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 9? 135

2. Add: 6 and -14? -8

3. Divide: 5 and 5? 1

4. Substract: 13 and 2? 11

5. Calculate: |-14 + 15 · 12 + 9| 175

6. Simplify the following expressions:

-1x – -5x – -14x 18x
3x – 17 – 16x – -10y -17-13x+10y
-4y + 17 + 17z + 2x – 1 16+2x-4y+17z
y³ × y^-15 × y^-9 × y¹⁸ y^-3
x^-7
x³
x^-10
(3x)⁸ 6561x⁸

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

( m × n ) × p = m × ( n × p )
( 5 × -10 ) + 7 = 7 + ( 5 × -10 )
5 × ( x + 4 + 3 ) = 5×x + 5×4 + 5×3
( m + n ) × 9 = 9 × ( m + n )

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

12 + ( 7 + 19 ) = ( 12 + 7 ) + 19
z × ( 16 + -3 ) = z × 16 + z × -3
( -16 × 3 ) × 12 = -16 × ( 3 × 12 )

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

9. Solve the following equations for x:

8 = 2 · x x = 4
15
20
x =
30
20
x = 2
-82 = -37 – 15x x = 3
-dx = f x = -f/d

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

2x – -21 < 19 x < -1

x ≠ 682
68 ≥ x ≥ -33

18
3
x < 12 x < 2

11. Convert the following numbers into scientific notation:

0.0000000341 3.41 × 10^-8
674000 6.74 × 10⁵

12. Add the following polynomials:

2z⁷ + -12z⁶ + 2z³ + 8z² + -3 and -9z⁷ + -7z⁶ + 7z³ + -9z² + -11

-7z⁷ + -19z⁶ + 9z³ + -1z² + -14
-12z⁹ + -4z⁴ + 9z¹ + 5 and 11z⁹ + 1z⁴ + 10z¹ + -8 -1z⁹ + -3z⁴ + 19z¹ + -3

13. Multiply the following polynomials and simplify:

(9x⁵ + 6x³ + 7)(9x⁴ + 9x³ + 9x)

81x⁹ + 81x⁸ + 54x⁷ + 135x⁶ + 117x⁴ + 63x³ + 63x
(2x⁵ + 4x⁴)(6x³ + 2x)

12x⁸ + 24x⁷ + 4x⁶ + 8x⁵

14. Divide:

2x² - 10x + 8 / 2x - 8
x - 1

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

90, 65, 36
1
91x⁶y, 78x⁸y⁹
13x⁶y

16. Factor the following polynomials:

20x⁴ - 50x³ + 31x²
20x²(x -
25 +
5
20
)(x -
25 -
5
20
)
x² + 13x + 42
(x + 6)(x + 7)
x⁸ + x⁷ - 2x⁶
x⁶(x - 1)(x + 2)

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

x =
-6
and

-7
x =
0
,
1

and
-2

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:

33, 8, 30, 5, 36, 39, 24

20. Suppose you toss a coin and spin a spinner numbered 1 through 13

What is the probability of getting heads and 10?

3.85%

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

23.08%

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

23.08%

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

23.08%

What is the probability of not tails and not 2?

46.15%

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 tails?

50%

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

x + y = 15
x - y = -20

A(-2.5,17.5)

3x - 2y = 8
2x + 7y = -19

B(0.72,-2.92)

22. Write the following fractions in simplest form:

9xy⁷
27x³y⁹

1
3x²y²

(x + 5)²
(x + 5)⁶

1
(x + 5)⁴

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

-24x = x² - 52
x₁ = 2, x₂ = -26

24. Convert the following repeating decimal into a fraction:

x = 0.406
406
999

25. Solve the following equation:

-6
x
+ 7 = -4
x
+ 5
x = 1

26. Rationalize the denominator of each fraction below:

3
10
10 +
7

10
10
-
70
31

27. Use a trigonometric ratio to find x:

x = 24.04 cm

28. The sum of two consecutive even integers is 58. What are the integers? (Hint: use 2x as the first even integer)

a=28, b=30

29. After you leave your house, you walk 9 blocks west and 12 blocks south. How far are you from your house?

I am
15
blocks from my house.

30. The length of a rectangle is 2 more than twice its width. The area of the rectangle is 312ft². What is the length and width of the rectangle?

width = 12, length = 26

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