Algebra test generator

Name _____________________ Date:_____________________

current difficulty level: Choose test difficulty: Easy Challenging
(current difficulty level: Easy)

Solve the following problems:

Important instructions

(or click here to generate a new test)

1. Multiply: -14 and 3? -42

2. Add: -7 and 2? -5

3. Divide: 17 and 17? 1

4. Substract: 5 and -1? 6

5. Calculate: |19 + -14 · -5| 89

6. Simplify the following expressions:

-2x – 15x – -10x -7x
4x + 15 + -19 – -20y -4+4x+20y
20y + 1y + 6z + 11z – 20x + -10 -10-20x+21y+17z
y² × x^-15 × y³ x^-15 × y⁵
x¹⁴
x¹⁸
x^-4
(9x³)² 81x⁶

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

a + b = b + a
-2 × 1 = -2
-1 × ( z + 3 + 4 ) = -1×z + -1×3 + -1×4
( x × y ) × z = x × ( y × z )

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

13 + 5 × -1 = 5 × -1 + 13
0 + -26 = -26
x × ( y + 1 ) = x × y + x × 1

Associative property of multiplication, Commutative property of addition and Identity property of multiplication
Commutative property of addition, Identity property of addition and Distributive property
Associative property of addition, Commutative property of addition and Commutative property of multiplication
Commutative property of multiplication, Associative property of multiplication and Distributive property

9. Solve the following equations for x:

-55 + x = 65 x = 120
19
2
= -
1
2
x x = -19
-23x – -64 = 87 x = -1
-d = gx + e x = (d+e)/(-g)

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

4x – -17 > -27 x > -11

x ≠ 79
51 < x > -57

20
10
x ≤
28
7
x ≤ 2

11. Convert the following numbers into scientific notation:

0.0000000164 1.64 × 10^-8
324000000000 3.24 × 10¹¹

12. Add the following polynomials:

12z⁹ + -8z⁵ + 5z¹ + -8 and 13z⁹ + 8

25z⁹ + -8z⁵ + 5z¹
8z¹² + 11z⁵ + -3z¹ and 5z¹⁷ + 7z¹² + -2z¹⁰ 5z¹⁷ + 15z¹² + -2z¹⁰ + 11z⁵ + -3z¹

13. Multiply the following polynomials and simplify:

(5x⁴ + 3x²)(9x⁵ + 8x⁴ - 8)

45x⁹ + 40x⁸ + 27x⁷ + 24x⁶ - 40x⁴ - 24x²
(4x³ + 6x)(10x⁴ + 2x + 8)

40x⁷ + 60x⁵ + 8x⁴ + 32x³ + 12x² + 48x

14. Divide:

8x² + 30x + 25 / 2x + 5
4x + 5

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

27, 18, 78
3
21x⁹y⁶, 84x⁷y⁷, 27x⁸y⁹
3x⁷y⁶

16. Factor the following polynomials:

52x⁴ - 40x³ - 12x²
52x²(x +
3
13
)(x - 1)
x² - 12x + 35
(x - 7)(x - 5)
x⁸ - 3x⁷ - 108x⁶
x⁶(x - 12)(x + 9)

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

x =
7
and

5
x =
0
,
12

and
-9

18. You have 3 pants, 2 shirts, and 3 shoes. How many different ways can you dress?

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

37, 9, 3, 21, 31, 25, 33, 16

20. Suppose you toss a coin and spin a spinner numbered 1 through 19

What is the probability of getting tails and 1?

2.63%

What is the probability of getting tails and an odd number?

23.68%

What is the probability of getting tails and a multiple of 3?

15.79%

What is the probability of getting heads and a prime number?

21.05%

What is the probability of not tails and not 10?

47.37%

What is the probability of getting not tails and not a whole number?

0%

What is the probability of heads or tails and a whole number?

100%

What is the probability of getting tails?

50%

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

x + y = -2
x - y = 7

A(2.5,-4.5)

2x - y = 18
4x + 10y = 11

B(7.96,-2.08)

22. Write the following fractions in simplest form:

22x⁷y
88x¹⁰y³

1
4x³y²

(x - 3)
(x² - 6x + 9)

1
x - 3

23. Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.

x² + 8x = 33
x₁ = 3, x₂ = -11

24. Convert the following repeating decimal into a fraction:

x = 0.46
42
90

25. Solve the following equation:

13
x
- 8 = 10
x
+ 4
x = 16

26. Rationalize the denominator of each fraction below:

35
6
15
14

21
3

27. Use a trigonometric ratio to find x:

x = 28.28 cm

28. The sum of two consecutive odd integers is 52. What are the integers? (Hint: use 2x+1 as the first odd integer)

a=25, b=27

29. After you leave your house, you walk 4 blocks east and 3 blocks north. How far are you from your house?

I am
5
blocks from my house.

30. A rectangle has a length 6 ft greater than its width. The area of the rectangle is 280ft². What are the length and width of the rectangle?

width = 14, length = 20

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