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: -4 and 6? -24

2. Add: 10 and 7? 17

3. Divide: 10 and -5? -2

4. Substract: -20 and -17? -3

5. Calculate: |16 + 16 · 7 + 8| 136

6. Simplify the following expressions:

-7 – -8 + 3x 1+3x
9y – -12y – 4x + -6y -4x+15y
7x – 8z – -9x – -6z + 1y 16x+1y-2z
x¹⁵ × y⁸ × y^-13 × y¹⁰ x¹⁵ × y⁵
x^-7
x¹⁰
x^-17
(3x²)⁶ 729x¹²

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

-10 + 1 = 1 + -10
5 × 1 = 5
-7x + -7 = -7 + -7x
( 9 × 2 ) × 7 = 9 × ( 2 × 7 )

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

( -12 × -18 ) × 6 = -12 × ( -18 × 6 )
x + 2 × 10 = 2 × 10 + x
0 + e + f = e + f

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

9. Solve the following equations for x:

-96 = -x – 67 x = 29
3
22
=
3
22
x x = 1
-14 = -3x + -56 x = -14
-d = ex + fx x = (-d)/(e+f)

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

15x – -4 ≤ 34 x ≤ 2

x ≠ -275
81 ≤ x > -37

6
3
x ≤ -
18
3
x ≤ -3

11. Convert the following numbers into scientific notation:

0.0000000000566 5.66 × 10^-11
9530000 9.53 × 10⁶

12. Add the following polynomials:

9z¹⁰ + 14z⁷ + -6z⁴ + -15z³ + -8z² and -9z⁹ + 8z⁷ + -5z⁴ + -2z²

9z¹⁰ + -9z⁹ + 22z⁷ + -11z⁴ + -15z³ + -10z²
12z¹⁵ + 15z⁸ + -13 and -15z¹⁵ + 6z⁸ + -15 -3z¹⁵ + 21z⁸ + -28

13. Multiply the following polynomials and simplify:

(5x³ + 6x² + 4x)(8x³ - 3)

40x⁶ + 48x⁵ + 32x⁴ - 15x³ - 18x² - 12x
(1x² + 2x)(8x³ + 2x)

8x⁵ + 16x⁴ + 2x³ + 4x²

14. Divide:

x² - 3x - 70 / x + 7
x - 10

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

30, 45, 66
3
90x⁸y, 52x⁹y⁶, 72x⁸y³
2x⁸y

16. Factor the following polynomials:

30x⁵ - 12x⁴ - 18x³
30x³(x +
3
5
)(x - 1)
x² - 9x + 14
(x - 7)(x - 2)
x⁴ + 2x³ - 195x²
x²(x - 13)(x + 15)

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

x =
7
and

2
x =
0
,
13

and
-15

18. You have 2 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:

25, 6, 24, 22, 1, 29, 37

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

A white ball?

25.00%

A blue ball or red ball?

75.00%

Two red balls?

17.36%

A blue ball and a white ball?

8.33%

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

x + y = 7
x - y = -2

A(2.5,4.5)

8x - 2y = 18
11x + 4y = 18

B(2,-1)

22. Write the following fractions in simplest form:

22x⁶y⁷z⁴
44x⁷y⁹z²

z²
2xy²

(x + 8)
(x² + 16x + 64)

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 - 34x = -33
x₁ = 1, x₂ = 33

24. Convert the following repeating decimal into a fraction:

x = 0.309
309
999

25. Solve the following equation:

-20 +
x + 1
= -2
x = 323

26. Rationalize the denominator of each fraction below:

4
6 -
10

12 + 2
10
13

27. Use a trigonometric ratio to find x:

x = 24.25 cm

28. The sum of two consecutive odd integers is 24. What are the integers? (Hint: use 2x+1 as the first odd integer)

a=11, b=13

29. After you leave your house, you walk 15 blocks west and 8 blocks north. How far are you from your house?

I am
17
blocks from my house.

30. A rectangle has a length 9 ft greater than its width. The area of the rectangle is 190ft². What are the length and width of the rectangle?

width = 10, length = 19

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