# 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:   -11 and 4? -44

2.   Add:   5 and 8? 13

3.   Divide:   -12 and 6? -2

4.   Substract:   8 and 16? -8

5.   Calculate: |1 + -8 · 7 + 9| 46

6.   Simplify the following expressions:
• 6x – -8x – 8x 6x

• 2 – -20 + 14y + 3y 22+17y

• -7z – 18y – 5z + 16y + -3z -2y-15z

• y5 × x4 × y-17 x4 × y-12

• x4
x-8
x12

• (10x)7 10000000x7

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

8.   Which properties are illustrated by the following three expressions?
• 1 × (c + 7) = c + 7
• 11 + 10y = 10y + 11
• (p + q) × -10 = -10 × (p + q)
• Commutative property of multiplication, Distributive property and Associative property of multiplication
• Commutative property of addition, Identity property of multiplication and Identity property of addition
• Distributive property, Associative property of multiplication and Identity property of multiplication
• Identity property of multiplication, Commutative property of addition and Commutative property of multiplication
D

9.   Solve the following equations for x:
• 48 = 3 · x x = 16

• 4
29
x = -
16
29
x = -4

• 51 = 43x + 94 x = -1

• fx + e = ax x = (-e)/(f-a)

10.   Solve the following inequalities. Then graph a) on the number line
• -x + -22 ≤ -29 x ≥ 7

• x ≠ -180
• 66 > x ≥ -84
• 22
11
x ≤ -18 x ≤ -9

11.   Convert the following numbers into scientific notation:
• 0.0000000218 2.18 × 10-8

• 19400 1.94 × 104

• -2z8 + -5z6 + 11z2  and  9z8 + -11z4 + 13z3 + -13z2
7z8 + -5z6 + -11z4 + 13z3 + -2z2

• -12z20 + -12z18 + 14z10  and  -9z18 + -12z10 + 7z9 + -4 -12z20 + -21z18 + 2z10 + 7z9 + -4

13.   Multiply the following polynomials and simplify:
• (10x5 + 10x)(5x + 8)
50x6 + 80x5 + 50x2 + 80x

• (9x2 + 4x - 8)(6x4 + 3x2)
54x6 + 24x5 - 21x4 + 12x3 - 24x2

14.   Divide:
• 20x2 + 45x + 10 / 4x + 1
5x + 10

15.   Find the greatest common factor of the following terms:
• 30, 54
6

• 52x10y4, 24x8y10
4x8y4

16.   Factor the following polynomials:
• 24x4 - 46x3 - 35x2
24x2(x +
7
12
)(x -
5
2
)

• x2 - 12x + 32
(x - 4)(x - 8)

• x7 + 7x6 - 44x5
x5(x + 11)(x - 4)

17.   For question 16, exercises b) and c), solve for x:
• x =
4
and
8

• x =
0
,
-11

and
4

18.   You are seating 6 people on 6 chairs. How many different ways can those people sit?
• 720

19.   Use the following data to construct a box and whiskers plot:
• 17, 20, 33, 37, 18, 19, 9

20.   Suppose you toss a coin and spin a spinner numbered 1 through 16
• What is the probability of getting heads and 4?
3.13%

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

• What is the probability of getting tails and a multiple of 5?
9.38%

• What is the probability of getting tails and a prime number?
18.75%

• What is the probability of not tails and not 14?
46.88%

• 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 tails?
50%

21.   Solve and graph the following systems of linear equations:
• x + y = 5
x - y = -10
A(-2.5,7.5)

• 6x - 5y = 4
x + 5y = 11

B(2.14,1.77)

22.   Write the following fractions in simplest form:
• 36x6y3
18x10y4
2
x4y

• (x - 5)2
(x - 5)4
1
(x - 5)2

23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
• -x2 = 9x + 20
x1 = -5,   x2 = -4

24.   Convert the following repeating decimal into a fraction:
• x = 0.8
8
9

25.   Solve the following equation:
• 12
x
+ 12 = 10
x
+ 14
x = 1

26.   Rationalize the denominator of each fraction below:
• 7
2
- 3
-
2
- 3

27.   Use a trigonometric ratio to find x:
x = 18.48 cm

28.   The sum of two consecutive even integers is 58. What are the integers? (Hint: use 2x as the first even integer)
a=28, b=30

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

30.   Each side of a square is lengthened by 4 ft. This makes the area of the square 81ft2. What is the original length of a side of the square?
• 5 ft

Name _____________________                                        Date:_____________________

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

Solve the following problems:

Important instructions

1.   Multiply:   5 and -19? -95

2.   Add:   20 and -9? 11

3.   Divide:   -14 and -2? 7

4.   Substract:   -13 and -7? -6

5.   Calculate: |18 + -13 · -1 + -14| 17

6.   Simplify the following expressions:
• 5x + 3x – 18x -10x

• 3x + 7 – 16y – 11y 7+3x-27y

• 13z + 1x – 1 – 12 – -2 + -14y -11+1x-14y+13z

• y19 × y5 × y0 y24

• x-15
x13
x-28

• (7x4)10 282475249x40

7.   Which of the following expressions show the associative property?
• ( x × y ) + 9 = 9 + ( y × x )
• a + b = b + a
• ( m × n ) × 7 = m × ( n × 7 )
• 2 + 5h + 10
C

8.   Which properties are illustrated by the following three expressions?
• 1 × (l + m + n) = l + m + n
• 17 × -15 + -6 = -6 + 17 × -15
• b × ( c × 1 ) = ( b × c ) × 1
• Identity property of multiplication, Commutative property of addition and Associative property of multiplication
• Commutative property of multiplication, Commutative property of addition and Associative property of multiplication
• Identity property of multiplication, Associative property of multiplication and Associative property of addition
B

9.   Solve the following equations for x:
• -54 = 27 · x x = -2

• -
2
3
x = -
6
9
x = 1

• -39x – -6 = -33 x = 1

• d = -gx x = -d/g

10.   Solve the following inequalities. Then graph a) on the number line
• 5x + 32 > -3 x > -7

• x ≠ 422
• -98 < x ≤ 8
• 26
13
x >
40
5
x > 4

11.   Convert the following numbers into scientific notation:
• 0.0000000891 8.91 × 10-8

• 3470000000 3.47 × 109

• 13z10 + -11z5 + 10z4  and  -2z10 + 14z5
11z10 + 3z5 + 10z4

• 5z20 + 14z19 + 2z18 + -13z17 + 4z5  and  13z18 + -5z10 + 7z5 + -1 5z20 + 14z19 + 15z18 + -13z17 + -5z10 + 11z5 + -1

13.   Multiply the following polynomials and simplify:
• (3x4 + 8x3 + 9x2)(1x3 + 8x - 6)
3x7 + 8x6 + 33x5 + 46x4 + 24x3 - 54x2

• (9x5 + 3x2)(1x4 + 8x2)
9x9 + 72x7 + 3x6 + 24x4

14.   Divide:
• 12x2 - 50x + 50 / 4x - 10
3x - 5

15.   Find the greatest common factor of the following terms:
• 35, 32, 30
1

• 42x7y5, 50x5y8
2x5y5

16.   Factor the following polynomials:
• 56x3 - 98x2 + 42x
56x(x -
3
4
)(x - 1)

• x2 - 2x - 80
(x - 10)(x + 8)

• x5 - 20x4 + 91x3
x3(x - 13)(x - 7)

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

• x =
0
,
13

and
7

18.   You have 7 CDs. How many different ways can you listen to them?
• 5040

19.   Use the following data to construct a box and whiskers plot:
• 13, 12, 28, 11, 22, 3, 9

20.   A bag contains 2 blue balls, 3 red balls, and 6 white balls.
You pick a ball from the bag and put it in your pocket.
What is the probability of picking:
• A white ball?
54.55%

• A blue ball or red ball?
45.45%

• Two red balls?
5.45%

• A blue ball and a white ball?
10.91%

21.   Solve and graph the following systems of linear equations:
• x + y = -13
x - y = -19
A(-16,3)

• 3x - 7y = 10
8x + 4y = 7

B(1.31,-0.87)

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

• (x - 5)3
(x - 5)2
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.
• -25 = x2 + 10x
x1 = -5,   x2 = -5

24.   Convert the following repeating decimal into a fraction:
• x = 0.32
29
90

25.   Solve the following equation:
• -
x + 3
+ 13 = -8
x = 438

26.   Rationalize the denominator of each fraction below:
• 49
21 -
15
1029 + 49
15
426

27.   Use a trigonometric ratio to find x:
x = 34.00 cm

28.   The sum of two consecutive even integers is 46. What are the integers? (Hint: use 2x as the first even integer)
a=22, b=24

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

30.   The length of a rectangle is 3 more than thrice its width. The area of the rectangle is 396ft2. What is the length and width of the rectangle?
• width = 11,  length = 36

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