# 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:   45 and 75? 3375

2.   Add:   -83 and 71? -12

3.   Divide:   38 and -1? -38

4.   Substract:   41 and -96? 137

5.   Calculate: |96 · -74 + 25 · 64| 5504

6.   Simplify the following expressions:
• 91x – -7x + 65x 163x

• -28x – -86x + -80y – -90 90+58x-80y

• 71z + 50x – 26x – -22x + -74y – 30z 46x-74y+41z

• y92 × y32 × x-65 x-65 × y124

• x-6
x62
x-68

• (5x)5 3125x5

7.   Which of the following expressions show the associative property?
• ( m + n ) + p = m + ( n + p )
• ( x + y ) × 3 = 3 × ( y + x )
• ( -5 × -9 ) + 8 = 8 + ( -5 × -9 )
• 0 + 5x = 5x
A

8.   Which properties are illustrated by the following three expressions?
• 1 × (s + t + u) = s + t + u
• 15 + 4y = 4y + 15
• 0 + 28 = 28
• Associative property of multiplication, Identity property of addition and Associative property of addition
• Identity property of addition, Distributive property and Associative property of multiplication
• Associative property of addition, Identity property of multiplication and Commutative property of addition
• Identity property of multiplication, Commutative property of addition and Identity property of addition
D

9.   Solve the following equations for x:
• -96 = -6 – x x = 90

• 2
14
=
2
14
x x = 1

• 71 = 48 + 23x x = 1

• -c – bx = d x = (c+d)/(-b)

10.   Solve the following inequalities. Then graph a) on the number line
• 2x – -4 ≥ 18 x ≥ 7

• x ≠ -644
• -80 > x ≥ 61
• -2x ≤
14
7
x ≥ -1

11.   Convert the following numbers into scientific notation:
• 0.000000000452 4.52 × 10-10

• 6600000 6.6 × 106

• 8z10 + -6z8 + 7z3 + 9z2 + 20z1  and  -12z10 + -3z8 + -3z3 + 19z1
-4z10 + -9z8 + 4z3 + 9z2 + 39z1

• -22z15 + -4z8 + -42z6 + 26z1  and  35z15 + 9z12 + 27z5 + 25z1 13z15 + 9z12 + -4z8 + -42z6 + 27z5 + 51z1

13.   Multiply the following polynomials and simplify:
• (5x2 + 9x)(10x5 + 7x3)
50x7 + 90x6 + 35x5 + 63x4

• (3x5 + 4x4)(10x4 + 2x2 + 6)
30x9 + 40x8 + 6x7 + 8x6 + 18x5 + 24x4

14.   Divide:
• 5x3 + 45x2 - 3x - 27 / x + 9
5x2 - 3

15.   Find the greatest common factor of the following terms:
• 90, 260
10

• 160xy5, 60x6y8
20xy5

16.   Factor the following polynomials:
• 22x4 + 22x3 - 44x2
22x2(x + 2)(x - 1)

• x2 + 18x + 80
(x + 8)(x + 10)

• x9 + 20x8 + 84x7
x7(x + 6)(x + 14)

17.   For question 16, exercises b) and c), solve for x:
• x =
-8
and
-10

• x =
0
,
-6

and
-14

18.   You have 4 pants, 2 shirts, and 2 shoes. How many different ways can you dress?
• 16

19.   Use the following data to construct a box and whiskers plot:
• 1, 5, 21, 27, 2, 14, 20, 6, 36 20.   A bag contains 6 blue balls, 2 red balls, and 7 white balls.
You pick a ball from the bag and return it to the bag.
What is the probability of picking:
• A white ball?
46.67%

• A blue ball or red ball?
53.33%

• Two red balls?
1.78%

• A blue ball and a white ball?
18.67%

21.   Solve and graph the following systems of linear equations:
• x + y = 3
x - y = 20
A(11.5,-8.5)

• 10x - 2y = 20
12x + 3y = -3

B(1,-5)

22.   Write the following fractions in simplest form:
• 22x8y7
88x8y6
y
4

• (x - 3)6
(x - 3)
(x - 3)5

23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
• -39 = x2 - 16x
x1 = 13,   x2 = 3

24.   Convert the following repeating decimal into a fraction:
• x = 0.7
7
9

25.   Solve the following equation:
• -
15
x
= -3
x = 25

26.   Rationalize the denominator of each fraction below:
• 9
4
9
2

27.   Use a trigonometric ratio to find x: x = 23.00 cm

28.   The sum of two consecutive even integers is 50. What are the integers? (Hint: use 2x as the first even integer)
a=24, b=26

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

30.   Each side of a square is decreased by 10 ft. The area of the newly created square is 16ft2. What was the original length of one side of the square?
• 14 ft

Name _____________________                                        Date:_____________________

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

Solve the following problems:

Important instructions

1.   Multiply:   61 and 57? 3477

2.   Add:   -80 and -11? -91

3.   Divide:   88 and -44? -2

4.   Substract:   79 and -39? 118

5.   Calculate: |2 – -38 – 85| 45

6.   Simplify the following expressions:
• -27x + -9x + -45 -45-36x

• 48y + 20x – -34y + -17y 20x+65y

• -5x – -55x – -36 – 76y + 46 – -13z 82+50x-76y+13z

• x83 × x11 × y61 × y-63 x94 × y-2

• x-27
x-40
x13

• (4x2)3 64x6

7.   Which of the following expressions show the associative property?
• 0 + -4x = -4x
• ( 2 × 8 ) × 3 = 2 × ( 8 × 3 )
• -8 × ( y + 9 + 5 ) = -8×y + -8×9 + -8×5
• -4 + 9 = 9 + -4
B

8.   Which properties are illustrated by the following three expressions?
• x × ( -1 + 8 ) = x × -1 + x × 8
• -2 + 11 × 18 = 11 × 18 + -2
• ( c + 0 ) + b = c + ( 0 + b )
• Commutative property of multiplication, Identity property of addition and Associative property of multiplication
• Distributive property, Commutative property of addition and Associative property of addition
• Associative property of addition, Identity property of addition and Identity property of multiplication
• Identity property of multiplication, Commutative property of multiplication and Identity property of addition
B

9.   Solve the following equations for x:
• -x – 76 = -45 x = -31

• -
1
9
x = -
7
9
x = 7

• -40 = -2x + 54 x = 47

• -dx – c = -f x = (-c+f)/d

10.   Solve the following inequalities. Then graph a) on the number line
• -2x + 38 ≥ -4 x ≤ 21

• x ≠ -283
• -30 ≤ x ≤ -73
• 20
10
x ≤
20
5
x ≤ 2

11.   Convert the following numbers into scientific notation:
• 0.0000000687 6.87 × 10-8

• 6340000 6.34 × 106

• -7z6 + 17z1  and  -4z10 + -13z7 + 13z6 + -4z4 + 13z1
-4z10 + -13z7 + 6z6 + -4z4 + 30z1

• -3z19 + 7z8 + 43z6 + -36z5  and  15z19 + -13z11 + -34z8 + 3z6 + 23z5 12z19 + -13z11 + -27z8 + 46z6 + -13z5

13.   Multiply the following polynomials and simplify:
• 6(8x3 - 5)
48x3 - 30

• (2x4 - 5)(3x4 + 5x2 + 4x)
6x8 + 10x6 + 8x5 - 15x4 - 25x2 - 20x

14.   Divide:
• 20x3 - 25x2 + 8x + 13 / 4x - 5
(5x2 + 2) with a remainder of 23

15.   Find the greatest common factor of the following terms:
• 132, 168
12

• 45x8y6, 490x9y8, 288x6y8
x6y6

16.   Factor the following polynomials:
• 7x3 + 49x2 + 56x
7x(x -
-7 +
17
2
)(x -
-7 -
17
2
)

• x2 + 2x - 35
(x + 7)(x - 5)

• x7 - 5x6 - 104x5
x5(x + 8)(x - 13)

17.   For question 16, exercises b) and c), solve for x:
• x =
-7
and
5

• x =
0
,
-8

and
13

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 or vanilla. How many choices do you have?
• 16

19.   Use the following data to construct a box and whiskers plot:
• 30, 22, 13, 21, 9, 18, 17, 2, 23 20.   Suppose you toss a coin and spin a spinner numbered 1 through 8
• What is the probability of getting heads and 6?
6.25%

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

• What is the probability of getting heads and a multiple of 4?
12.5%

• What is the probability of getting heads and a prime number?
25%

• What is the probability of not heads and not 3?
43.75%

• 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 heads?
50%

21.   Solve and graph the following systems of linear equations:
• x + y = 3
x - y = -8
A(-2.5,5.5)

• 6x - 8y = -19
8x + 7y = -17

B(-2.54,0.47)

22.   Write the following fractions in simplest form:
• 17x3y7
68x7y2
y5
4x4

• x6(x + 4)
x4 - 6x3 - 40x2
x4
(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.
• 90 = x2 + x
x1 = 9,   x2 = -10

24.   Convert the following repeating decimal into a fraction:
• x = 0.18
17
90

25.   Solve the following equation:
• 2x - 6
+ 1 = 5
x = 11

26.   Rationalize the denominator of each fraction below:
• 3
2 +
5
-(6 - 3
5
)

27.   Use a trigonometric ratio to find x: x = 28.00 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 8 blocks north and 6 blocks west. How far are you from your house?
• I am
10
blocks from my house.

30.   Each side of a square is lengthened by 10 ft. This makes the area of the square 361ft2. What is the original length of a side of the square?
• 9 ft

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