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: 9 and 2? 18

2. Add: 2 and 14? 16

3. Divide: -3 and 3? -1

4. Substract: 14 and -16? 30

5. Calculate: |-2 + -13 · 17 + 8| 215

6. Simplify the following expressions:

-5x – 9 – -11 2-5x
8y – -16x – 6x + 16y 10x+24y
13z + -5y – 16y – -17 – -18y – 1z 17-3y+12z
y⁰ × x^-13 x^-13 × y⁰
x^-14
x¹¹
x^-25
(9x)³ 729x³

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

a + b = b + a
5 + -10 = -10 + 5
( m × n ) × 9 = m × ( n × 9 )
( m × n ) + 6 = 6 + ( m × n )

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

0 + -24 = -24
-11 × -3 + -5 = -5 + -11 × -3
( -5 + 6 ) + 7 = -5 + ( 6 + 7 )

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

9. Solve the following equations for x:

-29 = -x + 50 x = 79
17
7
=
17
7
x x = 1
-74 = -18x – -88 x = 9
d – cx = gx x = d/(c+g)

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

-43x – 32 < 11 x > -1

x ≠ -764
31 > x ≤ -14

12
4
x ≤ -24 x ≤ -8

11. Convert the following numbers into scientific notation:

0.0000000902 9.02 × 10^-8
20800 2.08 × 10⁴

12. Add the following polynomials:

5z¹⁰ + 4z⁹ + -14z⁸ + -1z⁵ + 2z² and 7z¹⁰ + -5z⁹ + -1z⁸ + -13z⁵ + -13z²

12z¹⁰ + -1z⁹ + -15z⁸ + -14z⁵ + -11z²
-10z¹⁹ + -15z¹⁸ + 12z⁷ + -4z⁵ and 10z²⁰ + 9z⁷ + -10z⁵ 10z²⁰ + -10z¹⁹ + -15z¹⁸ + 21z⁷ + -14z⁵

13. Multiply the following polynomials and simplify:

(10x⁵ + 3x² + 10x)(3x⁵ + 7x⁴)

30x¹⁰ + 70x⁹ + 9x⁷ + 51x⁶ + 70x⁵
(9x³ + 4x + 10)(10x⁵ + x⁴ + 2)

90x⁸ + 9x⁷ + 40x⁶ + 104x⁵ + 10x⁴ + 18x³ + 8x + 20

14. Divide:

25x² - 10x - 24 / 5x - 6
5x + 4

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

66, 45
3
60x³y¹⁰, 84x⁶y⁶, 22x³y⁷
2x³y⁶

16. Factor the following polynomials:

30x⁴ - 99x³ + 81x²
30x²(x -
3
2
)(x -
9
5
)
x² + 3x - 54
(x - 6)(x + 9)
x⁸ + 9x⁷ - 22x⁶
x⁶(x + 11)(x - 2)

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

x =
6
and

-9
x =
0
,
-11

and
2

18. You are seating 4 people on 4 chairs. How many different ways can those people sit?

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

10, 35, 28, 8, 40, 19, 4

20. A bag contains 7 blue balls, 3 red balls, and 5 white balls.
You pick a ball from the bag and return it to the bag.
What is the probability of picking:

A white ball?

33.33%

A blue ball or red ball?

66.67%

Two red balls?

4.00%

A blue ball and a white ball?

15.56%

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

x + y = 5
x - y = -6

A(-0.5,5.5)

2x - 10y = -12
12x + 14y = 2

B(-1,1)

22. Write the following fractions in simplest form:

27x⁵y⁸
9x⁷y⁴

3y⁴
x²

(x - 8)⁶
(x - 8)⁷

1
x - 8

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

x² - 6 = -5x
x₁ = 1, x₂ = -6

24. Convert the following repeating decimal into a fraction:

x = 5.492
5438
990

25. Solve the following equation:

-
5x - 10
+ 10 = -5
x = 47

26. Rationalize the denominator of each fraction below:

7
18

7
2
6

27. Use a trigonometric ratio to find x:

x = 19.05 cm

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

a=13, b=15

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

I am
15
blocks from my house.

30. The length of a rectangle is 6 less than 2 times the width. What are the dimensions of the rectangle if the area is 360ft²?

width = 15, length = 24

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