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: -15 and 19? -285

2. Add: -15 and 2? -13

3. Divide: 12 and -6? -2

4. Substract: -18 and -14? -4

5. Calculate: |15 + -16 · 17 + 1| 256

6. Simplify the following expressions:

16x + 19 – 11 8+16x
-13y – -9x + 15 – -10y 15+9x-3y
3 – 10x + -4y + 19y – -8x + -19y 3-2x-4y
y¹⁷ × x^-20 × x⁷ x^-13 × y¹⁷
x¹²
x¹³
x^-1
(6x⁴)⁸ 1679616x³²

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

8( 2 + 6 ) = 8×2 + 8×6
4 + 9f + 2
-9 × 1 = -9
( m × n ) × 3 = m × ( n × 3 )

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

j × ( k × 1 ) = ( j × k ) × 1
( b + c ) + a = b + ( c + a )
11 + v + w = v + w + 11

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

9. Solve the following equations for x:

68 = -37 + -x x = -105
-
25
21
x =
25
21
x = -1
31 = -2x – -35 x = 2
b = cx + a x = (b-a)/c

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

-x + 35 ≤ -1 x ≥ 36

x ≠ -766
33 > x ≤ 41

-
38
19
x <
20
10
x > -1

11. Convert the following numbers into scientific notation:

0.0000744 7.44 × 10^-5
74600000 7.46 × 10⁷

12. Add the following polynomials:

12z⁸ + -6 and 12z⁸ + 8z⁷ + -15z⁶ + 10z² + -3

24z⁸ + 8z⁷ + -15z⁶ + 10z² + -9
-13z¹⁸ + 3z⁷ + -1z⁵ + -9z² and 1z¹⁹ + -4z¹⁸ + -6z⁷ + -15z⁵ + 5z² 1z¹⁹ + -17z¹⁸ + -3z⁷ + -16z⁵ + -4z²

13. Multiply the following polynomials and simplify:

8x⁴(5x³ + 4x²)

40x⁷ + 32x⁶
(5x⁴ + 8x³ - 4)(4x⁴ + 8x³ - 8)

20x⁸ + 72x⁷ + 64x⁶ - 56x⁴ - 96x³ + 32

14. Divide:

5x³ + 40x² + 10x + 106 / x + 8
(5x² + 10) with a remainder of 26

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

45, 26, 70
1
70x⁶y⁹, 72x²y¹⁰
2x²y⁹

16. Factor the following polynomials:

12x³ - 1x² - 6x
12x(x -
3
4
)(x +
2
3
)
x² + 11x + 28
(x + 7)(x + 4)
x⁴ - 2x³ - 24x²
x²(x - 6)(x + 4)

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

x =
-7
and

-4
x =
0
,
6

and
-4

18. You have 3 books to read. How many different ways can you read your books?

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

24, 5, 6, 18, 23, 13, 40

20. A bag contains 7 blue balls, 7 red balls, and 7 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?

10.00%

A blue ball and a white ball?

11.67%

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

x + y = 16
x - y = 17

A(16.5,-0.5)

7x - y = 18
6x + 10y = -6

B(2.29,-1.97)

22. Write the following fractions in simplest form:

22x⁶y⁷z⁴
44x⁷y⁹z²

z²
2xy²

(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 - 55 = 6x
x₁ = 11, x₂ = -5

24. Convert the following repeating decimal into a fraction:

x = 0.2466
2464
9990

25. Solve the following equation:

-1
x
+ 1 = 3
x
- 15
x = 16

26. Rationalize the denominator of each fraction below:

10
12
15
9

4
3
9

27. Use a trigonometric ratio to find x:

x = 28.00 cm

28. The sum of two consecutive even integers is 50. What are the integers? (Hint: use 2x as the first even integer)

a=24, b=26

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

I am
5
blocks from my house.

30. A rectangle has an area of 400ft². Its width is 9 ft less than its length. What are the dimensions of the rectangle?

width = 16, length = 25

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