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: -18 and -18? 324

2. Add: 7 and 2? 9

3. Divide: 11 and 1? 11

4. Substract: -1 and 18? -19

5. Calculate: |8 · 15 + 10| 130

6. Simplify the following expressions:

5x – 17x – 17 -17-12x
7x + 5y + -19x – 6y -12x-1y
15 – -20x – 10x + -19x + 9z 15-9x+9z
x^-18 × x^-4 × x^-18 × x⁸ x^-32
x^-3
x¹³
x^-16
(2x²)⁸ 256x¹⁶

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

( x + y ) × 2 = 2 × ( y + x )
a + b = b + a
( m × n ) + 6 = 6 + ( m × n )
( m + n ) + 2 = m + ( n + 2 )

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

67 + 53 = 67 + 53
(t + u) × 1 = t + u
(z + -4) × (y + -3) = (y + -3) × (z + -4)

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

9. Solve the following equations for x:

12 + x = -2 x = -14
23
25
=
23
25
x x = 1
-60 = 28x + 52 x = -4
-f = bx – c x = (-f+c)/b

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

-19x + -39 ≥ 37 x ≤ -4

x ≠ 587
53 > x < -97

26
13
x ≤ -
30
5
x ≤ -3

11. Convert the following numbers into scientific notation:

0.000787 7.87 × 10^-4
48700000000 4.87 × 10¹⁰

12. Add the following polynomials:

-3z¹⁰ + -15z⁹ + 13z⁸ + 9z⁶ + 3z⁴ and -10z⁶ + -12z⁴

-3z¹⁰ + -15z⁹ + 13z⁸ + -1z⁶ + -9z⁴
3z¹⁰ + 1z⁷ + 10z⁶ + -8z⁵ + -6z⁵ and -13z¹⁹ + 8z¹¹ + 10z⁷ + -12z⁵ + -6z⁴ -13z¹⁹ + 8z¹¹ + 3z¹⁰ + 11z⁷ + 10z⁶ + -26z⁵ + -6z⁴

13. Multiply the following polynomials and simplify:

(5x⁵ + 6x⁴ - 6)(9x⁴ + x)

45x⁹ + 54x⁸ + 5x⁶ + 6x⁵ - 54x⁴ - 6x
(1x⁴ + 9)(9x⁵ + 8x³ - 9)

9x⁹ + 8x⁷ + 81x⁵ - 9x⁴ + 72x³ - 81

14. Divide:

16x² - 4x - 56 / 4x + 7
4x - 8

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

56, 28
28
90x⁹y⁵, 72x³y², 75x²y⁷
3x²y²

16. Factor the following polynomials:

3x³ + 65x² - 22x
3x(x -
1
3
)(x + 22)
x² + 10x + 21
(x + 3)(x + 7)
x⁸ - 4x⁷ - 96x⁶
x⁶(x + 8)(x - 12)

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

x =
-3
and

-7
x =
0
,
-8

and
12

18. You are seating 8 people on 8 chairs. How many different ways can those people sit?

40320

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

10, 38, 40, 9, 11, 31, 2, 17, 27, 35

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

What is the probability of getting heads and 11?

2.50%

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

25%

What is the probability of getting tails and a multiple of 5?

10%

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

20%

What is the probability of not tails and not 7?

47.5%

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 = 15
x - y = 14

A(14.5,0.5)

3x - 10y = -9
10x + 3y = -4

B(-0.61,0.72)

22. Write the following fractions in simplest form:

23x⁴y⁸
46x⁸y⁴

y⁴
2x⁴

(x² - 14x + 49)
(x - 7)

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.

x² + 41x = -78
x₁ = -2, x₂ = -39

24. Convert the following repeating decimal into a fraction:

x = 0.31
28
90

25. Solve the following equation:

13 -
3x - 2
= -6
x = 121

26. Rationalize the denominator of each fraction below:

3
2
- 10

-
3
2
+ 30
98

27. Use a trigonometric ratio to find x:

x = 36.37 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 6 blocks south and 8 blocks east. How far are you from your house?

I am
10
blocks from my house.

30. A rectangle has a width that is 2 m less than its length. The area of the rectangle is 224m². What are the dimensions of the rectangle?

width = 14, length = 16

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