# 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:   -10 and -13? 130

2.   Add:   20 and -15? 5

3.   Divide:   -4 and 4? -1

4.   Substract:   4 and 9? -5

5.   Calculate: |18 + -12 · -19| 246

6.   Simplify the following expressions:
• -9x + 12x + 1x 4x

• 11x + 12x – 5x – 14x 4x

• -4x + 13x – -9x – 9 – -1 -8+18x

• x5 × x-15 x-10

• x-8
x-16
x8

• (6x3)8 1679616x24

7.   Which of the following expressions show the associative property?
• h × ( i + 8 ) = hi + 8i
• 2( 9 + 2 ) = 2×9 + 2×2
• -6x + -10 = -10 + -6x
• ( 5 × 8 ) × 3 = 5 × ( 8 × 3 )
D

8.   Which properties are illustrated by the following three expressions?
• s + t + u + 0 = s + t + u
• ( -18 × -19 ) × 9 = -18 × ( -19 × 9 )
• 12 + j + k = j + k + 12
• Identity property of addition, Associative property of addition and Associative property of multiplication
• Commutative property of multiplication, Identity property of addition and Associative property of multiplication
• Identity property of multiplication, Associative property of multiplication and Associative property of addition
• Identity property of addition, Associative property of multiplication and Commutative property of addition
D

9.   Solve the following equations for x:
• 21 · -x = 63 x = -3

• 30
28
=
5
14
x x = 3

• 180x – -97 = -83 x = -1

• -e + d = -bx x = (e-d)/b

10.   Solve the following inequalities. Then graph a) on the number line
• 33x + 24 ≤ -9 x ≤ -1

• x ≠ 666
• -26 ≥ x < 98
• 18
9
x ≤ -
22
11
x ≤ -1

11.   Convert the following numbers into scientific notation:
• 0.000000912 9.12 × 10-7

• 588000 5.88 × 105

• -1z9 + -6z8 + 7z7 + 8z3 + -8z2  and  -10z9 + 9z8 + 9z5 + -12z1
-11z9 + 3z8 + 7z7 + 9z5 + 8z3 + -8z2 + -12z1

• -2z17 + -9z16 + -3z9 + 5z1 + -9z1  and  -9z12 + -2z2 + -9z1 -2z17 + -9z16 + -9z12 + -3z9 + -2z2 + -13z1

13.   Multiply the following polynomials and simplify:
• (10x4 + x)5x2
50x6 + 5x3

• (10x3 + x2)(2x2 + 10x)
20x5 + 102x4 + 10x3

14.   Divide:
• 25x2 + 45x - 10 / 5x + 10
5x - 1

15.   Find the greatest common factor of the following terms:
• 84, 48, 100
4

• 60xy, 11x5y9
xy

16.   Factor the following polynomials:
• 34x4 - 22x3 + 3x2
34x2(x -
11 +
19
34
)(x -
11 -
19
34
)

• x2 - 4x - 45
(x + 5)(x - 9)

• x5 + 16x4 + 15x3
x3(x + 1)(x + 15)

17.   For question 16, exercises b) and c), solve for x:
• x =
-5
and
9

• x =
0
,
-1

and
-15

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:
• 34, 25, 6, 31, 21, 11, 5, 40, 27

20.   Suppose you toss a coin and spin a spinner numbered 1 through 9
• What is the probability of getting heads and 4?
5.56%

• What is the probability of getting heads and an odd number?
22.22%

• What is the probability of getting heads and a multiple of 3?
16.67%

• What is the probability of getting heads and a prime number?
22.22%

• What is the probability of not tails and not 1?
44.44%

• 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 heads?
50%

21.   Solve and graph the following systems of linear equations:
• x + y = 11
x - y = 16
A(13.5,-2.5)

• 5x - 6y = 19
2x + 3y = -14

B(-1,-4)

22.   Write the following fractions in simplest form:
• 14x10y
7x6y9
2x4
y8

• x3(x - 9)
x3 - 4x2 - 45x
x2
(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.
• -x2 = 13x + 36
x1 = -4,   x2 = -9

24.   Convert the following repeating decimal into a fraction:
• x = 0.5940
5935
9990

25.   Solve the following equation:
• -
x - 4
+ 13 = -19
x = 1028

26.   Rationalize the denominator of each fraction below:
• 21
15
- 15
-
15
+ 15
10

27.   Use a trigonometric ratio to find x:
x = 12.50 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 12 blocks west and 16 blocks north. How far are you from your house?
• I am
20
blocks from my house.

30.   Each side of a square is lengthened by 2 ft. This makes the area of the square 289ft2. What is the original length of a side of the square?
• 15 ft

Name _____________________                                        Date:_____________________

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

Solve the following problems:

Important instructions

1.   Multiply:   -6 and 18? -108

2.   Add:   -18 and -19? -37

3.   Divide:   -11 and 11? -1

4.   Substract:   20 and -20? 40

5.   Calculate: |5 + 14 · 2 + -16| 17

6.   Simplify the following expressions:
• -11x – 6x – -10x -7x

• -14 + -12 – 18y + -2x -26-2x-18y

• 12z + -13y – -13y – -15x – -2 – -12x 2+27x+12z

• y-20 × y7 × x7 x7 × y-13

• x-2
x10
x-12

• (3x)4 81x4

7.   Which of the following expressions show the associative property?
• 9 + 10e + 6
• 3 × 1 = 3
• ( 8 × 6 ) + -9 = -9 + ( 8 × 6 )
• ( m + n ) + p = m + ( n + p )
D

8.   Which properties are illustrated by the following three expressions?
• x × (v + w) = (v + w) × x
• h + ( i + j ) = ( h + i ) + j
• 1 × (i + 16) = i + 16
• Commutative property of multiplication, Associative property of addition and Identity property of multiplication
• Associative property of multiplication, Associative property of addition and Identity property of multiplication
• Distributive property, Associative property of multiplication and Associative property of addition
• Commutative property of addition, Distributive property and Associative property of addition
A

9.   Solve the following equations for x:
• -47 · -x = 94 x = 2

• -
11
3
= -
11
3
x x = 1

• -86 = -62 – 24x x = 1

• -f – a = bx x = (f+a)/(-b)

10.   Solve the following inequalities. Then graph a) on the number line
• -24x – 33 ≤ 15 x ≥ -2

• x ≠ 449
• 73 > x ≥ 23
• -
14
7
x ≤ -20 x ≥ 10

11.   Convert the following numbers into scientific notation:
• 0.000000000873 8.73 × 10-10

• 606000 6.06 × 105

• -11z7 + 6z4 + 12z2 + 15  and  15z3 + -5z2 + -6z1
-11z7 + 6z4 + 15z3 + 7z2 + -6z1 + 15

• -9z18 + 13z15 + 6z14 + -14z7  and  -11z20 + -9z18 + 13z15 + 8z13 + 5z5 -11z20 + -18z18 + 26z15 + 6z14 + 8z13 + -14z7 + 5z5

13.   Multiply the following polynomials and simplify:
• (4x5 + 4x4 + 9x2)(7x4 + 7)
28x9 + 28x8 + 63x6 + 28x5 + 28x4 + 63x2

• (3x5 + 7x4 + 5x)(10x4 + 2x2 + 2)
30x9 + 70x8 + 6x7 + 14x6 + 56x5 + 14x4 + 10x3 + 10x

14.   Divide:
• 8x3 - 8x2 - 24x + 24 / 4x - 4
2x2 - 6

15.   Find the greatest common factor of the following terms:
• 75, 36
3

• 12x6y4, 48x4y3, 39x4y6
3x4y3

16.   Factor the following polynomials:
• 9x3 - 51x2 - 84x
9x(x +
4
3
)(x - 7)

• x2 + 0x - 81
(x - 9)(x + 9)

• x5 - 15x4 + 50x3
x3(x - 10)(x - 5)

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

• x =
0
,
10

and
5

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?
• 32

19.   Use the following data to construct a box and whiskers plot:
• 38, 11, 9, 2, 27, 8, 33, 35, 32

20.   A bag contains 3 blue balls, 4 red balls, and 2 white balls.
You pick a ball from the bag and return it to the bag.
What is the probability of picking:
• A white ball?
22.22%

• A blue ball or red ball?
77.78%

• Two red balls?
19.75%

• A blue ball and a white ball?
7.41%

21.   Solve and graph the following systems of linear equations:
• x + y = 10
x - y = 7
A(8.5,1.5)

• x - 8y = -19
4x + 15y = 18

B(-3,2)

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

• (x + 4)3
(x + 4)6
1
(x + 4)3

23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
• -x2 = -7x - 18
x1 = -2,   x2 = 9

24.   Convert the following repeating decimal into a fraction:
• x = 0.164
163
990

25.   Solve the following equation:
• 7
x
- 13 = 6
x
- 5
x = 64

26.   Rationalize the denominator of each fraction below:
• 10
15
+ 35
-
15
- 35
121

27.   Use a trigonometric ratio to find x:
x = 32.53 cm

28.   The sum of two consecutive even integers is 18. What are the integers? (Hint: use 2x as the first even integer)
a=8, b=10

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

30.   The length of a rectangle is 2 more than twice its width. The area of the rectangle is 60ft2. What is the length and width of the rectangle?
• width = 5,  length = 12

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