CONFIDENTIAL 1

Good Afternoon!

Today we will do pre-quiz practice problems of

NUMBERS & ALGEBRAIC CONCEPTS

CONFIDENTIAL 2

Divisibility1. Which number divides evenly into 120,

240, and 360 with no remainder, but will not divide evenly into 160 and 320?

1. 22. 33. 44. 5

CONFIDENTIAL 3

Divisibility2. A number divides evenly into 27, 30,

33, and 36. Which of the following will the number also divide evenly into?

1. 472. 483. 494. 50

CONFIDENTIAL 4

Divisibility3. If all even numbers are divisible by 2,

is it true that all odd numbers are divisible by 3? If so, explain your reasoning. If not, give a number for which this is not true.

No; 17 is an odd number that is not divisible by 3.

CONFIDENTIAL 5

Divisibility4. List the number of ways 126 books can

be packaged for shipping to a school so that each package has the same number of books.

2 packages of 63 books;3 packages of 42 books;6 packages of 21 books;9 packages of 14 books;14 packages of 9 books;21 packages of 6 books;42 packages of 3 books;63 packages of 2 books

CONFIDENTIAL 6

Divisibility5. My mother is planning a large

gathering for Thanksgiving for 153 people. She has tables that seat 5,6 or 9 people. If all of the tables must be the same size and all of the tables must be full, what size table should she use?

9 seater

CONFIDENTIAL 7

Prime Factorization6. Which of the following best describes

the numbers 6, 15, 21, 28, and 32?1. Composite2. Even3. Odd4. Prime

CONFIDENTIAL 8

Prime Factorization7. Which figure represents a prime number?

1) 2)

3) 4)

CONFIDENTIAL 9

Prime Factorization8. Write 38 as a product of prime factors.

2 x 19

CONFIDENTIAL 10

Prime Factorization9. Find a counterexample for the

statement below.All even numbers are composite numbers.(A counterexample is an example that shows a statement is not true.)

(Hint: You need to find an even number that is not a composite number.)

The number 2 is a prime number because ti has two factors, 1 and itself.

CONFIDENTIAL 11

Prime Factorization10. Find the least prime number that is

greater than 70.

71

CONFIDENTIAL 12

Powers & Exponents11. How is 3 x 3 x 3 x 3 expressed using

exponents?1. 33

2. 43

3. 3 x 33

4. 34

CONFIDENTIAL 13

Powers & Exponents12. How is 46 written as a product?

4 x 4 x 4 x 4 x 4 x 4

CONFIDENTIAL 14

Powers & Exponents13. The length of one day on Venus is 35

Earth days. Express this exponent as a product. Then find the value of the product.

3 x 3 x 3 x 3 x 3 = 243 Earth Days

CONFIDENTIAL 15

Powers & Exponents14. A 100 pound person on Earth would

weigh about 4 x 4 x 4 x 4 pounds on Jupiter. Write 4 x 4 x 4 x 4 using an exponent. Then find the value of the power. How much would a 100pound person weigh on Jupiter?

44; 256 lbs

CONFIDENTIAL 16

Powers & Exponents15. The diameter of Mars is about 94

kilometers. Write 94 as a product. Then find the value of the product.

9 x 9 x 9 x 9;6,561km

CONFIDENTIAL 17

Order of Operations16. Which operation should be done first in

20 – 3 x 6 ÷ 2 + 3

3 x 6

CONFIDENTIAL 18

Order of Operations17. Find the value of the expression:

96 ÷ 42 + (25 x 2) - 15 - 3

38

CONFIDENTIAL 19

Order of Operations18. What is the value of ten plus fifty

divided by five times two minus 6?

24

CONFIDENTIAL 20

Order of Operations19. Javier and four friends go to the movies.

Each person buys a movie ticket, snack, and a soda. Find the total cost of the trip to the movies.

Cost of going to the Movies

Item ticket snack

Soda

Cost ($) 6 3 2

5 x $6 + 5 x $3 + 5 x $2 = $55

CONFIDENTIAL 21

Order of Operations20. Write an expression whose value is 10.

It should contain four numbers and two different operations.

Sample Answer: 25 ÷ 5 + 10 ÷ 2

CONFIDENTIAL 22

Variables & Expressions21. What is the value of (8 x r) – 4 if r= 4?

28

CONFIDENTIAL 23

Variables & Expressions22. What is the value of 4b ÷3, if b = 3?

4

CONFIDENTIAL 24

Variables & Expressions23. The table shows the

results of a survey in which people were asked to name the place they use technology when away from home. Write an expression to represent the total number of people who participated in the survey?

Place Number of responses

On vacation

57

While driving

57

Outdoors 42

Mall X

Gym 17

Public restrooms

10X + 183

CONFIDENTIAL 25

Variables & Expressions24. Distance traveled can be found using the

expression r x t, where r represents rate and t represents time. How far will you travel if you drive for 9 hours at a rate of 65 miles per hour?

585 miles

CONFIDENTIAL 26

Variables & Expressions25. The equation 13 + a = 51 describes the sum

of ages of Elizabeth and her mother. If a is Elizabeth’s mother’s age, what is the age of Elizabeth’s mother?

38 years old

CONFIDENTIAL 27

Problem Solving26. True or False? If 14 + b = 86, then b =

78.

False; b = 72

CONFIDENTIAL 28

Problem Solving27. The table shows the

distance Trevor rode his bike each day for a week. At this rate, how many miles will he ride on Saturday?

Day Distance (mi)

Sunday 2

Monday 5

Tuesday 8

Wednesday 11

Thursday ?

Friday ?

Saturday ?

20 miles

CONFIDENTIAL 29

Problem Solving28. The table shows how much

Kyle has earned in each of the last four weeks doing chores.

1. How much can he expect to earn the fifth week if this pattern continues?

2. Explain the pattern.

Week Amount ($)

1 2

2 3

3 5

4 9

$17; Add 1 to the first week and then add double the difference between the two previous weeks.

CONFIDENTIAL 30

Problem Solving29. Dave wants to buy a new computer system

that is priced at $2,475. He plans to put down $300 and will pay the rest in five equal payments. Find the amount of each payment.

$435

CONFIDENTIAL 31

Problem Solving30. The table shows the

number of pages of a book Elias read during the past 5 days. How many pages Elias will read on Saturday if he continues at this rate.

Pages read by Elias

Day Pages Read

Monday 5

Tuesday 11

Wednesday 19

Thursday 29

Friday 41

Saturday ?

55