# Algebra test generator

Name _____________________                                        Date:_____________________

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

Solve the following problems:

Important instructions

1.   Multiply:   -3 and 2? -6

2.   Add:   14 and 20? 34

3.   Divide:   -1 and -1? 1

4.   Substract:   2 and 11? -9

5.   Calculate: |-20 + 18 · -8| 164

6.   Simplify the following expressions:
• 18x – -3x + 20x 41x

• -4 + 4y + 3x + -3x -4+4y

• 9x + 2y – -4 – -3z + -15x 4-6x+2y+3z

• y16 × y0 × y-9 × x1 x1 × y7

• x-1
x-8
x7

• (5x5)6 15625x30

7.   Which of the following expressions show the associative property?
• 6( 7 + 6 ) = 6×7 + 6×6
• ( -1 × 8 ) + -4 = -4 + ( -1 × 8 )
• ( x × y ) × z = x × ( y × z )
• 7 + 5h + 6
C

8.   Which properties are illustrated by the following three expressions?
• c × (a + b) = (a + b) × c
• 37 + 0 = 37
• 1 × (v + w + x) = v + w + x
• Associative property of addition, Associative property of multiplication and Commutative property of addition
• Commutative property of multiplication, Identity property of addition and Identity property of multiplication
• Commutative property of addition, Associative property of multiplication and Identity property of multiplication
C

9.   Solve the following equations for x:
• -x – 72 = -43 x = -29

• 3
11
x =
3
11
x = 1

• 2 = -13 – 15x x = -1

• bx = e x = e/b

10.   Solve the following inequalities. Then graph a) on the number line
• x – -1 < -20 x < -21

• x ≠ -105
• -63 > x > -54
• -
34
17
x ≤ -22 x ≥ 11

11.   Convert the following numbers into scientific notation:
• 0.000000000928 9.28 × 10-10

• 267000000000 2.67 × 1011

• -8z5 + -5z3 + 10z2  and  -9z5 + 12z3 + 8z2 + -11
-17z5 + 7z3 + 18z2 + -11

• 7z17 + 9z7 + 10z5  and  -5z17 + 5z7 + -12z6 + -2z5 2z17 + 14z7 + -12z6 + 8z5

13.   Multiply the following polynomials and simplify:
• (8x2 + 4x + 9)4x4
32x6 + 16x5 + 36x4

• (4x - 1)(9x3 + 9x2)
36x4 + 27x3 - 9x2

14.   Divide:
• 6x2 - 42x + 72 / 3x - 9
2x - 8

15.   Find the greatest common factor of the following terms:
• 55, 22, 75
1

• 90y8, 15x4y4
15y4

16.   Factor the following polynomials:
• 3x3 - 27x2 - 66x
3x(x + 2)(x - 11)

• x2 - 4x - 5
(x + 1)(x - 5)

• x8 - 12x7 - 45x6
x6(x - 15)(x + 3)

17.   For question 16, exercises b) and c), solve for x:
• x =
-1
and
5

• x =
0
,
15

and
-3

18.   How many ways can 3 people wait in line?
• 6

19.   Use the following data to construct a box and whiskers plot:
• 18, 33, 14, 2, 11, 22, 34 20.   A bag contains 6 blue balls, 5 red balls, and 6 white balls.
You pick a ball from the bag and return it to the bag.
What is the probability of picking:
• A white ball?
35.29%

• A blue ball or red ball?
64.71%

• Two red balls?
8.65%

• A blue ball and a white ball?
12.46%

21.   Solve and graph the following systems of linear equations:
• x + y = 14
x - y = -10
A(2,12)

• 10x - 2y = -9
6x + y = -17

B(-1.95,-5.27)

22.   Write the following fractions in simplest form:
• 16x7y7
64x5y7
x2
4

• x4 + 9x3 - 10x2
x(x - 1)
x(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.
• 2x = x2 - 8
x1 = 4,   x2 = -2

24.   Convert the following repeating decimal into a fraction:
• x = 0.30
30
99

25.   Solve the following equation:
• x - 9
- 16 = -16
x = 9

26.   Rationalize the denominator of each fraction below:
• 5
14 +
7
70 - 5
7
189

27.   Use a trigonometric ratio to find x: x = 28.87 cm

28.   The sum of two consecutive odd integers is 52. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=25, b=27

29.   After you leave your house, you walk 6 blocks west and 8 blocks south. How far are you from your house?
• I am
10
blocks from my house.

30.   A rectangle has an area of 54ft2. Its width is 3 ft less than its length. What are the dimensions of the rectangle?
• width = 6,  length = 9

Name _____________________                                        Date:_____________________

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

Solve the following problems:

Important instructions

1.   Multiply:   9 and 15? 135

2.   Add:   -2 and -6? -8

3.   Divide:   16 and -1? -16

4.   Substract:   -16 and -11? -5

5.   Calculate: |18 · -1 + -2 · 13| 44

6.   Simplify the following expressions:
• 2 + -19 – -1x -17+1x

• 17x + -12 – 18y + -12x -12+5x-18y

• 2y – 1z + -9z + 13 – 6y + 8x 13+8x-4y-10z

• y8 × x15 × x-4 x11 × y8

• x-18
x14
x-32

• (2x4)9 512x36

7.   Which of the following expressions show the associative property?
• v × ( w + 2 ) = vw + 2w
• ( 3 + 6 ) + 8 = 3 + ( 6 + 8 )
• 6 + 2 = 2 + 6
• 3 × 1 = 3
B

8.   Which properties are illustrated by the following three expressions?
• x × ( y + 1 ) = x × y + x × 1
• z × (x + y) = (x + y) × z
• p + q + r + 0 = p + q + r
• Commutative property of multiplication, Identity property of multiplication and Associative property of multiplication
• Identity property of multiplication, Commutative property of addition and Associative property of multiplication
• Distributive property, Associative property of multiplication and Commutative property of addition
• Distributive property, Commutative property of multiplication and Identity property of addition
D

9.   Solve the following equations for x:
• 69 = -x + -88 x = -157

• 5
10
= -
1
2
x x = -1

• 2x – 1 = -33 x = -16

• cx = -f – dx x = (-f)/(c+d)

10.   Solve the following inequalities. Then graph a) on the number line
• 2x + 38 ≥ 34 x ≥ -2

• x ≠ -711
• 78 > x ≥ 10
• -
6
3
x ≤
24
3
x ≥ -4

11.   Convert the following numbers into scientific notation:
• 0.000000932 9.32 × 10-7

• 430000000 4.3 × 108

• -3z10 + 8z8 + -1z7 + -11z4 + -8z3  and  -3z8 + 11z4 + -8z3
-3z10 + 5z8 + -1z7 + -16z3

• -2z20 + -14z14 + -1z5 + -4z1  and  -13z20 + 11z14 + -10z2 + 5z1 -15z20 + -3z14 + -1z5 + -10z2 + 1z1

13.   Multiply the following polynomials and simplify:
• 4x(9x5 + 8x4 - 10)
36x6 + 32x5 - 40x

• (2x2 - 5)(2x2 + 6x - 3)
4x4 + 12x3 - 16x2 - 30x + 15

14.   Divide:
• 10x3 + 18x2 + 5x + 9 / 5x + 9
2x2 + 1

15.   Find the greatest common factor of the following terms:
• 66, 80
2

• 70x2y2, 72x7y5
2x2y2

16.   Factor the following polynomials:
• 28x5 + 35x4 - 63x3
28x3(x +
9
4
)(x - 1)

• x2 - 14x + 40
(x - 4)(x - 10)

• x5 + 8x4 - 105x3
x3(x - 7)(x + 15)

17.   For question 16, exercises b) and c), solve for x:
• x =
4
and
10

• x =
0
,
7

and
-15

• 24

19.   Use the following data to construct a box and whiskers plot:
• 17, 36, 23, 24, 34, 26, 35, 7, 14, 6 20.   A bag contains 5 blue balls, 4 red balls, and 5 white balls.
You pick a ball from the bag and return it to the bag.
What is the probability of picking:
• A white ball?
35.71%

• A blue ball or red ball?
64.29%

• Two red balls?
8.16%

• A blue ball and a white ball?
12.76%

21.   Solve and graph the following systems of linear equations:
• x + y = -7
x - y = 9
A(1,-8)

• 14x - 6y = 18
x + y = 17

B(6,11)

22.   Write the following fractions in simplest form:
• 22x6y7z4
44x7y9z2
z2
2xy2

• (x2 + 12x + 36)
(x + 6)
x + 6

23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
• x2 - 66 = 31x
x1 = 33,   x2 = -2

24.   Convert the following repeating decimal into a fraction:
• x = 8.673
7806
900

25.   Solve the following equation:
• -5
x
+ 6 = -7
x
+ 16
x = 25

26.   Rationalize the denominator of each fraction below:
• 10
2
+ 14
-
5
2
- 70
97

27.   Use a trigonometric ratio to find x: x = 17.68 cm

28.   The sum of two consecutive even integers is 30. What are the integers? (Hint: use 2x as the first even integer)
a=14, b=16

29.   After you leave your house, you walk 5 blocks west and 12 blocks south. How far are you from your house?
• I am
13
blocks from my house.

30.   A rectangle has a length 10 ft greater than its width. The area of the rectangle is 264ft2. What are the length and width of the rectangle?
• width = 12,  length = 22

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