Algebra test generator

Name _____________________ Date:_____________________

current difficulty level: Choose test difficulty: Easy Challenging
(current difficulty level: Easy)

Solve the following problems:

Important instructions

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1. Multiply: -12 and 5? -60

2. Add: 16 and -3? 13

3. Divide: 10 and -5? -2

4. Substract: -6 and 5? -11

5. Calculate: |1 + -1 · -7 + -11| 3

6. Simplify the following expressions:

-8x – 4 + 2 -2-8x
-12x + -6 + 11 – 18x 5-30x
-7x + -10 – -17x – -3y + -12y – 3x -10+7x-9y
y^-1 × y¹⁸ × y⁰ × y^-6 y¹¹
x¹²
x¹¹
x¹
(3x²)⁶ 729x¹²

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

6x + 4 = 4 + 6x
9 × -9 = -9 × 9
6 + 10u + 5
( x + y ) + z = x + ( y + z )

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

d + 15 + 0 = d + 15
( x × y ) × w = x × ( y × w )
u + ( v + w ) = ( u + v ) + w

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

9. Solve the following equations for x:

-67 – -x = 15 x = 82
6
4
= -
1
2
x x = -3
-19x + -3 = -60 x = 3
g = -cx x = -g/c

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

-4x – 1 ≥ -21 x ≤ 5

x ≠ 75
-33 > x ≥ 29

20
2
x <
40
2
x < 2

11. Convert the following numbers into scientific notation:

0.00000593 5.93 × 10^-6
48700 4.87 × 10⁴

12. Add the following polynomials:

-15z¹⁰ + 6z⁹ + 9z⁸ + -9z⁷ + 5z² and -2z⁹ + 4z⁸ + 2z⁷ + 2z³ + 14z²

-15z¹⁰ + 4z⁹ + 13z⁸ + -7z⁷ + 2z³ + 19z²
-13z¹³ + -9z⁷ + -5z² + 7z¹ and -4z¹⁶ + -8z¹³ + 9z⁷ + 11z² + 13z¹ -4z¹⁶ + -21z¹³ + 6z² + 20z¹

13. Multiply the following polynomials and simplify:

(1x⁴ + 9)5x⁵

5x⁹ + 45x⁵
(4x⁵ + 6x²)(7x⁵ + 4x⁴)

28x¹⁰ + 16x⁹ + 42x⁷ + 24x⁶

14. Divide:

20x³ - 36x² - 45x + 81 / 5x - 9
4x² - 9

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

52, 78, 36
2
54x⁶y, 78x⁵y²
6x⁵y

16. Factor the following polynomials:

34x⁵ + 69x⁴ + 27x³
34x³(x +
9
17
)(x +
3
2
)
x² - 8x + 12
(x - 2)(x - 6)
x⁸ + 20x⁷ + 96x⁶
x⁶(x + 12)(x + 8)

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

x =
2
and

6
x =
0
,
-12

and
-8

18. How many ways can 8 people wait in line?

40320

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

18, 25, 5, 17, 29, 14, 13, 32, 22

20. A bag contains 6 blue balls, 5 red balls, and 6 white balls.
You pick a ball from the bag and put it in your pocket.
What is the probability of picking:

A white ball?

35.29%

A blue ball or red ball?

64.71%

Two red balls?

7.35%

A blue ball and a white ball?

13.24%

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

x + y = 8
x - y = 6

A(7,1)

2x - 3y = -19
2x + 6y = 5

B(-5.5,2.67)

22. Write the following fractions in simplest form:

22x⁶y⁷z⁴
44x⁷y⁹z²

z²
2xy²

x⁵(x + 7)
x³ + 14x² + 49x

x⁴
(x + 7)

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

-x = x² - 20
x₁ = -5, x₂ = 4

24. Convert the following repeating decimal into a fraction:

x = 0.1224
1223
9990

25. Solve the following equation:

-
10
x
= -4
x =
100
16

26. Rationalize the denominator of each fraction below:

35
2

35
2
2

27. Use a trigonometric ratio to find x:

x = 15.00 cm

28. The sum of two consecutive odd integers is 32. What are the integers? (Hint: use 2x+1 as the first odd integer)

a=15, b=17

29. After you leave your house, you walk 5 blocks south and 12 blocks west. How far are you from your house?

I am
13
blocks from my house.

30. Each side of a square is lengthened by 6 ft. This makes the area of the square 196ft². What is the original length of a side of the square?

8 ft

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