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: -16 and 13? -208

2. Add: -13 and 10? -3

3. Divide: 12 and 4? 3

4. Substract: -6 and -18? 12

5. Calculate: |-2 + 3 · 13| 37

6. Simplify the following expressions:

-11 – 9 – 8x -20-8x
-7y + -18 – -9 + -7x -9-7x-7y
-16y + -16z – -16y – 18y – 2x -2x-18y-16z
y¹⁷ × y^-20 × y^-4 y^-7
x^-6
x^-9
x³
(5x⁴)⁴ 625x¹⁶

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

( m × n ) × 8 = m × ( n × 8 )
a + b = b + a
( x × y ) + 7 = 7 + ( y × x )
0 + 6x = 6x

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

( 5 × -17 ) × -19 = 5 × ( -17 × -19 )
( -2 + 18 ) + 15 = -2 + ( 18 + 15 )
(w + x) × 1 = w + x

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

9. Solve the following equations for x:

-36 = 18 · x x = -2
-
1
9
x = -
1
9
x = 1
-58 + -109x = 51 x = -1
-g = cx x = -g/c

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

26x – 39 < -13 x < 1

x ≠ -212
15 ≥ x ≥ 41

-
30
15
x > -
12
3
x < 2

11. Convert the following numbers into scientific notation:

0.0000000928 9.28 × 10^-8
9700000000 9.7 × 10⁹

12. Add the following polynomials:

13z⁹ + -13 and -9z⁹ + 9z⁶

4z⁹ + 9z⁶ + -13
5z²⁰ + 15z¹⁶ + 13z¹⁴ + -14z¹¹ + -9z⁴ and -1z²⁰ + 5z¹⁴ + 15z⁷ 4z²⁰ + 15z¹⁶ + 18z¹⁴ + -14z¹¹ + 15z⁷ + -9z⁴

13. Multiply the following polynomials and simplify:

(4x⁵ + 6x⁴)(7x⁵ + 10x³)

28x¹⁰ + 42x⁹ + 40x⁸ + 60x⁷
(8x² + 4x)(1x⁵ + 5x² + x)

8x⁷ + 4x⁶ + 40x⁴ + 28x³ + 4x²

14. Divide:

6x² - 8x + 10 / 2x - 4
(3x + 2) with a remainder of 18

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

48, 30, 70
2
33x⁷y³, 77x⁷y⁸, 27xy⁶
xy³

16. Factor the following polynomials:

45x³ + 21x² - 24x
45x(x -
8
15
)(x + 1)
x² + 0x - 36
(x + 6)(x - 6)
x⁵ + 8x⁴ - 20x³
x³(x - 2)(x + 10)

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

x =
-6
and

6
x =
0
,
2

and
-10

18. You have 4 pants, 5 shirts, and 5 shoes. How many different ways can you dress?

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

4, 32, 17, 21, 33, 29, 36, 26, 22

20. A bag contains 3 blue balls, 5 red balls, and 4 white balls.
You pick a ball from the bag and put it in your pocket.
What is the probability of picking:

A white ball?

33.33%

A blue ball or red ball?

66.67%

Two red balls?

15.15%

A blue ball and a white ball?

9.09%

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

x + y = -14
x - y = 6

A(-4,-10)

3x - 4y = 7
10x + 3y = 5

B(0.84,-1.12)

22. Write the following fractions in simplest form:

14x¹⁰y⁴
7x⁷y⁵

2x³
y

x(x - 1)
x⁵ - 6x⁴ + 5x³

1
x²(x - 5)

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

16x + 15 = -x²
x₁ = -15, x₂ = -1

24. Convert the following repeating decimal into a fraction:

x = 0.6
6
9

25. Solve the following equation:

6 -
5x + 10
= -9
x = 43

26. Rationalize the denominator of each fraction below:

49
14
- 6

-
49
14
+ 294
22

27. Use a trigonometric ratio to find x:

x = 15.00 cm

28. The sum of two consecutive odd integers is 36. What are the integers? (Hint: use 2x+1 as the first odd integer)

a=17, b=19

29. After you leave your house, you walk 12 blocks north and 9 blocks west. How far are you from your house?

I am
15
blocks from my house.

30. A rectangle has a width that is 4 m less than its length. The area of the rectangle is 21m². What are the dimensions of the rectangle?

width = 3, length = 7

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