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 19? 76

2. Add: -19 and 15? -4

3. Divide: -4 and 2? -2

4. Substract: 1 and 13? -12

5. Calculate: |-11 + 7 · -10| 81

6. Simplify the following expressions:

13x – -7x – 5 -5+20x
19 – 19x + -18y – -4 23-19x-18y
10y + 1y – -1y + -8x – 1 -1-8x+12y
x^-13 × y^-20 x^-13 × y^-20
x^-16
x^-20
x⁴
(2x⁴)⁵ 32x²⁰

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

a + b = b + a
1( 6 + 9 ) = 1×6 + 1×9
( 5 × 6 ) × 9 = 5 × ( 6 × 9 )
1x + 1 = 1 + 1x

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

13 × (2 + x) = (2 + x) × 13
e + f + 13 = 13 + e + f
43 + 0 = 43

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

9. Solve the following equations for x:

44 – -x = -86 x = -130
3
28
x = -
27
28
x = -9
-41 – 3x = -59 x = 6
fx = d + cx x = d/(f-c)

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

2x + -11 < -25 x < -7

x ≠ -622
53 ≤ x < -56

-
26
13
x ≤
10
5
x ≥ -1

11. Convert the following numbers into scientific notation:

0.00000000829 8.29 × 10^-9
754000000 7.54 × 10⁸

12. Add the following polynomials:

3z⁸ + 7z⁵ + 4z⁴ + -5z² + -6 and 7z⁸ + -12z⁵

10z⁸ + -5z⁵ + 4z⁴ + -5z² + -6
15z¹⁶ + 13z⁷ + -6z⁵ + 6z¹ + -12 and 12z¹⁸ + -12z⁷ + -9z⁵ + -15z¹ + 10 12z¹⁸ + 15z¹⁶ + 1z⁷ + -15z⁵ + -9z¹ + -2

13. Multiply the following polynomials and simplify:

(1x³ - 8)3x⁴

3x⁷ - 24x⁴
(8x³ + 7x)(7x⁴ - 2)

56x⁷ + 49x⁵ - 16x³ - 14x

14. Divide:

8x³ - 8x² + 20x - 20 / 2x - 2
4x² + 10

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

65, 52, 60
1
30x⁷y⁹, 36x⁷y⁸
6x⁷y⁸

16. Factor the following polynomials:

24x⁵ - 95x⁴ - 4x³
24x³(x +
1
24
)(x - 4)
x² + 14x + 48
(x + 8)(x + 6)
x⁶ + 15x⁵ + 56x⁴
x⁴(x + 8)(x + 7)

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

x =
-8
and

-6
x =
0
,
-8

and
-7

18. You can purchase your ice cream in a cup or a cone. Orders can be one, two, three, or four scoops. Flavors can be chocolate, vanilla, strawberry or peach. How many choices do you have?

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

21, 4, 30, 25, 26, 34, 27, 7

20. Suppose you toss a coin and spin a spinner numbered 1 through 9

What is the probability of getting heads and 5?

5.56%

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

22.22%

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

22.22%

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

22.22%

What is the probability of not tails and not 4?

44.44%

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 = 3
x - y = 5

A(4,-1)

x - 9y = -1
2x + 2y = -10

B(-4.6,-0.4)

22. Write the following fractions in simplest form:

22x⁶y⁷z⁴
44x⁷y⁹z²

z²
2xy²

x³ - 7x² + 10x
x⁵(x - 5)

(x - 2)
x⁴

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

20 = x² - x
x₁ = -4, x₂ = 5

24. Convert the following repeating decimal into a fraction:

x = 3.679
3312
900

25. Solve the following equation:

-12
x
+ 12 = -13
x
+ 16
x = 16

26. Rationalize the denominator of each fraction below:

15
2 +
35

-
30 - 15
35
31

27. Use a trigonometric ratio to find x:

x = 32.33 cm

28. The sum of two consecutive odd integers is 48. What are the integers? (Hint: use 2x+1 as the first odd integer)

a=23, b=25

29. After you leave your house, you walk 12 blocks south and 16 blocks east. How far are you from your house?

I am
20
blocks from my house.

30. A rectangle has a length 10 m greater than its width. The area of the rectangle is 200m². What are the length and width of the rectangle?

width = 10, length = 20

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