# Algebra 1 test

Name _____________________                                        Date:_____________________

Solve the following problems

1. What is the product of -10 and +5? ____________

2. Add: -10 + 5 ____________

3. What is the quotient of -16 and -4? _____________

4. Subtract: -1 − -8 ______________

5. Calculate: |-6 × 2 + -4 × -3| ___________

6. Simplify the following expressions:

a) 4x + 5 + 2x ____________

b) -6x + 4z + -3x − 10z ____________

c) 10y − -2y − 3z − 9z − 6y ____________

d) x5 × y4 × x-7 × y10 ______________

e) x8 ÷ x2 ____________

f) (4x)3 _________________

g) (-5c)4 _________________

7. Which of the following expressions show the associative property?

A. 5 × 7 + 2 = 2 + 5 × 7      B. 5 + 7 = 7 + 5      C. (5 × 7) × 2 = 5 × (7 × 2)      D. 2 + 7x

8. Which properties are illustrated by the following three expressions?

a) -1 × 7 + 2 = 2 + -1 × 7

b) 9 * 1 = 9

c) 4 × ( 2 + 6) = 4 × 2 + 4 × 6

A. Identity property of addition, distributive property, and commutative property of addition
B. Identity property of addition, distributive property, and associative property of addition
C. Identity property of multiplication, distributive property, and commutative property of addition
D. Identity property of multiplication, distributive property, and commutative property of multiplication

9. Solve the following equations for x:

a) x − 2 = -7

b) x − -2 = -7

c) (2/3)x = 6

d) -2x + 5 = -11

e) ax + b = -e

10. Solve the following inequalities. Then graph a) on the number line

a) 3x - 2 > -11

b) x ≠ 5

c) -1 ≤ x < 4

d) -5f < -10

11.

Convert the following numbers into scientific notation:

a) 0.0000000000245 _______________

b) 890000000 ______________

a) 9z8 + 2z5 + 4z2 + 2 and 5z8 + -6z5 + -4z2 + -1z + -8

b) z6 + 5z4 + -10z3 + -7 and -z6 + 8z4 + 4z3 − 8

13. Multiply the following polynomials and simplify

a ) 4x3( 2x2 + x − 5) _______________

b) (4x3 + 4x )( 2x2 + x − 5)_________________

14. Divide: x3 - 6x2 + 5x - 30 / x - 6 ________________

15. Find the greatest common factor of the following expressions:

a) 15, 30

b) 15x3, 30x2

16. Factor the following polynomials

a) 12x2 + 24x3 + - 18x ________________

b) x2 − 3x − 18 ________________

c) x6 + 13x5 + 42x4 _________________

17. For question 16, exercises b) and c), solve for x

b) x = ___________ and ____________

c) x = ___________, _____________, and, _______________

18. How many ways can you and 3 other friends sit on 4 chairs? _____________

19. Use the following data to construct a box and whiskers plot:

12, 5, 2, 20, 7, 24, 10, 21

20. Solve and graph the following inequality: 2x + 5 > 12

A bag contains 2 blue balls, 5 red balls, and 3 white balls.

You pick a ball from the bag and put in your pocket. What is the probability of picking:

a) a white ball?_______________

b)a blue ball or a red ball? _______________

c) two red balls? ________________

d) a blue ball and a white ball

21. Solve and graph the following systems of linear equations:

a)

x + y = 9

x − y = 7

b)

4x - 3y = 10

8x + 5y = -10

22. Write the following fractions in simplest form:

a) (25x6 36 z7) / (50x8 6z5)

b) (x6 + 13x5 + 42x4) / x3 (x + 6)

23.

Solve the equation below: two different ways.

First, solve using the quadratic formula:

Second, solve it by completing the square

x2 = -3x + 10

24.

Convert the following repeating decimal into a fraction

x = 1.01255555555555

25. Solve the following equation:

3 - √(x - 2) = 1

26. Rationalize the denominator of each fraction below:

a) 2 / √( 5)

b) 4 / (√( 5) - 2)

27.

Use a trigonometric ratio to find x:

Word problems

28.

The sum of two consecutive even integers is 18. What are the integers? (Hint: use 2x as the first even integer)

The integers are _______________ and ________________

29.

After you leave your house, you walk 10 blocks east and 6 blocks south. How far are you from your house?

I am __________________ blocks from my house

30.

The length of a rectangle is two more than the width. The area is 35. Find the length and the width (Hint: Let x be the width).

Width = ______________ length = ___________________