and Place value
Example: Which of the following shows the number 6,300,900 in words?
1) Six million, three hundred, nine hundred 2) Six million, three thousand, nine hundred 3) Six million, three hundred thousand, nine 4) Six million, three hundred thousand, nine hundred
Answer: Six million, three hundred thousand, nine hundred

Example: Which of the following shows the correct number in numerals: Four million, nine hundred fifteen thousand, sixty?
1) 4,915,060 2) 4,915,600 3) 4,950,060 4) 4,950,600
Answer: 4,915,060

Example: Which digit is in the thousands place in the number 756,947?
1) 4 2) 6 3) 7 4) 9
Answer: 6

Example: What is the place value of 7 in 173,569?
1) 7,000 2) 10,000 3) 70,000 4) 700,000
Answer: 70,000

Example: Which of the following is the expanded form of the number 8,003,004?
1) 8,000,000 + 30,000 + 4 2) 8,000,000 + 3,000 + 4 3) 8,000,000 + 300 + 4 4) 8,000 + 300 + 4
Answer: 8,000,000 + 3,000 + 4

Example: What is the value of 7,000,000 + 20,000 + 500 + 8?
1) 72,508 2) 720,508 3) 7,020,508 4) 7,258,000
Answer: 7,020,508

Example: Select the missing digit: Two million eight hundred nine thousand eight hundred twenty nine: 2,8_9,829
1) 0 2) 1 3) 2 4) 9
Answer: 0

Example: Rearrange the following digits to make the smallest possible number while using each digit only once. 7, 4, 9, 5, 8
1) 45,879 2) 45,987 3) 45,789 4) 98,754
Answer: 45,789

Example: Rearrange the following digits to make the greatest possible number while using each digit only once. 3, 2, 7, 9, 6
1) 69,732 2) 97,632 3) 23,679 4) 79,632
Answer: 97,632

Example: Which of the following is correct?
1) 46,495 = 46,459 2) 162,864 < 162,846 3) 809,302 > 908,203 4) 3,405,199 < 3,504,199
Answer: 3,405,199 < 3,504,199

Example: Write the missing number for the following sequence: 51,789; 52,889; 53,989; ; 56,189; 57,289
1) 54,1089 2) 54,089 3) 54,989 4) 55,089
Answer: 55,089

Example: As estimated by the United States Census Bureau, the population of San Diego on June 1st, 2009 was approximately 1,306,300. Which of the following shows the population of San Diego in words?
1) One million, thirty six thousand, three hundred 2) One million, three hundred thousand, three hundred 3) One million, three hundred six thousand, three hundred 4) One million, three hundred and six hundred thousand, three hundred
Answer: One million, three hundred six thousand, three hundred


Addition
Example: Add:
1) 676 2) 679 3) 776 4) 779
Answer: 779

Example: Add:
1) 1,992 2) 1,922 3) 1,292 4) 1,229
Answer: 1,292

Example: Add:
Answer: 928

Example: John went to a department store and bought a shoe that costs $141 and a sports coat that costs $250. How much total money (in $) did he pay for both items?
Answer: 381

Example: Add:
1) 1,807 2) 5,807 3) 6,007 4) 6,807
Answer: 6,807

Example: Add
1) 7,723 2) 7,823 3) 7,832 4) 8,823
Answer: 7,823

Example: At a pop concert there were 3,468 people in section A, 2,895 people in section B and 4,637 people in section C. How many people in all were there to watch the concert?
Answer: 11,000

Example: Add:
1) 80,999 2) 81,999 3) 85,999 4) 90,999
Answer: 80,999

Example: Add:
1) 93,335 2) 103,445 3) 103,435 4) 103,335
Answer: 103,335

Example: Deposits of 3 members of a family in a savings bank account are $23,000, $50,500 and $29,900 respectively. Find the total amount of deposits (in $) of the family members.
Answer: 103,400

Example: Find the missing digit:
1) 2 2) 4 3) 5 4) 7
Answer: 2

Example: 4,005 + 4,005 ____ 2,005 + 6,005
1) < 2) > 3) = 4) None of the above
Answer: =

Example: Estimate the sum by first rounding off each number to the nearest thousand, and then adding 3,409 + 5,317 + 9,505 = .
1) 16,000 2) 17,000 3) 18,000 4) 19,000
Answer: 18,000

Example: A newspaper report states that the lengths of the major rivers Missouri, Mississippi and Ohio in United States are 2,540 miles, 2,340 miles and 1,310 miles respectively. If Eric wants to set a world record by rafting the entire length of all the 3 rivers, estimate the total length he would cover by first rounding off each length to the nearest hundred and then adding.
1) 6,000 2) 6,100 3) 6,200 4) 6,300
Answer: 6,100


Subtraction
Example: Subtract:
1) 24 2) 25 3) 35 4) 52
Answer: 25

Example: Subtract:
1) 77 2) 76 3) 67 4) 66
Answer: 67

Example: Robert went to a book store and bought a pen that costs $32. If he gave the cashier $50, how much money (in $) should he get back from the cashier?
Answer: $18

Example: Subtract:
1) 222 2) 322 3) 412 4) 423
Answer: 222

Example: Subtract:
1) 483 2) 482 3) 481 4) 438
Answer: 482

Example: John was reading the book “Harry Potter and the Deathly Hallows” that has 759 pages. He read 378 pages on Friday and rest of the pages on Saturday. How many pages did he read on Saturday?
Answer: 381

Example: Subtract:
1) 200 2) 1,000 3) 2,000 4) 2,200
Answer: 2,000

Example: Subtract:
1) 3,172 2) 3,177 3) 3,272 4) 3,227
Answer: 3,172

Example: A free medical camp was conducted by Florida Medical Board in Casselberry, Florida. 9,685 people participated in the camp, out of which 4,399 were males. Find the number of female participants in the camp.
Answer: 5,286

Example: Find the missing digit:
1) 0 2) 1 3) 2 4) 3
Answer: 1

Example: How much more is 6,731 than 4,120?
Answer: 2,611

Example: Estimate the following by first rounding off each number to the nearest thousand and then subtracting. 6,342  1,044
Answer: 5,000

Example: Mr. Thomson is an Arts teacher. He has $9,132 budgeted to buy supplies for his class. He used $3,972 to buy some craft material. Estimate the amount of money left with him for his class supplies by rounding off the amounts to the nearest hundreds.
1) $4,100 2) $4,200 3) $5,100 4) $5,200
Answer: $5,100
 

Multiplication
Example: Multiply 9 by 7.
1) 42 2) 54 3) 63 4) 72
Answer: 63

Example: Fill in the blanks: ___ X (178 X 25) = 0
Answer: 0

Example: Solve, 5 x 2 x 1 = .
Answer: 10

Example: 9,833 x 1,000 = _________.
1) 983,300 2) 9,833,000 3) 9,833,100 4) 98,331,000
Answer: 9,833,000

Example: Multiply: 350 x 200
1) 7,000 2) 35,000 3) 70,000 4) 352,000
Answer: 70,000

Example: There are 8 boxes of pens each containing 6 pens. How many total pens are there in the eight boxes?
Answer: 48

Example: The product of 213 and 13 is .
1) 2,796 2) 2,769 3) 2,729 4) 2,679
Answer: 2,769

Example: Mr. Harris works part time in an animal farm. He earns an average of $32 each day. If he works for 28 days in a month, how much money would he earn in a month?
1) $696 2) $866 3) $896 4) $986
Answer: $896

Example: Multiply: 135 x 246
1) 34,310 2) 33,210 3) 32,310 4) 32,210
Answer: 33,210

Example: 76 x 5 x 2 = .
1) 607 2) 670 3) 706 4) 760
Answer: 760

Example: Find the missing number: Product of 225 and __ is 2,700
Answer: 12

Example: Find the missing digit:
1) 3 2) 5 3) 8 4) 9
Answer: 8

Example: 224 garlands each with 125 flowers were used to decorate an auditorium for a wedding reception. Find the total number of flowers used for decorating the auditorium.
Answer: 28,000

Example: Fill in the blanks:  x 25 = 25 x 75
Answer: 75

Example: Which of the following shows the associative property of multiplication?
1) 4 x 1 = 1 x 4 2) 19 x 48 = (19 x 50) – (19 x 2) 3) 4 x 25 = 5 x 5 x 4 4) (11 x 4) x 25 = 11 x (4 x 25)
Answer: (11 x 4) x 25 = 11 x (4 x 25)

Example: Fill in the blanks: 32 x 198 = 32 x   32 x 2
Answer: 200

Example: Cameron owns a small coffee shop in a mid western city in the US. Each day he sells around 17 gallons of coffee in the morning and 13 gallons in the afternoon. If he makes a profit of $12 for each gallon of coffee he sells, how much profit does he make each day by selling coffee?
Answer: $360

Example: Estimate the following by first rounding off each number to the nearest ten then solving. 248 X 29
Answer: 250 x 30 = 7,500

Example: Austin is a motor bike dealer. He recently bought 22 Honda motor bikes for $7,975 each. Which of the following is the best estimate for the total cost of 22 bikes?
1) 76,000 2) 140,000 3) 176,000 4) 200,000
Answer: 176,000
 

Division
Example: Divide 696 by 6.
Answer: 116

Example: At an office, there are 104 computers to be placed into 8 rooms. If the same number of computers is placed in each room, how many computers will be in each room?
1) 12 2) 13 3) 14 4) 15
Answer: 13

Example: 750 ÷ 25 = ___
Answer: 30

Example: If a metallic sphere of 255 lbs is melted and recast into smaller spheres of 15 lbs each, how many such smaller spheres can be made?
1) 11 2) 15 3) 17 4) 19
Answer: 17

Example: 630 ÷ 30
1) 21 2) 22 3) 210 4) 220
Answer: 21

Example: The floor area of a rectangular room is 600 square feet. If the length of the room is 40 feet, find the width of the room.
Answer: 15 feet

Example: Find the divisor: 136 ÷  = 17
Answer: 8

Example: Kayla wants to decorate each of the 9 designs she made for a craft project with beads. If she purchases a packet containing 144 beads and uses an equal number of beads on each design, how many maximum number of beads could she use to decorate each design?
1) 6 2) 12 3) 16 4) 26
Answer: 16

Example: Find the dividend:  ÷ 8 = 24
1) 3 2) 162 3) 192 4) 248
Answer: 192

Example: Sara and her mom Andrea are designing a vegetable garden in their backyard. They decided to divide the usable area in the backyard into 12 soil beds with a walking path between each bed. How many vegetable plants should they purchase if each soil bed should have 8 plants?
1) 48 2) 72 3) 96 4) 108
Answer: 96

Example: Find the remainder when dividend = 355 and divisor = 70
1) 4 2) 5 3) 6 4) 7
Answer: 5

Example: There are a total of 100 paintings in an art exhibition. The exhibition director wants to display an equal number of these paintings in 12 rooms each, and the remaining paintings at the entrance of the exhibition. Which of the following could be the number of paintings he could display at the entrance?
1) 12 2) 8 3) 6 4) 4
Answer: 4

Example: Find the missing number: 72 ÷ (9 ÷ ___) = 72
Answer: 9

Example: A mobile phone company manufactures 3,000 mobile phones in 15 days. Assuming the company manufactures the same number of mobile phones every day, how many mobile phones are manufactured each day?
1) 150 2) 200 3) 1,500 4) 4,500
Answer: 200

Example: Estimate the following by first rounding off each number to the nearest ten and then solving. 297 ÷ 49
Answer: 6

Example: Timothy works at a bakery. This week he will bake around 2,448 cookies in all and pack them in packets. If he can pack around 21 cookies in each pack, approximately how many packets does he need to buy to pack all the cookies?
1) 100 2) 120 3) 140 4) 160
Answer: 120


Mixed applications
Example: 'Add 2 and 8 and then divide the sum by the sum of 2 and 3'. Which of the following represents the above sentence?
1) 2 + 8 ÷ (2 + 3) 2) (2 + 3) ÷ 2 + 8 3) (2 + 3) ÷ (2 + 8) 4) (2 + 8) ÷ (2 + 3)
Answer: (2 + 8) ÷ (2 + 3)

Example: Mackenzie bought a box of cookies. She and her friends ate 12 cookies after which 38 cookies were left in the box. Which of the following can be used to find the number of cookies (c) in the box when Mackenzie bought the box?
1) c – 12 = 38 2) 38  12 = c 3) 38 ÷ 12 = c 4) 12c = 38
Answer: c – 12 = 38

Example: Which number is missing in the following number sentence? (218 – 212) x (____ + 5) = 60
1) 2 2) 5 3) 8 4) 10
Answer: 5

Example: Which of the following question has the solution in which 12 and 36 are factors and 432 is multiple?
1) Anna had 36 beads; Andrea gave her 12 more beads. How many beads does Anna have in all? 2) Brianna had 12 crayons. She bought some more crayons and now she has 36 crayons. How many crayons did Brianna buy? 3) Destiny has 12 photo albums. Each photo album contains 36 photos. How many photos does Destiny have in her photo albums? 4) Courtney wants to buy 36 cookies. How many packs of cookies would she have to purchase if each pack contains 12 cookies?
Answer: Destiny has 12 photo albums. Each photo album contains 36 photos. How many photos does Destiny have in her photo albums?

Example: Find the value of 4,789 – 111 + 411 = .
Answer: 5,089

Example: A CD case contains 12 game CDs, 5 software CDs and 13 music CDs. 2 game CDs, 3 software CDs and 8 music CDs are taken out from the CD case. How many CDs are left in the CD case?
1) 15 2) 17 3) 12 4) 10
Answer: 17

Example: Find the value of 4 X 7 + 15
Answer: 43

Example: 10 adults and 7 children went to a museum. The adult tickets at the museum cost $8 each, and children tickets cost $4 each. How much would be the total cost of the tickets for 10 adults and 7 children?
1) $80 2) $98 3) $108 4) $118
Answer: $108

Example: Find the value of (12 + 8) ÷ (2 + 3)
Answer: 4

Example: Mrs. Jackson is arranging trophies for the winners of different events conducted in her school’s Annual Meet. The trophies are kept in two boxes, 65 in one and 40 in the other. If she has to arrange all the trophies equally in 7 rows in a showcase, how many trophies would she arrange in each row?
1) 7 2) 13 3) 15 4) 25
Answer: 15

Example: Find the value of 16 x 6 – 12 x 7
1) 588 2) 12 3) 6 4) 2
Answer: 12

Example: A school auditorium has 15 rows of chairs, and each row has 9 chairs. If 120 chairs are occupied in a school function, how many more people can still be accommodated in the auditorium for the function?
1) 12 2) 14 3) 15 4) 16
Answer: 15

Example: Find the value of 100 – 55 ÷ 11
Answer: 95

Example: Victoria volunteers at a hospital. She works 4 hours a day each time she goes to the hospital. In the first and second week of this month she worked a total of 40 hours in the hospital. If in the first week she worked every day of the week, how many days during the second week did she work at the hospital?
Answer: (40  7 x 4) ÷ 4 = 3

Example: Solve 144 ÷ 4 X 3
Answer: 108

Example: Zachary works at a furniture shop and can make a table in 8 hours. He works 6 hours a day. If he takes the same time to make each table, about how many days will it take Zachary to make 9 such tables?
1) 10 2) 12 3) 15 4) 72
Answer: 12

Example: 13 + (34 ÷ 17) + (14 X 3)
Answer: 57
 

Algebra
Example: Which of the following is a variable?
1) 23 2) π 3) 7 4) x
Answer: x

Example: Which of the following is a constant?
1) y 2) 2x 3) 10 4) 5xy
Answer: 10

Example: Which of the following is an algebraic expression?
1) 27 – 3 2) 1 + x 3) 67 ÷ 13 + 85 4) 89 + 34 – 54
Answer: 1 + x

Example: Identify the pair with like terms.
1) 7x, 11yz 2) 9ab, 6b 3) 5xy, 7xy 4) 4a, 4a2
Answer: 5xy, 7xy

Example: What is the numerical coefficient in the following? '35xy'
Answer: 35

Example: What is the coefficient of y in the following? '4xyz'
1) 4 2) 4x 3) 4yz 4) 4xz
Answer: 4xz

Example: Which of the following option does not represent the given algebraic expression in words? 'y + 6'
1) 6 added to y 2) 6 groups of y 3) The sum of 6 and y 4) 6 more than y
Answer: 6 groups of y

Example: Which of the following option represents the below phrase as an algebraic expression? 'Take away 23 from k'.
1) 23 + k 2) 23 – k 3) k – 23 4) k ÷ 23
Answer: k – 23

Example: Write an expression for the following statement. 'Half the sum of a and 4 subtracted from one third of b'.
Answer:

Example: William solved a Math worksheet that has some essay type questions and some multiple choice questions. He solved ‘n’ essay type questions and 7 multiple choice questions correctly. If each essay type question in the worksheet carries 5 points and each multiple choice question carries 2 points, how many points did he get in all?
1) 5n + 14 2) 5n  14 3) 5 + n + 7 + 2 4) (5 + n)(7 + 2)
Answer: 5n + 14

Example: Which expression best represents the value of n?
1) n + 10 2) n + 11 3) 2n 4) 2n + 1
Answer: 2n + 1

Example: If a = 2 and b = 3, then find the value of a³ – b².
1) 2 2) 1 3) 0 4) 1
Answer: 1

Example: Find the missing value in the table.
1) 37 2) 42 3) 44 4) 52
Answer: 37

Example: Which of the following option does not represent an equation?
1) 13 – a = 8 2) 17 = b + 2 3) 2a + b + c 4) 5c – 7 = 3
Answer: 2a + b + c

Example: Write an equation for the following statement. 'Three more than twice a number equals 15'.
1) 2x + 15 = 3 2) 3x + 15 = 2 3) 2x + 3 = 15 4) 3x + 2 = 15
Answer: 2x + 3 = 15

Example: Mackenzie bought a box of cookies. She and her friends ate 12 cookies after which 38 cookies were left in the box. Which of the following can be used to find the number of cookies (c) in the box when Mackenzie bought the box?
1) c + 12 = 38 2) 38  12 = c 3) c – 12 = 38 4) 12c = 38
Answer: c – 12 = 38

Example: Solve and find the value of the variable in the given equation. 17 + y = 43
1) 60 2) 36 3) 34 4) 26
Answer: 26

Example: Solve and find the value of the variable in the given equation. x – 55 = 19
1) 74 2) 64 3) 36 4) 36
Answer: 74

Example: Solve and find the value of the variable in the given equation. 14a = 98
1) 2 2) 6 3) 7 4) 12
Answer: 7

Example: Solve and find the value of the variable in the given equation.
1) 1 2) 25 3) 30 4) 36
Answer: 25

Example: As part of a Nature Conservation Campaign, the students of St. Paul Elementary school planted a total of 75 fruit and nonfruit trees in different parks of the nearby communities. If the number of nonfruit trees were 3 more than three times the number of fruit trees, what was the number of fruit trees they planted?
1) 18 2) 22 3) 27 4) 57
Answer: 18
 

Number Theory
Example: Two groups of numbers are given below. 3, 7, 11, 13 5, 7, 9, 11 Which of the following is correct about the groups?
1) Each group is an example of odd numbers. 2) Each group is an example of even numbers. 3) Each group is an example of prime numbers. 4) None of these.
Answer: Each group is an example of odd numbers.

Example: Which of the following is a group of only prime numbers?
1) 23, 27, 31, 37, 41 2) 23, 29, 31, 37, 39 3) 23, 29, 31, 35, 41 4) 23, 29, 31, 37, 41
Answer: 23, 29, 31, 37, 41

Example: Which of the following is a group of only composite numbers?
1) 4, 5, 6, 7, 8 2) 3, 4, 5, 6, 7 3) 4, 6, 8, 9, 10 4) 4, 6, 7, 9, 10
Answer: 4, 6, 8, 9, 10

Example: Which of the following is divisible by 6?
1) 1,156 2) 2,114 3) 2,121 4) 6,072
Answer: 6,072

Example: Select the missing digit: The number 3_2 is divisible by 9.
1) 4 2) 5 3) 6 4) 7
Answer: 4

Example: During a daylong adventure trip, 354 students of St. Joseph private school are to be divided into smaller groups. If each group should have the same number of students, which of the following could be the number of students in a group?
1) 4 2) 5 3) 6 4) 7
Answer: 6

Example: Which of the following shows the first 5 multiples of 15?
1) 15, 30, 45, 60, 75 2) 30, 45, 60, 75, 90 3) 15, 30, 45, 65, 75 4) 15, 35, 45, 60, 75
Answer: 15, 30, 45, 60, 75

Example: Which number should be subtracted from 33 to make it a multiple of both 4 and 5?
1) 1 2) 3 3) 8 4) 13
Answer: 13

Example: Find the Least Common Multiple (LCM) of 9 and 12.
1) 36 2) 72 3) 96 4) 108
Answer: 36

Example: Mrs. Martin needs to distribute full boxes of snack packets to the 4th and 5th graders at a school event. The snack packets are in individual boxes labeled separately for 4th and 5th graders. The 4th grade boxes have 8 snack packets each and the 5th grade boxes have 6 snack packets each. What is the minimum number of snack packets Mrs. Martin can distribute to each class such that each class gets an equal number of snack packets?
1) 12 2) 24 3) 36 4) 48
Answer: 24

Example: Which group shows all the factors of 56?
1) 1, 2, 5, 6, 8 2) 1, 2, 4, 7, 28, 56 3) 1, 2, 4, 7, 8, 14, 28, 56 4) 4, 7, 8, 9, 14, 28, 56
Answer: 1, 2, 4, 7, 8, 14, 28, 56

Example: Write the missing factors in the following product. ___ x 16 = 80
Answer: 5

Example: Which of the following is not a factorization of the number 90?
1) 3 X 30 2) 2 X 45 3) 45 X 45 4) 6 X 15
Answer: 45 X 45

Example: Which of the following is the prime factorization of the number 100?
1) 4 X 25 2) 2 X 2 X 25 3) 4 X 5 X 5 4) 2 X 2 X 5 X 5
Answer: 2 X 2 X 5 X 5

Example: Which of the following shows all the common factors of 12 and 18?
1) 2, 3 2) 1, 3, 6 3) 1, 2, 3, 6 4) 1, 2, 3, 6, 12
Answer: 1, 2, 3, 6

Example: Find the Greatest Common Factor (GCF) of 12 and 20.
1) 2 2) 4 3) 8 4) 12
Answer: 4

Example: Eric wants to pack 60 color markers and 35 crayons in packets such that each packet contains the same number of each type of item (i.e. an equal number of color markers, say x, in every packet and an equal number of crayons, say y, in every packet). What is the maximum possible number of packets that can be made in such a way?
Answer: 5
 

Fractions


Example: Which of the following is a set of like fractions?
Answer:

Example: Which of the following is a set of unlike fractions?
Answer:




Example: Write the simplest form of the fraction
Answer:


Example:
Answer: Math


Example:
1) Timothy 2) Steven 3) Sean
Answer: Timothy

Example: Fill in the blanks:
1) < 2) = 3) >
Answer: >

Example:
Answer:

Example: Order the fractions from greatest to the lowest.
Answer:

Example:
1) Bracelet, Bangles, Earrings, Necklace 2) Earrings, Necklace, Bracelet, Bangles 3) Bangles, Bracelet, Earrings, Necklace 4) Necklace, Earrings, Bracelet, Bangles
Answer: Bangles, Bracelet, Earrings, Necklace



 

Addition and Subtraction of Fractions

Example:
Answer:


Example:
Answer:

Example: Select the correct sign for the following question:
1) < 2) = 3) >
Answer: >


Example:
Answer:

Example: Estimate the following by first rounding each number to the nearest whole number, then solving.
Answer: 29

Example:
Answer: $22




Example:
Answer:

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


Example:
Answer:

Example: Estimate the following by first rounding each number to the nearest whole number, then solving
Answer: 14

Example:
Answer: $10

Example: Find the missing number
Answer: 1


 

Multiplication and Division of Fractions
Example: Multiply the whole number and the fraction below and express the product in its simplest form:
Answer:

Example:
1) 9 dollars and 20 cents 2) 9 dollars and 60 cents 3) 19 dollars and 20 cents 4) 19 dollars and 60 cents
Answer: 19 dollars and 20 cents

Example: Multiply the fractions and express the product in its simplest form:
Answer:

Example:
Answer:

Example: Multiply and write the answer in the simplest form of the fraction or mixed number:
Answer:

Example:
Answer: $39

Example: Multiply and write the answer in the simplest form of the fraction or mixed number:
Answer:


Example:
Answer: 32



Example:
Answer:

Example: Divide
1) 2) 3) 4)
Answer:

Example:
Answer: 18


Example:
Answer: 12

Example: Write the missing number
Answer: 14

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

Example:
Answer:

Example:
Answer:

Example:
Answer:
 

Decimals
Example: 100th part of 7 is written as,
1) 0.007 2) 7 3) 0.7 4) 0.07
Answer: 0.07

Example: Which of the following shows the decimal number below in standard form? 'Two hundred eightyfour and five hundred thirtytwo thousandths'.
1) 28.4532 2) 284.352 3) 284.532 4) 2845.32
Answer: 284.532

Example: Which of the following shows the number 120.11 in words?
1) One hundred twenty and eleven 2) One hundred twenty and eleven tenths 3) One hundred twenty and eleven hundred 4) One hundred twenty and eleven hundredths
Answer: One hundred twenty and eleven hundredths

Example: Write the place value of 3 in 1.0613.
Answer: 0.0003

Example:
Answer: 6.425

Example: Which of the following shows the expanded form of the decimal 21.06?
1) 20 + 1 + 0.006 2) 20 + 1 + 0.06 3) 20 + 1 + 0.6 4) 2,000 + 100 + 6
Answer: 20 + 1 + 0.06

Example: Round off the given number to two decimal places. 2.078
1) 2.008 2) 2.07 3) 2.08 4) 2.1
Answer: 2.08

Example: Which of the following will be equal to 25 when rounded off to the nearest whole number?
1) 24.44 2) 24.37 3) 25.39 4) 25.96
Answer: 25.39

Example: Which of the following is correct?
1) 10.021 > 10.012 2) 10.021 < 10.012 3) 10.021 = 10.012
Answer: 10.021 > 10.012

Example: Write the decimals given below in order from the greatest to the smallest. 1.01, 10.001, 1.001, 1.110, 1.101
1) 10.001, 1.110, 1.010, 1.101 2) 10.001, 1.101, 1.110, 1.010 3) 10.001, 1.101, 1.010, 1.110 4) 10.001, 1.110, 1.101, 1.010
Answer: 10.001, 1.110, 1.101, 1.010

Example: Select the number which is greater than 3.014.
1) 3.01 2) 2.032 3) 3.004 4) 3.02
Answer: 3.02

Example: Write the following fraction as a decimal.
1) 0.225 2) 2.250 3) 2.50 4) 22.50
Answer: 2.250

Example: Write the following mixed number as a decimal.
1) 7.325 2) 7.350 3) 7.375 4) 7.378
Answer: 7.375


Example: Add
1) 634.222 2) 643.222 3) 643.242 4) 643.442
Answer: 643.222

Example: The Statue of Liberty is one of the most famous statues in the world and the most recognizable icon of the United States. The Statue of Liberty is 46.7 m tall. It stands on a 27.13 m high pedestal which sits atop an elevenpointed star base of height 19.81 m. what is the total height of the Statue of Liberty with the pedestal and base?
Answer: 93.64 m

Example: Round off the following decimal numbers to one decimal place and then find the sum. 30.91 and 700.02
1) 7,309 2) 730.8 3) 730.9 4) 730.0
Answer: 730.9

Example: 4 pipes of lengths 12.2 feet, 7.9 feet, 8.7 feet and 6.8 feet were joined in an underground pipe fitting. Which of the following is the best estimate for the total length of the 4 pipes?
1) 34 feet 2) 36 feet 3) 38 feet 4) 40 feet
Answer: 36 feet

Example: Subtract
1) 148.733 2) 149.525 3) 149.255 4) 149.265
Answer: 149.255

Example: Find the missing digit: 1.001  0.02 = 0._81
1) 8 2) 7 3) 1 4) 9
Answer: 9

Example: Brenda wants to visit a beach 5.45 miles away from her home. After driving 2.62 miles her car breaks down. How much more distance does she need to travel to reach her destination?
1) 2.23 miles 2) 2.83 miles 3) 3.23 miles 4) 3.83 miles
Answer: 2.83 miles

Example: Multiply
1) 756 2) 75.8 3) 75.4 4) 75.6
Answer: 75.6

Example: Multiply 9.53 x 1,000
1) 95.30 2) 953.00 3) 9,530 4) 95,300
Answer: 9,530

Example: Multiply 60.5 x 60
1) 36,300 2) 3,630 3) 363.0 4) 36.300
Answer: 3,630

Example: A dinner fork and knife set costs $1.50. Grace bought 12 such equally priced sets. How much did she spend in all for the fork and knife sets?
1) $18.00 2) $15.50 3) $15.00 4) $10.50
Answer: $18.00

Example: Multiply 4.2 by 2.2
1) 924.0 2) 92.4 3) 9.24 4) 0.924
Answer: 9.24

Example: The cost to paint one square foot area of a board is $1.5. How much money (in $) would Eric need to pay to get 6.8 square feet of the board painted?
Answer: $10.2

Example: Divide 522.8 by 16
1) 32.625 2) 32.675 3) 34.625 4) 34.675
Answer: 32.675

Example: A plumber cut a 21.5 feet pipe into 5 pieces. What is the average length of each of the 5 pipe pieces?
1) 4.1 feet 2) 4.3 feet 3) 4.5 feet 4) 107.25 feet
Answer: 4.3 feet

Example: An incomplete number sentence is given below. _ ÷ _ = 2 Which of the following set of numbers complete the above number sentence?
1) 1.5, 3 2) 2, 1.5 3) 5, 2.5 4) 4, 2.5
Answer: 5, 2.5

Example: Sara bought 2 coffee mugs that cost $9.50 each, 4 bowls that cost $15.25 each and a jug that cost $11. How much did Sara spend in all?
1) 23 2) 32 3) 91 4) 233
Answer:91
 

Ratio and Proportions
Example: In the picture shown below, what is the ratio of the number of triangles to the number of circles?
1) 5:3 2) 3:5 3) 3:8 4) 2:8
Answer: 5:3

Example: Convert the following ratio in the simplest form.
21:81
1) 1:3 2) 1:7 3) 7:9 4) 7:27
Answer: 7:27

Example: Find the ratio of the following. 8 cups to 2 gallons
1) 1:4 2) 4:1 3) 1:16 4) 16:1
Answer: 1:4

Example: Ryan and Tyler, two brothers, went to their uncle’s house with their families for thanksgiving. Ryan drove his car 25 km in 30 minutes. Tyler drove his car 30 km in 30 minutes. Find the ratio of the average speed of Ryan’s car to the average speed of Tyler’s car?
1) 6:5 2) 5:6 3) 1:25 4) 30:1
Answer: 5:6

Example: Find the missing number from the following. 18:27 = __:9
Answer: 6

Example: In St. Xavier's Elementary School, the ratio of the number of boys to the number of girls is 9:8. There are 480 girls in the school. How many boys are there in the school?
Answer: 540

Example: Are the ratios 6:15 and 14:35 in proportion?
1) Yes 2) No
Answer: Yes

Example: Which of the following ratios are in proportion?
1) 2:3 and 4:6 2) 5:8 and 4:7 3) 16:28 and 4:5 4) 12:24 and 13:25
Answer: 2:3 and 4:6

Example: Find the missing term to complete the proportion given below. 16:28 = 28:_
1) 12 2) 16 3) 40 4) 49
Answer: 49

Example: Zachary owns a printing press and prints books for several authors. One of the Math books he recently printed had 500 pages. Some of the pages in the book have only text while others have both text and pictures. The ratio of the number of pages with only text to the total number of pages is 7:10. If Zachary charges $1.2 per page for pages with pictures and $0.8 per page for pages with only plain text, find the total charge to print all pages of the book.
1) $460 2) $500 3) $520 4) $580
Answer: $460


Rates and Percentages
Example: Which option shows the unit rate in fraction form for the following? 198 words in 18 lines
1) 11 words/1 line 2) 12 words/1 line 3) 198 words/1 line 4) 198 words/18 lines
Answer: 11 words/1 line

Example: Rebecca types 4,800 words in 120 minutes. Find the unit rate for her typing?
1) 140 words per minute 2) 100 words per minute 3) 60 words per minute 4) 40 words per minute
Answer: 40 words per minute

Example: Logan bought 2 gallons of oil for $38 from one shop and 3 gallons of oil for $62 from another shop. Now he wants to sell all 5 gallons of the oil. At what unit price should he sell the oil such that he earns a 20% profit?
1) $4 per gallon 2) $20 per gallon 3) $24 per gallon 4) $100 per gallon
Answer: $24 per gallon

Example: Write the missing number for the unit rate assuming that the first term is equally distributed among the second term. 525 students in 7 groups = _ students per group
Answer: 75

Example: Kevin and his classmates went on a school field trip to a science research center in their school bus. The bus took 2 hours to reach the science research center but took 3 hours to travel back to the school due to heavy traffic congestion. In the return trip the average speed of the bus was 60 km/hour. Find the average speed of the bus for the entire trip.
1) 45 km/hour 2) 60 km/hour 3) 72 km/hour 4) 90 km/hour
Answer: 72 km/hour

Example: What per cent is shaded in the following figure?
1) 28% 2) 38% 3) 62% 4) 68%
Answer: 38%

Example: Write the following fraction as a percent.
Answer: 40%

Example: Convert the following percent to a fraction. 60%
Answer:

Example: Find 30% of 350.
1) 50 2) 95 3) 105 4) 115
Answer: 105

Example: Victoria had 500 leather handbags in her shop to sell. During an inspection she found out that 5% of them were defective. She packed the defective handbags for sending back to the company and sold 20% of the remaining handbags today. How many handbags did she sell today?
1) 95 2) 100 3) 115 4) 125
Answer: 95

Example: What percent is 16 of 80?
1) 5% 2) 20% 3) 40% 4) 50%
Answer: 20%

Example: Mr. Jackson owns a fruit shop. He dried 75 pounds of grapes for a Christmas sale. After drying, the grapes only weighed 30 pounds. By how much percent did the weight of the grapes reduce after drying?
Answer: 60%

Example: If 4% of a number equals 72, what is that number?
1) 288 2) 900 3) 1,800 4) 7,200
Answer: 1,800

Example: Mr. Lewis donated $4,800 to his child's school. The amount of donation was 15% of his business profit for the month of December. What was his business profit in the month of December?
Answer: $32,000


Sequence and Pattern
Example: A pattern of numbers is shown below. 7, ____, 63, 189, 567 Which of the following is a way to find the missing number in the pattern?
1) Add 14 to each term to get the next term of the sequence. 2) Add 28 to each term to get the next term of the sequence. 3) Multiply each term by 3 to get the next term of the sequence. 4) Multiply each term by 9 to get the next term of the sequence.
Answer: Multiply each term by 3 to get the next term of the sequence.

Example: Write the missing number in the sequence given below: 3, 19, 35, ___, 67, 83, 99
Answer: 51

Example: Select the missing term in the sequence given below, 568, 549, 530, 511, ____, 473
1) 482 2) 484 3) 492 4) 494
Answer: 492

Example: Select the missing term in the sequence given below, 2, 6, 18, 54, 162, ___,
1) 386 2) 486 3) 496 4) 586
Answer: 486

Example: Which of the following sequence follows the rule given below? Start with 4; multiply by 2
1) 4, 8, 12, 16, 20 … 2) 4, 8, 16, 32, 64 … 3) 4, 6, 8, 10, 12 … 4) 1, 4, 8, 16, 32, 64 …
Answer: 4, 8, 16, 32, 64 …

Example: Which of the following number pair is different from the other pairs?
1) (30, 6) 2) (95, 19) 3) (7, 35) 4) (55, 11)
Answer: (7, 35)

Example: Some number pairs of a group are given below. (26, 41), (53, 68), (71, 86), (49, 64) Which of the following belongs to the above group of number pairs?
1) (1, 15) 2) (24, 49) 3) (12, 27) 4) (40, 53)
Answer: (12, 27)


Example: A pattern of shapes is shown below. Which of the following would be the seventh figure of the pattern?
Answer:

Example: A pattern of blocks is shown below. Which of the following would be the next figure of the above pattern?
Answer:

Example: A pattern is shown in the table below. According to the given pattern, what would be the product of 111111 and 111111?
1) 11111111 2) 123464321 3) 1234564321 4) 12345654321
Answer: 12345654321

Example: Gabrielle is making a design on a piece of art by using the pattern shown below. 4 figures of the pattern are given in the picture below. How many triangles will there be in the sixth figure of the pattern?
1) 27 2) 81 3) 243 4) 253
Answer: 243


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

Example: Which of the following is not correct?
1) A ray is a part of a line. 2) A ray has length but no thickness; its length can be measured by measuring tools. 3) A ray extends endlessly in one direction only. 4) A ray has a starting point or a point of origin.
Answer: A ray has length but no thickness; its length can be measured by measuring tools.

Example: Which of the following figure does not contain parallel lines?
Answer:

Example: Sara pasted some colored strips on a white board that is shown in the figure below. Look at the figure shown below and answer the question.
1) 4 2) 5 3) 3 4) 2
Answer: 5

Example: Look at the figure shown below and answer the question.
1) n and q 2) p and l 3) l and m 4) p and q
Answer: p and l

Example: Find the measure of angle ABC.
1) 0 degree 2) 60 degree 3) 120 degree 4) 180 degree
Answer: 60 degree

Example: Select the approximate value of angle x?
1) 25 degree 2) 100 degree 3) 150 degree 4) 170 degree
Answer: 150 degree

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

Example: Rachel’s room is in the shape of a rectangular prism. What type of angles do all the corners of the room form?
1) Acute angle 2) Obtuse angle 3) Right angle 4) Straight angle
Answer: Right angle

Example: Ashley pasted the arrow shown below on a wall. How many acute angles does the arrow appear to have?
1) 6 2) 5 3) 4 4) 3
Answer: 4

Example: Select the angle made by the hands (hour’s hand and minute’s hand) of a clock at 06:00 hours.
1) 0 degree 2) 60 degree 3) 90 degree 4) 180 degree
Answer: 180 degree

Example: Alfred has a grandfather clock in his living room. The clock’s hands were at a right angle when Alfred started his travel to his uncle’s house. Alfred traveled in a train for 2 hours 30 minutes and in a cab for 30 minutes. The clock’s hands were at a zero angle when he reached his uncle’s house. Which of the following could be the time at which he started his travel to his uncle's house?
1) 3 O’clock 2) 6 O’clock 3) 9 O’clock 4) 12 O’clock
Answer: 9 O’clock

Example: Find the value of the unknown angle x in the following figure.
1) 45 degree 2) 90 degree 3) 135 degree 4) 145 degree
Answer: 45 degree
 

Geometry – Polygons and Solid figures
Example:
1) Acute 2) Obtuse 3) Right
Answer: Right

Example: Sydney had a rectangle shaped piece of paper. She divided the paper into two congruent triangles. Which of the following could be the type of those two congruent triangles?
1) Acute angled triangles 2) Obtuse angled triangles 3) Right angled triangles 4) None of the above
Answer: Right angled triangles

Example: ______ triangle has two equal sides.
1) A scalene 2) An isosceles 3) An equilateral
Answer: An isosceles

Example: The sum of the lengths of any two sides of a triangle is ______ the length of the third side.
1) less than 2) greater than 3) equal to
Answer: greater than

Example: Can you construct a triangle with the angles given below:
1) Yes 2) No
Answer: No

Example: Emma wants to stitch 6 new square pillow covers for her living room couches. She purchases two different fabrics to make the covers similar to a pillow cover she saw in a magazine as shown below. Which of the following best represents the shape of each of the fabric piece Emma would cut to stitch the covers?
1) Acute triangle 2) Scalene triangle 3) Equilateral triangle 4) Right angled triangle
Answer: Right angled triangle

Example: In the triangle ABC given below, angle B and angle C are equal. Find the measure of angle C.
1) 35 degree 2) 55 degree 3) 70 degree 4) 110 degree
Answer: 55 degree

Example: Brian is standing on a ladder that is resting against a wall. The angle made by the ladder and the ground is 10 degrees less than the angle made by the ladder and the wall. What is the measure of the angle made by the ladder and the wall?
1) 35 degree 2) 40 degree 3) 50 degree 4) 60 degree
Answer: 50 degree

Example: What is the name of the closed figure shown below?
1) Parallelogram 2) Rectangle 3) Rhombus 4) Trapezoid
Answer: Trapezoid

Example: Which of the following is not a property of a rectangle?
1) A rectangle has 4 sides. 2) A rectangle has 4 right angles. 3) The lengths of opposite sides of a rectangle are equal. 4) A rectangle has 4 faces.
Answer: A rectangle has 4 faces.

Example: Which of the following is incorrect?
1) A circle is a closed shape. 2) A polygon is made up of straight line segments. 3) A circle is a closed shape. It is made up of straight line segments. 4) A circle is a closed shape. It is made up of a curved line.
Answer: A circle is a closed shape. It is made up of straight line segments.

Example: Caleb painted some shapes shown below. Which of the following is correct about the shapes painted by Caleb?
1) All green colored shapes are quadrilateral 2) All violet colored shapes are circles 3) All green colored shapes are polygon. 4) All violet colored shapes are polygons
Answer: All green colored shapes are polygon.

Example: What is the name of the closed figure shown below?
1) Hexagon 2) Heptagon 3) Pentagon 4) Octagon
Answer: Pentagon

Example: Lauren had a paper as shown below in the figure. She cut the paper into 5 pieces. 4 of them are cut from the 4 corners and in the shape of isosceles triangle with equal sides of 5 cm. What could be the shape of the fifth piece?
1) Square 2) Rectangle 3) Octagon 4) Hexagon
Answer: Hexagon

Example: Which of the following is incorrect?
1) An octagon has 8 vertices. 2) A quadrilateral has 4 vertices. 3) A pentagon has 7 vertices. 4) A hexagon has 6 vertices.
Answer: A pentagon has 7 vertices.

Example:
1) Yes 2) No
Answer: No

Example: Select the name of the solid figure given below.
1) Triangular prism 2) Rectangular prism 3) Square pyramid 4) None of the above
Answer: Triangular prism

Example:
1) Sphere 2) Cube 3) Cone 4) Cylinder
Answer: Cone

Example: Which of the following has the most number of faces?
1) Pentagonal prism 2) Rectangular prism 3) Square pyramid 4) Pentagonal pyramid
Answer: Pentagonal prism

Example: Ashley noticed that a solid glass object separates white light into a group of seven colors. The solid object has exactly 3 rectangular faces and 2 triangular faces. Which of the following was that solid object?
1) Triangular prism 2) Rectangular prism 3) Triangular pyramid 4) Square pyramid
Answer: Triangular prism

Example: A triangular prism is shown below.
1) AB, BC, CA, DE, EF, FD 2) AB, BC, CA, DE, EF, FD, CD, BE, AF 3) AB, BC, CA, DE, EF, FD, CD, BE 4) AB, BC, CA, DE, EF, FD, CD, BE, FC
Answer: AB, BC, CA, DE, EF, FD, CD, BE, AF

Example: Find the number of vertices and edges in the figure given below.
1) 6 vertices and 12 edges 2) 8 vertices and 12 edges 3) 8 vertices and 18 edges 4) 12 vertices and 18 edges
Answer: 12 vertices and 18 edges

Example: Luke had 2 cubes of same size and color shown below. The color of each face of the cubes is different. He joined the two cubes and made a new prism such that the red color is not displayed and the other colors line up properly. How many faces will there be in the new prism?
1) 6 2) 8 3) 12 4) 16
Answer: 6

Example: Which of the following is the front view of the hexagonal prism shown below?
Answer:

Example:
1) Triangular pyramid 2) Triangular prism 3) Square pyramid 4) Rectangular prism
Answer: Triangular prism

Example:
Answer:


Customary Measurement
Example: Convert 60 inches to feet
1) 10 2) 6 3) 5 4) 4
Answer: 5

Example: The deepest lake in North America, The Great Slave Lake, is around 2,016 feet deep. It is one of the deepest and the biggest fresh water bodies on the earth. What would be the depth of The Great Slave Lake in yards?
Answer: 672

Example: Fill in the blanks 5 yards 2 feet =  feet.
1) 10 2) 17 3) 22 4) 62
Answer: 17

Example: Which of the following is less than 2 yards?
1) 73 inches 2) 72 inches 3) 5 feet 14 inches 4) 5 feet 4 inches
Answer: 5 feet 4 inches

Example: Add 7 yards 9 inches + 8 feet 5 inches
1) 10 yards 2 inches 2) 10 yards 14 inches 3) 29 feet 2 inches 4) 30 feet 14 inches
Answer: 10 yards 2 inches

Example: Mrs. White wants to make a dress for her daughter’s upcoming dance competition. She needs 5 feet 4 inches of green ribbon, 3 feet 6 inches of yellow ribbon and 4 feet 8 inches of violet ribbon to decorate the dress. Find the total length of all the ribbons she should purchase.
Answer: 13 feet 6 inches

Example: Subtract 7 yards 1 foot – 5 yards 2 feet = .
1) 1 yard 1 foot 2) 1 yard 2 feet 3) 2 yards 1 foot 4) 2 yards 2 feet
Answer: 1 yard 2 feet

Example: Amanda bought a 4 feet 7 inches long craft wire to create some candle holders and a hanging bird feeder for her backyard. If she used 2 feet 9 inches of the wire to make the bird feeder, how much wire is left with her to make the candle holders?
1) 1 foot 8 inches 2) 1 foot 10 inches 3) 2 feet 2 inches 4) 2 feet 8 inches
Answer: 1 foot 10 inches

Example: Multiply 7 yards 1 feet x 8 = .
1) 56 yards 2 feet 2) 58 yards 3) 58 yards 2 feet 4) 58 yards 8 feet
Answer: 58 yards 2 feet

Example: Julia plans to purchase fabric for window curtains for her home. Each of the 5 windows in her home is around 38 inches in length. If she needs three times the total length of the windows for curtains, how many feet of fabric would Julia need to buy?
1) 15 feet 10 inches 2) 37 feet 3 inches 3) 47 feet 3 inches 4) 47 feet 6 inches
Answer: 47 feet 6 inches

Example: Divide 19 feet 6 inches ÷ 6 = .
1) 3 feet 1 inch 2) 3 feet 2 inches 3) 3 feet 3 inches 4) 4 feet 1 inch
Answer: 3 feet 3 inches

Example: A plumber cut a 21.5 feet long pipe into 5 pieces. What is the average length of each of the 5 pipe pieces?
1) 3 feet 2) 4.3 feet 3) 5 feet 4) 107.25 feet
Answer: 4.3 feet

Example: Which of the following measure would you use to measure the weight of a ship?
1) Ounce 2) Pound 3) Ton 4) Gallon
Answer: Ton

Example: 12,000 lbs =  tons
1) 3 2) 6 3) 8 4) 12
Answer: 6

Example: A white rhino usually found in the woodlands of Southern and Central Africa weighs around 3 tons. What would be its weight in pounds?
1) 1500 pounds 2) 3000 pounds 3) 5000 pounds 4) 6000 pounds
Answer: 6000 pounds

Example: Which of the following is correct?
1) 4,004 lbs = 4 tons 4 lbs 2) 2,523 lbs = 2 tons 235 lbs 3) 4,320 lbs = 2 tons 320 lbs 4) 4,230 lbs = 2 tons 460 lbs
Answer: 4,320 lbs = 2 tons 320 lbs

Example: Add 9 lbs 7 oz + 7 lbs 9 oz = .
1) 16 lbs 2) 16 lbs 6 oz 3) 17 lbs 4) 17 lbs 6 oz
Answer: 17 lbs

Example: Christopher is an Army food supply truck driver and can carry 3 tons of food items together in his truck. This week he is supplying food packets to a Tsunami relief center and has breakfast packets weighing 14 ounces, lunch packets weighing 20 ounces and dinner packets weighing 18 ounces. What is the maximum weight of food he supplies to each disaster victim in a day, if he gives all the 3 meals to each victim daily?
1) 2 pounds 2) 3 pounds 2 ounces 3) 3 pounds 4 ounces 4) 4 pounds 3 ounces
Answer: 3 pounds 4 ounces

Example: Subtract 7 lbs 17 oz – 19 oz = .
1) 5 lbs 8 oz 2) 5 lbs 14 oz 3) 6 lbs 8 oz 4) 6 lbs 14 oz
Answer: 6 lbs 14 oz

Example: Mrs. Morris is an arts teacher. She purchased 12 pounds of modeling clay to teach her 5th grade students how to make models of human and animal shapes. The students made human shapes with 6 pounds 12 ounces of clay. If they used the rest of the clay for making animal models, how many pounds of clay did the students use to make animal models?
1) 4 pounds 5 oz 2) 5 pounds 4 oz 3) 5 pounds 88 oz 4) 6 pounds 4 oz
Answer: 5 pounds 4 oz

Example: Multiply 6 tons 900 pounds x 5 = .
1) 32 tons 500 pounds 2) 32 tons 4500 pounds 3) 34 tons 500 pounds 4) 34.5 tons
Answer: 32 tons 500 pounds

Example: A survey indicates that a person in a large American city drinks an average of 10 cups of water per day. What is the average amount of water consumed by a person in a 30 day month?
1) 19 gallons 2) 18 gallons 22 cups 3) 18 gallons 3 quarts 4) 17 gallons 22 cups
Answer: 18 gallons 3 quarts

Example: Divide 21 pounds 14 ounces ÷ 7 = .
Answer: 3 pounds 2 ounces

Example: Mr. Wright purchased 210 pounds of oranges for his grocery store. If each of his fruit rack can display 26 pounds 4 ounces of oranges, how many such racks can hold all the oranges?
1) 4 2) 6 3) 7 4) 8
Answer: 8

Example: Which of the following measure would you use to measure the water in an aquarium?
1) Fluid ounce 2) Cup 3) Pint 4) Gallon
Answer: Gallon

Example: Convert: 15 gallons =  quarts
1) 60 2) 64 3) 120 4) 128
Answer: 60

Example: Fill in the blank using the correct sign 15 pints  2 gallons
1) < 2) > 3) =
Answer: <

Example: Add
1) 19 quarts 2 cups 2) 20 quarts 6 cups 3) 5 gallons 2 cups 4) 5 gallons 2 quarts
Answer: 5 gallons 2 cups

Example: Emma wants to prepare some fruit punch for her friends. She needs 16 oz orange juice, 8 oz grenadine, 16 oz lemon juice, 2 gallons chilled ginger ale and 4 oz corn syrup for the fruit punch. How much ingredients does she need in all?
1) 46 fl oz 2) 36 cups 4 fl oz 3) 18 pints 2 fl oz 4) 9 quarts 12 fl oz
Answer: 9 quarts 12 fl oz

Example: Subtract
1) 12 gallons 2 pints 2) 12 gallons 6 pints 3) 13 gallons 2 pints 4) 13 gallons 6 pints
Answer: 12 gallons 6 pints

Example: Sean purchased 50 gallons of gasoline for his car in the month of March. If he used 36 gallons 3 quarts in the first 3 weeks, how many gallons of gasoline did he use during rest of the month?
1) 13 gallons 1 quart 2) 13 gallons 7 quarts 3) 14 gallons 1 quart 4) 14 gallons 7 quarts
Answer: 13 gallons 1 quart

Example: Multiply 15 gallons 3 quarts x 5 = .
1) 75 gallons 5 quarts 2) 76 gallons 5 quarts 3) 78 gallons 3 quarts 4) 79 gallons
Answer: 78 gallons 3 quarts

Example: Abigail is preparing a cake for a party. She knows that 1.5 pounds of cake can serve 10 children. How many pounds of cake would she have to prepare to serve 50 children?
1) 2.5 pounds 2) 7.5 pounds 3) 10 pounds 4) 12 pounds
Answer: 7.5 pounds

Example: Divide 48 gallons 3 quarts ÷ 5 = .
1) 7 gallons 7 quarts 2) 7 gallons 8 quarts 3) 8 gallons 6 quarts 4) 9 gallons 3 quarts
Answer: 9 gallons 3 quarts

Example: Taylor is making a gallon of corn soup to serve at dinner with her friends. If 7 of her friends are coming to the party, how many cups of soup can she serve each person including herself?
1) 1 cup 4 fl oz 2) 2 cups 3) 2 cups 4 fl oz 4) 3 cups
Answer: 2 cups

Example: 4 pipes of lengths 12.2 feet, 7.9 feet, 8.7 feet and 6.8 feet were joined in an underground pipe fitting. Which of the following is the best estimate for the total length of 4 pipes?
1) 34 feet 2) 36 feet 3) 38 feet 4) 40 feet
Answer: 36 feet


Metric Measurement
Example: How many millimeters are there in half meter?
1) 20 millimeters 2) 50 millimeters 3) 500 millimeters 4) 5000 millimeters
Answer: 500 millimeters

Example: William sold 7 m 75 cm of a rope to a customer. If the rope was priced at $1 per 50 cm, how much money would William get from the customer for the rope?
1) $77 2) $38.5 3) $15.5 4) $11.55
Answer: $15.5

Example: Which of the following is correct?
1) 120 cm > 10 dm 2) 120 m < 120 cm 3) 2 km > 300 m 4) 300 dm > 2 m
Answer: 120 cm > 10 dm

Example: Add
1) 12 km 2) 12 km 100 m 3) 11 km 100 m 4) 11 km
Answer: 11 km 100 m

Example: Hannah plans to stitch some new pillow covers for her living room couch. If she needs 2 m 50 cm of silk fabric and 2 m 30 cm of taffeta fabric, how much fabric does she need to purchase in all to stitch the pillow covers?
1) 48.0 cm 2) 4.80 m 3) 5 m 4) 48.0 m
Answer: 4.80 m

Example: Subtract
1) 11 km 90 m 2) 11 km 990 m 3) 10 km 90 m 4) 10 km 990 m
Answer: 10 km 990 m

Example: Amanda bought a 2 m 50 cm long copper wire from a home improvement store. Using a cutter, she cut off 80 cm of wire from the longer wire to install a light bulb. What is the length of the remaining wire?
1) 1 m 970 cm 2) 1 m 70 cm 3) 1 m 30 cm 4) 1 m 20 cm
Answer: 1 m 70 cm

Example: Solve 12 meters X 4 meters = ?
1) 16 meters 2) 16 square meters 3) 48 meters 4) 48 square meters
Answer: 48 square meters

Example: Dean decided to make a creative rope bookshelf for his room. He needs to purchase 6 wooden boards, some mounting screws, a measuring tape, super glue and some rope. If he needs 8 pieces each of 3m 25 cm ropes, how many meters of rope would he purchase in all for making the shelf?
Answer: 26 meters

Example: How many 100 meters are there in 3 kilometer?
1) 3 2) 30 3) 300 4) 3,000
Answer: 30

Example: Joseph, Daniel, David and Justin planned a driving trip to Brownsville from their home town Austin. Brownsville is around 566 km away from Austin. If they divide the driving distance equally among them, how much distance would each drive from Austin to Brownsville?
Answer: 141 km 500 m

Example: How many kilograms are there in 5,900 grams?
1) 0.59 kilograms 2) 5.9 kilograms 3) 590 kilograms 4) 59 kilograms
Answer: 5.9 kilograms

Example: Matthew used 0.45 decagrams gold to make a bracelet. If gold costs $40 per gram, how much would it cost Matthew to make the bracelet?
1) $108.0 2) $118.5 3) $180.0 4) $1,800
Answer: $180.0

Example: Which of the following is correct?
1) 100 kg = 10,000 grams 2) 2 kg 60 grams < 2600 grams 3) 4 kg 6 grams = 4600 grams 4) 5 kg 70 grams > 5700 grams
Answer: 2 kg 60 grams < 2600 grams

Example: Add
1) 10 kg 110 grams 2) 10 kg 10 grams 3) 9 kg 110 grams 4) 9 kg 10 grams
Answer: 9 kg 110 grams

Example: Nicole bought 2.25 kg of green vegetables and put it in an empty bag that weighed 75 grams. Then she bought 1 kg potatoes and 500 gm tomatoes and put those in the same bag. How much does her bag with all the vegetables weigh now?
1) 3,250 grams 2) 3,500 grams 3) 3,750 grams 4) 3,825 grams
Answer: 3,825 grams

Example: Subtract
1) 4 kg 375 grams 2) 4 kg 635 grams 3) 5 kg 375 grams 4) 5 kg 635 grams
Answer: 4 kg 375 grams

Example: Mrs. Reed is preparing some cakes and cookies for a family gathering. She purchased 5 kg 200 grams of flour and used 2 kg 750 grams of it to bake the cookies. How much flour is left for her to bake the cakes?
1) 2 kg 350 grams 2) 2 kg 450 grams 3) 3 kg 450 grams 4) 3 kg 550 grams
Answer: 2 kg 450 grams

Example: Multiply 45 decagram x 18 = .
1) 810 grams 2) 8 decagrams 10 grams 3) 8 kg 10 grams 4) 8 kg 100 grams
Answer: 8 kg 100 grams

Example: Divide 2 kg 750 grams ÷ 125 grams
1) 18 2) 19 3) 21 4) 22
Answer: 22

Example: Alexis’ luggage weighed 15 kg. She put a box of weight 1.7 kg in the luggage and took out another box of weight 1.2 kg from the luggage. How many grams does her luggage weigh now?
1) 15,500 grams 2) 1,550 grams 3) 155 grams 4) 15.5 grams
Answer: 15,500 grams

Example: How many milliliters are there in 0.2 liters?
1) 20 milliliters 2) 100 milliliters 3) 200 milliliters 4) 50 milliliters
Answer: 200 milliliters

Example: A medical store sold 15 bottles of Robitussin cough syrup in a day. How many liters of syrup did they sell if each bottle contains 250 ml of Robitussin syrup?
1) 0.3750 liters 2) 3.750 liters 3) 37.50 liters 4) 375 liters
Answer: 3.750 liters

Example: Choose True or False 7 liters 80 milliliters < 7,700 milliliters
1) True 2) False
Answer: True

Example: Add 4 liter 28 ml + 2 liter 92 ml
1) 6 liters 20 ml 2) 6 liters 120 ml 3) 7 liters 20 ml 4) 7 liters 120 ml
Answer: 6 liters 120 ml

Example: Christopher is the energy drink supplier to a gas station grocery store. Last week he supplied the store 17 liter 500 ml energy drink in the first 3 days of the week and 22 liter 750 ml in the last 4 days of the week. How much total energy drink did Christopher supply to the gas station store last week?
Answer: 40.250 liters

Example: Subtract 7 liter 200 ml – 4 liter 750 ml
Answer: 2 liter 450 ml

Example: Sophia bought 4 liters of milk to make pudding and milkshake. She made pudding with 2 liters 750 milliliters of milk and kept the rest of milk for the milkshake. How much milk did Sophia keep to make the milkshake?
Answer: 1 liter 250 milliliters

Example: Nicole bought 19 meters of cloth to make some dresses for a drama class. The cloth cost $32 per meter. Which of the following is the best estimate of the total cost of the cloth?
1) $68 2) $400 3) $600 4) $4,000
Answer: $600
 

Measurement of Time and Temperature
Example: Convert 2 hours 15 minutes =  min
1) 75 min 2) 125 min 3) 135 min 4) 145 min
Answer: 135 min

Example: Convert 420 days =  weeks
1) 70 weeks 2) 60 weeks 3) 7 weeks 4) 6 weeks
Answer: 60 weeks

Example: Find the time that is 2 hours 45 minutes before 2:15 pm.
1) 11:15 am 2) 11:30 am 3) 11:15 pm 4) 11:30 pm
Answer: 11:30 am

Example: Mrs. Williams is baking a cake for her friends. She prepared and kept the cake batter in the oven for baking. At 12:20 pm she took out the baked cake from the oven and plans to decorate it with icing after cooling. If the total baking time was 75 minutes, at what time did she keep the cake mix in the oven?
1) 11:05 am 2) 11:35 am 3) 11:05 pm 4) 11:35 pm
Answer: 11:05 am

Example: Starting time and ending time for an activity is given below, find the elapsed time. Starting time: 1:15 P.M. Ending time: 4:45 P.M.
1) 3 hours 15 minutes 2) 3 hours 30 minutes 3) 3 hours 45 minutes 4) 5 hours 30 minutes
Answer: 3 hours 30 minutes

Example: Brianna starts to watch a movie on her DVD player at 3:45 pm. She stops the movie at 4:35 pm since she has to attend her regular music classes. After the music classes at 6:05 pm Brianna starts to watch the rest of the movie and finishes the movie at 6:45 pm. How much time does Brianna spend in her music class?
Answer: 1 hour 30 min

Example: Find the time 3 hours 20 minutes after 11:40 pm.
1) 2:20 am 2) 3:00 am 3) 2:20 pm 4) 3:20 pm
Answer: 3:00 am

Example: Zachary works in a restaurant for 8 hours daily. If he starts his work at 8:45 am and takes a lunch break of half an hour in between, at what time would he be able to go home?
1) 4:45 pm 2) 5:00 pm 3) 5:15 pm 4) 5:30 pm
Answer: 5:15 pm

Example: Add 4 hours 24 min + 5 hours 50 min.
1) 9 hours 14 min 2) 9 hours 24 min 3) 10 hours 14 min 4) 10 hours 24 min
Answer: 10 hours 14 min

Example: Subtract 6 hours – 4 hours 25 minutes.
1) 55 min 2) 1 hour 35 min 3) 1 hour 45 min 4) 2 hours 25 min
Answer: 1 hour 35 min

Example: Convert
1) 68 2) 70 3) 72 4) 78
Answer: 68

Example: Convert
1) 40 2) 50 3) 52 4) 60
Answer: 50

Example:
Answer: 45 degree celsius
 

Measurement of length, perimeter and circumference
Example: Find the length of line segment AB.
1) 3.5 cm 2) 4.5 cm 3) 5.5 cm 4) 7.5 cm
Answer: 4.5 cm

Example: Find the perimeter of the triangle shown below.
1) 70 cm 2) 72 cm 3) 73 cm 4) 144 cm
Answer: 72 cm

Example: Find the perimeter of the rectangle shown below.
1) 31 cm 2) 60 cm 3) 61 cm 4) 62 cm
Answer: 62 cm

Example: Find the value of x in the following figure:
1) 3 2) 4 3) 8 4) 12
Answer: 4

Example: Mr. Williams is the physical trainer at St. Jones Middle School. He asks the students to take two rounds of the rectangular school track each day as a warm up exercise. If the school track is 120 meter by 100 meter, how many meters would the students run each day?
1) 220 meter 2) 440 meter 3) 660 meter 4) 880 meter
Answer: 880 meter

Example: If a side of a square is 7.2 inches long, what is the perimeter of the square?
1) 14.2 inches 2) 14.8 inches 3) 28.2 inches 4) 28.8 inches
Answer: 28.8 inches

Example: Lauren is making flower beds in her backyard. She made 5 square flower beds of equal sides and now she wants to protect each flower bed with small fences. If each side of the flower bed measures 1.5 meters, what would be the total length of the fence she needs for the flower beds.
Answer: 30 meters

Example: Find the perimeter of the regular pentagon shown below.
1) 10 cm 2) 12.25 cm 3) 12.5 cm 4) 125 cm
Answer: 12.5 cm

Example: The perimeter of a regular hexagon is 24 cm. Find the length of a side of that hexagon.
1) 15 cm 2) 12 cm 3) 6 cm 4) 4 cm
Answer: 4 cm

Example: Find the perimeter of the following figure.
1) 78 mm 2) 70 mm 3) 69 mm 4) 60 mm
Answer: 78 mm

Example: The figure below is made up of a rectangle and an equilateral triangle. Find the perimeter of the figure.
1) 12.5 cm 2) 14 cm 3) 15 cm 4) 17 cm
Answer: 14 cm

Example: Find the perimeter of a rectangular carpet whose drawing is shown below.
1) 6 cm 2) 10 m 3) 30 m 4) 40 m
Answer: 30 m

Example: Find the missing length CD from the given diagram.
1) 1 cm 2) 2 cm 3) 3 cm 4) 4 cm
Answer: 2 cm

Example: Taylor made a painting that measures 5 feet by 8 feet and wants to frame the borders of the painting with wood trims. The wood trim cost $3 per foot. How much would it cost Taylor to frame the painting?
1) $39 2) $78 3) $88 4) $108
Answer: $78

Example: Luke needs to make some craft wire squares of 4 cm side for a school project. He decides to reuse the craft wire from a rectangle of length 80 cm and width 40 cm. How many craft wire squares would he be able to make if no wire gets wasted?
1) 8 2) 10 3) 12 4) 15
Answer: 15

Example: If the side of a square is doubled, then what will be the ratio of the resulting square’s perimeter to that of the original square’s perimeter?
1) 1:2 2) 2:1 3) 1:4 4) 4:1
Answer: 2:1

Example: Find the circumference of the circle. Radius = 5 cm, (use π = 3.14)
1) 127 cm 2) 12.70 cm 3) 3.14 cm 4) 31.4 cm
Answer: 31.4 cm

Example: Emma wants to stitch a lace pattern on the edge of her circular dining table cover. If the radius of the table is 1.5 meter, find the length of the lace required. (Use π = 3.14)
Answer: 9.42 meter

Example: Find the circumference of the circle. Diameter = 14 cm, (use π = 22/7)
1) 3.14 cm 2) 66 cm 3) 44 cm 4) 22 cm
Answer: 44 cm

Example: What is the distance traveled by a wheel in two revolution if the diameter of that wheel is 42 cm. (Use π = 22/7)
1) 122 cm 2) 132 cm 3) 244 cm 4) 264 cm
Answer: 264 cm


Measurement of Area and Volume
Example: Find the area of a rectangle whose length and width are given below: Length = 7.8 cm Width = 2.5 cm
1) 1.95 m² 2) 19.5 cm² 3) 19.5 m² 4) 195 cm²
Answer: 19.5 cm²

Example: Find the area of a square whose side is given below: Side = 0.1 cm
1) 10 cm² 2) 1 cm² 3) 0.4 cm² 4) 0.01 cm²
Answer: 0.01 cm²

Example: A room’s floor is 5.6 m long and 4 m wide. If it is to be covered by square tiles of size 40 cm by 40 cm, how many tiles would be needed to cover the whole area?
1) 14 2) 140 3) 160 4) 1,400
Answer: 140

Example: Find the area of the triangle whose base and height are given below: Base = 24 cm Height = 8 cm
1) 76 cm² 2) 86 cm² 3) 96 cm² 4) 192 cm²
Answer: 96 cm²

Example: Find the area of the parallelogram whose base and height are given below: Base = 15 cm Height = 9 cm
1) 57.5 cm² 2) 67.5 cm² 3) 125.0 cm² 4) 135.0 cm²
Answer: 135.0 cm²

Example: Nicholas bought a board in the shape of a parallelogram with base 22 cm and height 20 cm for displaying the clay model he made for an upcoming craft exhibition. Before fixing the model he wants to paint the board with silver color. How much would it cost Nicholas to paint both faces of the board if it costs $1.5 per 10 cm²?
1) $66.0 2) $132.0 3) $660.0 4) $1,320.0
Answer: $132.0

Example: Find the base of the parallelogram whose area and height are given below: Area = 420 cm ² Height = 7 cm
1) 6 cm 2) 7 cm 3) 60 cm 4) 70 cm
Answer: 60 cm

Example: What will happen to the area of a triangle if its base is doubled and height is kept same?
1) Area will be half 2) Area will be 2 times 3) Area will be 4 times 4) Area will be 6 times
Answer: Area will be 2 times

Example: Calculate the area of the shaded region given below.
1) 8 m² 2) 9 m² 3) 10 m² 4) 12 m²
Answer: 12 m²

Example: Find the area of a circle with radius 6 m.
1) 6π m² 2) 12π m² 3) 24π m² 4) 36π m²
Answer: 36π m²

Example: Find the volume of a rectangular prism whose length, width and height are given below: Length = 7 m, Width = 5 m, Height = 4 m
1) 140 m³ 2) 120 m³ 3) 35 m³ 4) 16 m ³
Answer: 140 m³

Example: How many cubic centimeter of sand is required to fill a rectangular shaped sand box up to a height of 5 centimeters if the box is of length 4 centimeters and width 5 centimeters.
1) 14 cubic centimeter 2) 20 cubic centimeter 3) 28 cubic centimeter 4) 100 cubic centimeter
Answer: 100 cubic centimeter

Example: Find the height of a rectangular prism whose length, width and volume are given below: Length = 6 cm, Width = 6 cm, volume = 36 cm³
1) 1 cm 2) 2 cm 3) 3 cm 4) 36 cm
Answer: 1 cm

Example: Brianna bought a rectangular open container with 64,000 cm³ capacity and 40 cm height, for rain water harvesting. To keep the container in the backyard she needs a platform that has an area equal to the base area of the container. What would be the width of the platform if the container Brianna bought is 80 cm long?
1) 320 cm 2) 80 cm 3) 30 cm 4) 20 cm
Answer: 20 cm

Example: Find the volume of a cube whose side is given below:
Answer:

Example: What is the volume of the figure shown below?
1) 32 cubic cm 2) 64 cubic cm 3) 96 cubic cm 4) 128 cubic cm
Answer: 64 cubic cm

Example: Find the volume of a triangular prism that has the following dimensions: Length = 10 mm Width = 8 mm Height = 6 mm
1) 560 mm³ 2) 480 mm³ 3) 240 mm³ 4) 48 mm³
Answer: 240 mm³

Example: The figure below shows a model made up of 1 cm cubes. Find the volume of the model.
1) 4 cm³ 2) 9 cm³ 3) 10 cm³ 4) 16 cm³
Answer: 10 cm³

Example: A water tank is 2 m long, 1.5 m wide and 50 cm high. Find its capacity.
1) 1.5 m³ 2) 6.0 m³ 3) 15.0 m³ 4) 150.0 m³
Answer: 1.5 m³

Example: Find the volume of a cylinder for which the base area and height are given below. Area of the base = 12.56 cm² Height = 1 cm,
1) 6.28 cm³ 2) 12.56 cm³ 3) 24.56 cm³ 4) 25.12 cm³
Answer: 12.56 cm³

Example: Find the volume of a cylinder for which the radius of the base and height are given below. Radius = 2 cm Height = 7 cm, (Use π = 22/7)
1) 14 cm³ 2) 22 cm³ 3) 44 cm³ 4) 88 cm³
Answer: 88 cm³

Example: Find the surface area of the following model.
1) 12 m² 2) 14 m² 3) 28 m² 4) 56 m²
Answer: 28 m²

Example: Find the surface area of the following model.
1) 6 cm² 2) 8 cm² 3) 12 cm² 4) 24 cm²
Answer: 24 cm²
 

Data and Graph
Example: In a cheer leader audition organized by a club, the number of admission forms submitted by candidates on each day of the week is shown in the table below. What is the average number of forms submitted per day?
1) 5 2) 9 3) 10 4) 11
Answer: 9

Example:
1) 6 2) 7 3) 8 4) 9
Answer: 8

Example: Cody and his 9 friends volunteer for a charity that helps physically disabled children. They plan to conduct a charity show to raise funds for the charity. If Cody and his friends need to raise a sum of $1,010 for the show, which of the following could be the mean amount of money each of them should collect for the show?
1) $100 2) $101 3) $102 4) $110
Answer: $101

Example: Kayla borrowed the novel Catch–22 written by Joseph Heller from her local library. She has to return the book in 12 days. So she plans to complete reading the book in the next 11 days. If she reads an average of 42 pages each day, which option best represents the number of pages she will read in the next 11 days?
1) 422 2) 442 3) 462 4) 504
Answer: 462

Example: The pictograph below shows the number of tickets sold for a charity show by 5 boys. What is the mean number of tickets sold by each boy?
Answer: 35

Example: The heights of 9 players of a team are 68 inches, 70 inches, 72 inches, 68 inches, 67 inches, 71 inches, 73 inches, 71 inches, and 68 inches. What is their median height?
1) 72 inches 2) 71 inches 3) 70 inches 4) 68 inches
Answer: 70 inches

Example: The points scored by 15 students in an exam are shown below. 34, 23, 45, 49, 50, 48, 34, 23, 34, 12, 10, 45, 34, 34, 28 Select the mode for the above data.
1) 34 2) 23 3) 50 4) 45
Answer: 34

Example: The sum of 5 numbers is 35. Which of the following measure of central tendency could be obtained from the above information?
1) Mode 2) Median 3) Mean 4) None of above
Answer: Mean

Example: The maximum temperature in a city for each day of a week is shown in the table. Find the range of the data.
Answer: 5

Example: The pictograph below shows the number of stamps of different countries collected by 6 boys. Study the pictograph and answer "How many stamps did Caleb and Jason collect in all"?
Answer: 130

Example:
Answer: 16

Example: The 6th and 7th graders of St. Luke Middle school were asked in a school survey to vote for their favorite color. The results of the survey are represented using a frequency table below. How many more votes did the color with the most votes receive than the color with the least votes did?
1) 52 2) 50 3) 29 4) 23
Answer: 29

Example: The frequency table below shows the number of different types of CDs John has in his collection. Study the table and find out the value of Q.
Answer: 100

Example:
Answer:

Example: Mrs. Long, a 5th grade teacher in an all girls school, asked her students to name their favorite activity during vacations. She
recorded the answers of her students in a tally table shown below.
Which bar graph below displays this information correctly?
Answer:

Example: The numbers of different colored rose plants in a rose garden are shown in the graph below.
1) 15 2) 30 3) 45 4) 50
Answer: 15

Example: Mrs. Miller’s son had fever one morning, so she gave him some medicine and recorded his temperature every 2 hours. The recorded temperatures are shown in the graph below. Study the graph and answer the question given below.
Answer:

Example: The data below shows the points scored by the students of a class in a Math exam. 12, 38, 40, 32, 30, 38, 41, 41, 32, 40, 22, 41, 32, 41, 18 Which of the following Stemandleaf plots shows the above data?
Answer:

Example: The stemandleaf plot below shows the Science test scores of students in a class. Study the plot and answer the question given below.
1) 8 2) 12 3) 14 4) 16
Answer: 16

Example: Select the ordered pair for the ‘Point E’ on the grid shown below:
1) (3.5, 9.5) 2) (3, 3.5) 3) (3.5, 9) 4) (9, 3.5)
Answer: (9, 3.5)

Example: A figure is shown on the grid below. Which of the following group of ordered pairs represent the 3 vertices of the figure?
1) (3, 3), (5, 5), (7, 7) 2) (3, 3), (3, 7), (7, 5) 3) (3, 7), (7, 3), (5, 7) 4) (3, 3), (7, 3), (5, 7)
Answer: (3, 3), (7, 3), (5, 7)
 

Probability
Example: Which of the following event is certain?
1) Spinning a number greater than 8 on a spinner that has 4 sections numbered 2, 4, 6 and 8 2) Spinning an even number on a spinner that has 4 sections numbered 2, 4, 6 and 8 3) Spinning an odd number on a spinner that has 4 sections numbered 2, 4, 6 and 8 4) Spinning a number 2 or 4 on a spinner that has 4 sections numbered 2, 4, 6 and 8
Answer: Spinning an even number on a spinner that has 4 sections numbered 2, 4, 6 and 8

Example: Which of the following event is impossible?
1) Selecting a number which is divisible by 2 from the set of one digit odd numbers 2) Selecting a number which is divisible by 2 from the set of one digit even numbers 3) Selecting a number which is divisible by 3 from the set of one digit odd numbers 4) Selecting a number which is divisible by 3 from the set of one digit even numbers
Answer: Selecting a number which is divisible by 2 from the set of one digit odd numbers

Example: How many possible outcomes are there in a throw of a dice?
1) 1 2) 2 3) 3 4) 6
Answer: 6



Example: Gabriel tosses 2 coins simultaneously (at the same time). Find the probability of getting one head and one tail?
1) 1 out of 4 2) 3 out of 4 3) 1 out of 2 4) 3 out of 8
Answer: 1 out of 2




Example: The table below shows the results of a survey of 50 students asking them for their favorite subject.
1) P(Mathematics) < P(Science) 2) P(Science) < P(English) 3) P(English) < P(Mathematics) 4) P(Science) < P(Mathematics)
Answer: P(Mathematics) < P(Science)

Example: For the science week of his school, Ryan wants to make a science project. The tables below show the different subjects and types of models from which he can choose. Find the number of all the different combinations of 1 subject and 1 type of model Ryan can choose.
1) 5 2) 6 3) 7 4) 9
Answer: 6
 

Geometry – Polygon Relationships
Example: Two figures with a label are shown below. Select True or False for the label and figures.
1) True 2) False
Answer: True

Example:
1) Figure 1 is congruent to figure 2. 2) Figure 1 is similar but not congruent to figure 2. 3) Figure 1 is neither similar nor congruent to figure 2. 4) None of the above
Answer: Figure 1 is similar but not congruent to figure 2.

Example: Is the red line below a line of symmetry for the given figure?
1) Yes 2) No
Answer: No

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

Example:
1) 3 2) 4 3) 8 4) 16
Answer: 8

Example: The figure below shows half of an alphabet and a dotted line. The dotted line shows a line of symmetry for the whole alphabet. Which of the following word contains that alphabet?
1) SHAPE 2) POLYGON 3) CURVE 4) BOUND
Answer: CURVE

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

Example: The figure shown below has rotational symmetry. What is the angle of each turn?
1) 90 degree 2) 45 degree 3) 30 degree 4) 60 degree
Answer: 45 degree

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

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

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

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

Example: Mackenzie made the pattern shown below by using different transformations. What moves did she make to transform each figure into its next position?
1) Reflection, then translation, then reflection, then rotation. 2) Reflection, then rotation, then translation. 3) Reflection, then rotation, then reflection, then translation. 4) None of the above
Answer: Reflection, then rotation, then reflection, then translation.

Example: Anthony has a board with 26 English alphabets written on it. He is looking at the alphabets on the board in a plane mirror. How many alphabets in the mirror image will look the same as the original alphabets on the board?
1) 5 2) 7 3) 10 4) 11
Answer: 11

Example:
Answer:

Example:
1) East 2) West 3) North 4) South
Answer: South

