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 9? 126

2. Add: -8 and 14? 6

3. Divide: -5 and 1? -5

4. Substract: -10 and -4? -6

5. Calculate: |8 · -19 + 10 · 7| 82

6. Simplify the following expressions:

7 + 19x + -20 -13+19x
-7y – -1y – -9x + 1x 10x-6y
12y – 19x – -12y – 8z + 1z -19x+24y-7z
y⁹ × y¹ × x¹⁷ × x⁰ x¹⁷ × y¹⁰
x⁹
x²⁰
x^-11
(10x⁴)¹⁰ 10000000000x⁴⁰

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

r × ( s + 4 ) = rs + 4s
( x × y ) × z = x × ( y × z )
7( 5 + 2 ) = 7×5 + 7×2
0 + 9x = 9x

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

0 + p + 13 = p + 13
-16 × ( 4 × -19 ) = ( -16 × 4 ) × -19
( -1 + -15) × -17 = -1 × -17 + -15 × -17

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

9. Solve the following equations for x:

53 – -x = 8 x = -45
-
9
13
x =
9
13
x = -1
-64 = -17x + -13 x = 3
-gx = d x = -d/g

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

57x + -24 > 33 x > 1

x ≠ 738
39 < x > -1

-
40
10
x ≤
40
2
x ≥ -5

11. Convert the following numbers into scientific notation:

0.0000000284 2.84 × 10^-8
392000 3.92 × 10⁵

12. Add the following polynomials:

-13z⁷ + 9z⁴ + 4z² and 1z⁷ + 9z² + 14

-12z⁷ + 9z⁴ + 13z² + 14
-9z¹⁹ + -10z¹² + -1z¹¹ + 5z⁴ + -12z² and -13z¹⁹ + -9z¹² + -13z¹¹ + 11z² -22z¹⁹ + -19z¹² + -14z¹¹ + 5z⁴ + -1z²

13. Multiply the following polynomials and simplify:

(2x³ + 3)(4x² - 5)

8x⁵ - 10x³ + 12x² - 15
(9x² - 9)(3x⁵ + 5x²)

27x⁷ - 27x⁵ + 45x⁴ - 45x²

14. Divide:

15x³ - 27x² + 20x - 36 / 5x - 9
3x² + 4

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

12, 36, 75
3
27x⁴y⁵, 60x⁴y⁷
3x⁴y⁵

16. Factor the following polynomials:

33x⁵ - 22x⁴ - 11x³
33x³(x +
1
3
)(x - 1)
x² - 12x + 36
(x - 6)(x - 6)
x⁷ + 5x⁶ - 36x⁵
x⁵(x + 9)(x - 4)

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

x =
6
and

6
x =
0
,
-9

and
4

18. How many ways can 6 people wait in line?

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

32, 8, 27, 26, 4, 33, 36, 31

20. Suppose you toss a coin and spin a spinner numbered 1 through 14

What is the probability of getting tails and 10?

3.57%

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

25%

What is the probability of getting heads and a multiple of 4?

10.71%

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

21.43%

What is the probability of not heads and not 13?

46.43%

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 tails?

50%

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

x + y = -10
x - y = -1

A(-5.5,-4.5)

14x - y = -14
5x + 6y = -5

B(-1,0)

22. Write the following fractions in simplest form:

16x¹⁰y⁴
64x⁹y⁷

x
4y³

(x + 4)
(x² + 8x + 16)

1
x + 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 + 6x = 40
x₁ = 4, x₂ = -10

24. Convert the following repeating decimal into a fraction:

x = 0.5184
5133
9900

25. Solve the following equation:

3x + 4
- 12 = 7
x = 119

26. Rationalize the denominator of each fraction below:

2
35
- 6

-2
35
- 12

27. Use a trigonometric ratio to find x:

x = 41.01 cm

28. The sum of two consecutive even integers is 26. What are the integers? (Hint: use 2x as the first even integer)

a=12, b=14

29. After you leave your house, you walk 16 blocks west and 12 blocks south. How far are you from your house?

I am
20
blocks from my house.

30. The length of a rectangle is 8 less than 4 times the width. What are the dimensions of the rectangle if the area is 192m²?

width = 8, length = 24

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