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 -15? 225

2. Add: -17 and 15? -2

3. Divide: -8 and 8? -1

4. Substract: -9 and -13? 4

5. Calculate: |-10 + -4 · 6| 34

6. Simplify the following expressions:

13x + 17x + 6 6+30x
-1x + -2y – -17x – -18x 34x-2y
17x – -2 + 16 + -1y + 11 + -5x 29+12x-1y
x⁴ × x⁰ × x^-19 × y^-17 x^-15 × y^-17
x¹⁹
x¹⁴
x⁵
(10x)⁴ 10000x⁴

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

( x + y ) + z = x + ( y + z )
s × ( t + 2 ) = st + 2t
7( 6 + 3 ) = 7×6 + 7×3
-7x + 1 = 1 + -7x

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

a × ( b × 1 ) = ( a × b ) × 1
(w + x + y) × 1 = w + x + y
y × ( z + 1 ) = y × z + y × 1

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

9. Solve the following equations for x:

82 = -92 – -x x = 174
-
17
6
=
1
6
x x = -17
-93 + 18x = -75 x = 1
-gx = b x = -b/g

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

-x – 3 ≥ -38 x ≤ 35

x ≠ -564
8 < x < -12

34
17
x ≤ -
36
9
x ≤ -2

11. Convert the following numbers into scientific notation:

0.000000000503 5.03 × 10^-10
730000000 7.3 × 10⁸

12. Add the following polynomials:

-10z² + -8z¹ and -15z¹⁰ + 3z⁶ + 6z² + -7z¹

-15z¹⁰ + 3z⁶ + -4z² + -15z¹
-9z⁹ + -9z² + 4z¹ and 10z⁵ + 13z² + 7z¹ -9z⁹ + 10z⁵ + 4z² + 11z¹

13. Multiply the following polynomials and simplify:

(7x⁵ + 9x³)(2x⁵ + 5x³ + 4x²)

14x¹⁰ + 53x⁸ + 28x⁷ + 45x⁶ + 36x⁵
(2x³ + 6x² - 6)(3x⁵ + 6x)

6x⁸ + 18x⁷ - 18x⁵ + 12x⁴ + 36x³ - 36x

14. Divide:

12x² + 51x + 54 / 4x + 9
3x + 6

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

100, 16, 11
1
36x⁵y⁷, 45x⁵y⁹
9x⁵y⁷

16. Factor the following polynomials:

10x⁵ + 20x⁴ - 30x³
10x³(x - 1)(x + 3)
x² + 2x - 48
(x - 6)(x + 8)
x⁵ + 9x⁴ - 52x³
x³(x - 4)(x + 13)

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

x =
6
and

-8
x =
0
,
4

and
-13

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:

9, 13, 22, 26, 12, 35, 2, 36, 34, 7

20. Suppose you toss a coin and spin a spinner numbered 1 through 7

What is the probability of getting tails and 1?

7.14%

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

21.43%

What is the probability of getting heads and a multiple of 2?

21.43%

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

28.57%

What is the probability of not heads and not 5?

42.86%

What is the probability of getting not tails 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 = 18
x - y = 9

A(13.5,4.5)

8x - 9y = -18
2x + 6y = 14

B(0.27,2.24)

22. Write the following fractions in simplest form:

22x⁶y⁷z⁴
44x⁷y⁹z²

z²
2xy²

(x² - 18x + 81)
(x - 9)

x - 9

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

x² + 36 = -12x
x₁ = -6, x₂ = -6

24. Convert the following repeating decimal into a fraction:

x = 8.561
8476
990

25. Solve the following equation:

7
x
+ 10 = 8
x
+ 5
x = 25

26. Rationalize the denominator of each fraction below:

15
7
- 5

-
5
7
+ 25
6

27. Use a trigonometric ratio to find x:

x = 35.36 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 4 blocks west and 3 blocks north. How far are you from your house?

I am
5
blocks from my house.

30. The length of a rectangle is 2 less than 2 times the width. What are the dimensions of the rectangle if the area is 84m²?

width = 7, length = 12

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