# 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:   -70 and 46? -3220

2.   Add:   -61 and -90? -151

3.   Divide:   -18 and -1? 18

4.   Substract:   -39 and -15? -24

5.   Calculate: |4 + -68 · -91 + 15| 6207

6.   Simplify the following expressions:
• -59x – -71 – 66 5-59x

• -11y + 42 – 70 – 93x -28-93x-11y

• 5 – 82x + 42y + 7z – 35 – -2 -28-82x+42y+7z

• y-35 × x-96 × y-66 × x-4 x-100 × y-101

• x21
x-90
x111

• (4x)7 16384x7

7.   Which of the following expressions show the associative property?
• 4x + 10 = 10 + 4x
• ( 6 × -5 ) + 10 = 10 + ( 6 × -5 )
• 3( 4 + 7 ) = 3×4 + 3×7
• ( m × n ) × 8 = m × ( n × 8 )
D

8.   Which properties are illustrated by the following three expressions?
• (a + b + c) × 1 = a + b + c
• 16 × -14 = 16 × -14
• ( 20 × 2 ) × 19 = 20 × ( 2 × 19 )
• Identity property of multiplication, Commutative property of multiplication and Associative property of multiplication
• Identity property of addition, Identity property of multiplication and Associative property of addition
• Distributive property, Commutative property of addition and Associative property of multiplication
• Associative property of addition, Commutative property of multiplication and Associative property of multiplication
A

9.   Solve the following equations for x:
• 70 + -x = -65 x = 135

• -
21
17
=
1
17
x x = -21

• 84 = -13x + 71 x = -1

• dx = c – ex x = c/(d+e)

10.   Solve the following inequalities. Then graph a) on the number line
• -15x + -25 ≤ 35 x ≥ -4

• x ≠ -237
• 26 ≥ x > 21
• -
8
4
x > -
16
2
x < 4

11.   Convert the following numbers into scientific notation:
• 0.0000000000930 9.3 × 10-11

• 646000 6.46 × 105

• -5z10 + 13z8 + 2z6 + 18z5 + 19z3  and  -13z10 + -9z6 + 9z3
-18z10 + 13z8 + -7z6 + 18z5 + 28z3

• 49z10 + -9z9 + -50z7 + 13z2  and  30z9 + -10z7 + -13z2 49z10 + 21z9 + -60z7

13.   Multiply the following polynomials and simplify:
• (4x4 + 5x2 + 7x)(9x5 + 3x3)
36x9 + 57x7 + 63x6 + 15x5 + 21x4

• (6x4 + 7x)(5x3 + 9x2 + 6)
30x7 + 54x6 + 71x4 + 63x3 + 42x

14.   Divide:
• 10x2 - 45x + 35 / 5x - 5
2x - 7

15.   Find the greatest common factor of the following terms:
• 78, 180, 60
6

• 147xy7, 300y2
3y2

16.   Factor the following polynomials:
• 6x3 - 14x2 + 6x
6x(x -
7 +
13
6
)(x -
7 -
13
6
)

• x2 + 8x + 7
(x + 7)(x + 1)

• x5 - 19x4 + 70x3
x3(x - 5)(x - 14)

17.   For question 16, exercises b) and c), solve for x:
• x =
-7
and
-1

• x =
0
,
5

and
14

18.   You can purchase your ice cream in a cup or a cone. Orders can be one or two scoops. Flavors can be chocolate, vanilla, strawberry, peach or kiwi. How many choices do you have?
• 20

19.   Use the following data to construct a box and whiskers plot:
• 16, 10, 25, 7, 22, 26, 27, 31, 20

20.   A bag contains 6 blue balls, 4 red balls, and 4 white balls.
You pick a ball from the bag and put it in your pocket.
What is the probability of picking:
• A white ball?
28.57%

• A blue ball or red ball?
71.43%

• Two red balls?
6.59%

• A blue ball and a white ball?
13.19%

21.   Solve and graph the following systems of linear equations:
• x + y = -20
x - y = -15
A(-17.5,-2.5)

• 5x - 9y = 17
6x + y = -6

B(-0.63,-2.24)

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

• (x + 5)
(x2 + 10x + 25)
1
x + 5

23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
• 14 = x2 + 5x
x1 = -7,   x2 = 2

24.   Convert the following repeating decimal into a fraction:
• x = 0.5
5
9

25.   Solve the following equation:
• 13
x
= 4
x =
169
16

26.   Rationalize the denominator of each fraction below:
• 10
6
5 +
2
50
6
- 20
3
23

27.   Use a trigonometric ratio to find x:
x = 15.59 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 12 blocks south and 5 blocks east. How far are you from your house?
• I am
13
blocks from my house.

30.   The sides of a square are increased by 6 ft. The area of the newly created square is 361ft2. What was the original length of one side of the square?
• 13 ft

Name _____________________                                        Date:_____________________

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

Solve the following problems:

Important instructions

1.   Multiply:   -20 and 4? -80

2.   Add:   -39 and -38? -77

3.   Divide:   88 and -22? -4

4.   Substract:   -27 and 99? -126

5.   Calculate: |83 · 3 + -48| 201

6.   Simplify the following expressions:
• 70x + -72x – -74 74-2x

• -96x – 68y – -62y – 71x -167x-6y

• -2y + 77y – 49 – 19x + 57x + 24 -25+38x+75y

• x-17 × y-87 × y-92 x-17 × y-179

• x-96
x44
x-140

• (10x)4 10000x4

7.   Which of the following expressions show the associative property?
• ( 9 × 6 ) × 4 = 9 × ( 6 × 4 )
• a + b = b + a
• ( x × y ) + 6 = 6 + ( y × x )
• -4 + -10 = -10 + -4
A

8.   Which properties are illustrated by the following three expressions?
• (h + i) × 2 = 2 × (h + i)
• 0 + e + 4 = e + 4
• a × ( b × 1 ) = ( a × b ) × 1
• Commutative property of multiplication, Associative property of multiplication and Identity property of multiplication
• Commutative property of multiplication, Identity property of addition and Associative property of multiplication
• Commutative property of addition, Commutative property of multiplication and Identity property of addition
• Associative property of addition, Associative property of multiplication and Identity property of multiplication
B

9.   Solve the following equations for x:
• 10 = x · 10 x = 1

• -
8
17
= -
2
17
x x = 4

• 89 + -29x = 60 x = 1

• cx = -a x = -a/c

10.   Solve the following inequalities. Then graph a) on the number line
• -x + -24 < 29 x > -53

• x ≠ -449
• -83 ≤ x ≤ 41
• -5x > 10 x < -2

11.   Convert the following numbers into scientific notation:
• 0.0000000000214 2.14 × 10-11

• 92600000000 9.26 × 1010

• 10z8 + -14z5 + 3z3 + 2z1  and  4z9 + -13z8 + 16z5 + -10z3 + 11z1
4z9 + -3z8 + 2z5 + -7z3 + 13z1

• 2z13 + 18z8 + 47z4 + 29  and  40z8 + -43z6 + -40z4 + -4z1 + 1 2z13 + 58z8 + -43z6 + 7z4 + -4z1 + 30

13.   Multiply the following polynomials and simplify:
• (5x4 + 3)3x4
15x8 + 9x4

• (9x4 + 7)(4x4 + x)
36x8 + 9x5 + 28x4 + 7x

14.   Divide:
• 20x2 - 45x + 25 / 4x - 5
5x - 5

15.   Find the greatest common factor of the following terms:
• 200, 390
10

• 468x2y8, 264x6y2, 252x5y3
12x2y2

16.   Factor the following polynomials:
• 21x5 - 21x4 - 42x3
21x3(x + 1)(x - 2)

• x2 - 6x - 27
(x + 3)(x - 9)

• x4 - 10x3 - 75x2
x2(x - 15)(x + 5)

17.   For question 16, exercises b) and c), solve for x:
• x =
-3
and
9

• x =
0
,
15

and
-5

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:
• 20, 25, 39, 21, 14, 11, 2

20.   A bag contains 2 blue balls, 6 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?
38.46%

• A blue ball or red ball?
61.54%

• Two red balls?
21.30%

• A blue ball and a white ball?
5.92%

21.   Solve and graph the following systems of linear equations:
• x + y = -11
x - y = -10
A(-10.5,-0.5)

• 6x - 3y = 14
6x + 7y = 16

B(2.43,0.2)

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

• (x - 1)6
(x - 1)
(x - 1)5

23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
• 4x - 60 = -x2
x1 = -10,   x2 = 6

24.   Convert the following repeating decimal into a fraction:
• x = 0.35
35
99

25.   Solve the following equation:
• 4
x
= 8
x =
16
64

26.   Rationalize the denominator of each fraction below:
• 15
27
5
3
3

27.   Use a trigonometric ratio to find x:
x = 13.28 cm

28.   The sum of two consecutive even integers is 54. What are the integers? (Hint: use 2x as the first even integer)
a=26, b=28

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

30.   The length of a rectangle is 10 less than 2 times the width. What are the dimensions of the rectangle if the area is 252ft2?
• width = 14,  length = 18

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