# Algebra test generator

Name _____________________                                        Date:_____________________

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

Solve the following problems:

Important instructions

1.   Multiply:   6 and -37? -222

2.   Add:   -57 and -15? -72

3.   Divide:   -71 and -1? 71

4.   Substract:   74 and -53? 127

5.   Calculate: |89 · -81 + -52 · -3| 7053

6.   Simplify the following expressions:
• -82x – -29x – 93x -146x

• 23x + 84x – 72 + -7 -79+107x

• 84y – -34 – -69z + -42y – 8 26+42y+69z

• x-58 × y14 × y35 x-58 × y49

• x15
x13
x2

• (9x)3 729x3

7.   Which of the following expressions show the associative property?
• ( x × y ) + 9 = 9 + ( y × x )
• 10 × ( x + 4 + 3 ) = 10×x + 10×4 + 10×3
• ( x × y ) × z = x × ( y × z )
• k × ( l + 6 ) = kl + 6l
C

8.   Which properties are illustrated by the following three expressions?
• x + y + z + 0 = x + y + z
• ( z + 0 ) × y = z × y + 0 × y
• e + ( f + g ) = ( e + f ) + g
• Distributive property, Identity property of multiplication and Identity property of addition
• Commutative property of multiplication, Commutative property of addition and Identity property of multiplication
• Identity property of addition, Distributive property and Associative property of addition
D

9.   Solve the following equations for x:
• -13 + x = 9 x = 22

• 5
14
x = -
25
14
x = -5

• -151x + -53 = 98 x = -1

• e = ax x = e/a

10.   Solve the following inequalities. Then graph a) on the number line
• 2x – 14 ≥ -22 x ≥ -4

• x ≠ 570
• 28 ≤ x > -35
• -5x ≤
35
7
x ≥ -1

11.   Convert the following numbers into scientific notation:
• 0.0000000612 6.12 × 10-8

• 5850000000 5.85 × 109

• 17z10 + -11z7 + -18z5  and  20z10 + -17z9
37z10 + -17z9 + -11z7 + -18z5

• -50z12 + -7z8 + -39z5 + -37z3 + -33  and  -26z17 + -50z3 + 48z1 -26z17 + -50z12 + -7z8 + -39z5 + -87z3 + 48z1 + -33

13.   Multiply the following polynomials and simplify:
• (1x5 + 9x3)(5x4 + 2)
5x9 + 45x7 + 2x5 + 18x3

• (4x4 - 10)(1x - 8)
4x5 - 32x4 - 10x + 80

14.   Divide:
• 4x3 - 2x2 + 18x - 9 / 2x - 1
2x2 + 9

15.   Find the greatest common factor of the following terms:
• 234, 390, 264
6

• 225x4, 210y2, 486x3y4
3

16.   Factor the following polynomials:
• 12x3 + 5x2 - 3x
12x(x -
1
3
)(x +
3
4
)

• x2 - 2x - 15
(x + 3)(x - 5)

• x5 - 20x4 + 99x3
x3(x - 9)(x - 11)

17.   For question 16, exercises b) and c), solve for x:
• x =
-3
and
5

• x =
0
,
9

and
11

18.   You have 6 CDs. How many different ways can you listen to them?
• 720

19.   Use the following data to construct a box and whiskers plot:
• 10, 15, 11, 20, 7, 18, 12

20.   Suppose you toss a coin and spin a spinner numbered 1 through 20
• What is the probability of getting tails and 4?
2.50%

• What is the probability of getting heads and an even number?
25%

• What is the probability of getting heads and a multiple of 10?
5%

• What is the probability of getting tails and a prime number?
20%

• What is the probability of not heads and not 15?
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 = 7
x - y = 8
A(7.5,-0.5)

• 6x - 2y = -9
3x + 3y = -3

B(-1.38,0.38)

22.   Write the following fractions in simplest form:
• 6x9y10
2x6y8
3x3y2

• (x + 10)
(x + 10)2
1
x + 10

23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
• -16x + 60 = -x2
x1 = 10,   x2 = 6

24.   Convert the following repeating decimal into a fraction:
• x = 0.783
783
999

25.   Solve the following equation:
• 14
x
= 9
x =
196
81

26.   Rationalize the denominator of each fraction below:
• 3
21 +
14
63 - 3
14
427

27.   Use a trigonometric ratio to find x:
x = 31.18 cm

28.   The sum of two consecutive odd integers is 28. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=13, b=15

29.   After you leave your house, you walk 9 blocks south and 12 blocks east. How far are you from your house?
• I am
15
blocks from my house.

30.   The length of a rectangle is 8 less than 2 times the width. What are the dimensions of the rectangle if the area is 234m2?
• width = 13,  length = 18

Name _____________________                                        Date:_____________________

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

Solve the following problems:

Important instructions

1.   Multiply:   -7 and -28? 196

2.   Add:   47 and -25? 22

3.   Divide:   15 and -1? -15

4.   Substract:   53 and 52? 1

5.   Calculate: |59 · -19 + 41 · -96| 5057

6.   Simplify the following expressions:
• -5x – 15x + -81x -101x

• -20y – 60y – 32x + -33 -33-32x-80y

• 54y + -83z – 42z – -80z – 11y 43y-45z

• x-19 × y29 x-19 × y29

• x68
x71
x-3

• (7x)9 40353607x9

7.   Which of the following expressions show the associative property?
• -1 + 2 = 2 + -1
• 9 + 4h + 7
• ( x × y ) + 9 = 9 + ( y × x )
• ( m × n ) × 9 = m × ( n × 9 )
D

8.   Which properties are illustrated by the following three expressions?
• y × ( z + 1 ) = y × z + y × 1
• 14 × (6 + x) = (6 + x) × 14
• 0 + u + 9 = u + 9
• Distributive property, Commutative property of multiplication and Identity property of addition
• Associative property of multiplication, Distributive property and Identity property of multiplication
• Commutative property of multiplication, Associative property of addition and Commutative property of addition
• Distributive property, Commutative property of multiplication and Associative property of multiplication
A

9.   Solve the following equations for x:
• -48 = -x · -6 x = -8

• -
1
2
x = -
15
30
x = 1

• -27 = -15x – -3 x = 2

• f = -ex x = -f/e

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