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: -8 and -6? 48

2. Add: 17 and 1? 18

3. Divide: 1 and -1? -1

4. Substract: -19 and -16? -3

5. Calculate: |-6 · 9 + 18| 36

6. Simplify the following expressions:

10x + -7 – 6x -7+4x
11 + 2 + 5x + 11x 13+16x
1z + -6 + -10y – 17z – 10z – -1 -5-10y-26z
x^-16 × x^-11 × x⁹ x^-18
x¹⁹
x^-1
x²⁰
(7x²)³ 343x⁶

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

9 + 7w + 3
( 5 × 2 ) × 3 = 5 × ( 2 × 3 )
0 + 7x = 7x
4( 7 + 1 ) = 4×7 + 4×1

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

12 × (7 + z) = (7 + z) × 12
1 × 88 = 88
f × ( g × h ) = ( f × g ) × h

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

9. Solve the following equations for x:

10 = 2 · x x = 5
-
24
30
=
4
30
x x = -6
52 + -35x = -18 x = 2
a = ex x = a/e

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

-8x + 16 ≥ 40 x ≤ -3

x ≠ -262
-22 ≥ x ≥ -91

-
9
3
x ≥ -15 x ≤ 5

11. Convert the following numbers into scientific notation:

0.00000000503 5.03 × 10^-9
35000000 3.5 × 10⁷

12. Add the following polynomials:

12z⁸ + 1z⁴ + 1z¹ and -8z⁸ + 12z⁶

4z⁸ + 12z⁶ + 1z⁴ + 1z¹
6z¹⁹ + 14z¹⁸ + -9z¹⁵ + 5z³ + -1z² and -9z¹⁹ + 11z¹⁸ + 5z¹⁵ + 15z² -3z¹⁹ + 25z¹⁸ + -4z¹⁵ + 5z³ + 14z²

13. Multiply the following polynomials and simplify:

3x(3x⁵ + 5x⁴ + 8)

9x⁶ + 15x⁵ + 24x
(5x⁵ + 4x³)(10x⁵ + 8x² + 3x)

50x¹⁰ + 40x⁸ + 40x⁷ + 15x⁶ + 32x⁵ + 12x⁴

14. Divide:

2x³ - 14x² - 8x + 56 / x - 7
2x² - 8

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

45, 96, 90
3
44x⁸y¹⁰, 52x⁶y⁵
4x⁶y⁵

16. Factor the following polynomials:

48x⁴ + 72x³ + 26x²
48x²(x -
-9 +
3
12
)(x -
-9 -
3
12
)
x² - 8x - 20
(x + 2)(x - 10)
x⁵ - 17x⁴ + 66x³
x³(x - 11)(x - 6)

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

x =
-2
and

10
x =
0
,
11

and
6

18. You have 4 books to read. How many different ways can you read your books?

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

16, 18, 15, 28, 20, 26, 21, 36, 10, 34

20. Suppose you toss a coin and spin a spinner numbered 1 through 18

What is the probability of getting heads and 5?

2.78%

What is the probability of getting heads and an even number?

25%

What is the probability of getting tails and a multiple of 7?

5.56%

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

19.44%

What is the probability of not tails and not 15?

47.22%

What is the probability of getting not heads 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 heads?

50%

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

x + y = -3
x - y = 6

A(1.5,-4.5)

10x - 9y = 7
7x + 2y = -7

B(-0.59,-1.43)

22. Write the following fractions in simplest form:

5x²y⁹
20x⁵y¹⁰

1
4x³y

(x - 5)⁶
(x - 5)²

(x - 5)⁴

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

x² + 9x = 90
x₁ = 6, x₂ = -15

24. Convert the following repeating decimal into a fraction:

x = 0.9830
9732
9900

25. Solve the following equation:

-
7
x
= -5
x =
49
25

26. Rationalize the denominator of each fraction below:

15
10
+ 1

5
10
- 5
3

27. Use a trigonometric ratio to find x:

x = 15.00 cm

28. The sum of two consecutive odd integers is 44. What are the integers? (Hint: use 2x+1 as the first odd integer)

a=21, b=23

29. After you leave your house, you walk 6 blocks west and 8 blocks north. How far are you from your house?

I am
10
blocks from my house.

30. A rectangle has an area of 24ft². Its width is 10 ft less than its length. What are the dimensions of the rectangle?

width = 2, length = 12

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