# 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:   8 and 19? 152

2.   Add:   14 and 15? 29

3.   Divide:   11 and 11? 1

4.   Substract:   -9 and -8? -1

5.   Calculate: |-14 + -15 · -10| 136

6.   Simplify the following expressions:
• -13x + -2x – -17x 2x

• 7y – 20y – -13y – 19y -19y

• 10 + -12y + -19z – -14y – 14 – 20 -24+2y-19z

• x-4 × x-13 x-17

• x-7
x-3
x-4

• (2x)8 256x8

7.   Which of the following expressions show the associative property?
• w × ( x + 7 ) = wx + 7x
• 7 × 9 = 9 × 7
• ( m + n ) + 8 = m + ( n + 8 )
• ( -6 × -2 ) + 3 = 3 + ( -6 × -2 )
C

8.   Which properties are illustrated by the following three expressions?
• v + 3 + 0 = v + 3
• 1 × (w + x) = w + x
• o + ( p + 0 ) = ( o + p ) + 0
• Identity property of addition, Identity property of multiplication and Associative property of addition
• Associative property of multiplication, Distributive property and Identity property of addition
• Commutative property of addition, Identity property of addition and Associative property of multiplication
• Associative property of multiplication, Associative property of addition and Commutative property of multiplication
A

9.   Solve the following equations for x:
• 33 = -11 · -x x = 3

• 20
15
= -
5
15
x x = -4

• 20 = -96 – -4x x = 29

• g = -a – bx x = (-g-a)/b

10.   Solve the following inequalities. Then graph a) on the number line
• -x – -40 ≤ -1 x ≥ 41

• x ≠ 88
• 99 > x ≤ 67
• 28
14
x > -
26
13
x > -1

11.   Convert the following numbers into scientific notation:
• 0.000000805 8.05 × 10-7

• 692000000000 6.92 × 1011

• 10z8 + -14z3  and  -10z8 + 3z3
-11z3

• -12z19 + 9z16 + 7z14 + -2z8 + -5z7  and  -9z17 + -9z14 + -7z12 + -7z8 + 1z1 -12z19 + -9z17 + 9z16 + -2z14 + -7z12 + -9z8 + -5z7 + 1z1

13.   Multiply the following polynomials and simplify:
• -7(4x5 + x4 + 4x2)
-28x5 - 7x4 - 28x2

• (4x5 + 2x3 + 8x)(9x3 + 5)
36x8 + 18x6 + 20x5 + 72x4 + 10x3 + 40x

14.   Divide:
• 20x2 + 51x + 28 / 4x + 7
5x + 4

15.   Find the greatest common factor of the following terms:
• 56, 100
4

• 45xy8, 50x9y6, 22x6y7
xy6

16.   Factor the following polynomials:
• 8x5 - 15x4 - 2x3
8x3(x - 2)(x +
1
8
)

• x2 - x - 90
(x + 9)(x - 10)

• x5 - 15x4 + 56x3
x3(x - 8)(x - 7)

17.   For question 16, exercises b) and c), solve for x:
• x =
-9
and
10

• x =
0
,
8

and
7

18.   You have 4 pants, 4 shirts, and 3 shoes. How many different ways can you dress?
• 48

19.   Use the following data to construct a box and whiskers plot:
• 23, 3, 21, 34, 7, 37, 27, 39, 22, 36 20.   A bag contains 5 blue balls, 3 red balls, and 2 white balls.
You pick a ball from the bag and put it in your pocket.
What is the probability of picking:
• A white ball?
20.00%

• A blue ball or red ball?
80.00%

• Two red balls?
6.67%

• A blue ball and a white ball?
11.11%

21.   Solve and graph the following systems of linear equations:
• x + y = 18
x - y = -7
A(5.5,12.5)

• 9x - 10y = 10
2x + 9y = -11

B(-0.2,-1.18)

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

• x3 - 2x2 - 24x
x4(x + 4)
(x - 6)
x3

23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
• 12x = x2 + 11
x1 = 1,   x2 = 11

24.   Convert the following repeating decimal into a fraction:
• x = 0.531
531
999

25.   Solve the following equation:
• 40
x
= 2
x = 10

26.   Rationalize the denominator of each fraction below:
• 14
6 -
14
42 + 7
14
11

27.   Use a trigonometric ratio to find x: x = 9.81 cm

28.   The sum of two consecutive even integers is 34. What are the integers? (Hint: use 2x as the first even integer)
a=16, b=18

29.   After you leave your house, you walk 4 blocks east and 3 blocks north. How far are you from your house?
• I am
5
blocks from my house.

30.   A rectangle has an area of 7m2. Its width is 6 m less than its length. What are the dimensions of the rectangle?
• width = 1,  length = 7

Name _____________________                                        Date:_____________________

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

Solve the following problems:

Important instructions

1.   Multiply:   20 and 16? 320

2.   Add:   -16 and 8? -8

3.   Divide:   3 and 3? 1

4.   Substract:   10 and -20? 30

5.   Calculate: |-20 · -9 + 6 · -18| 72

6.   Simplify the following expressions:
• -12 – -20 + -16x 8-16x

• -4x + -18y + 17 + 3x 17-1x-18y

• 14y + 17 + -5x + -11 + 17 + 12x 23+7x+14y

• y10 × y-7 × x-1 × x-17 x-18 × y3

• x-17
x17
x-34

• (5x)4 625x4

7.   Which of the following expressions show the associative property?
• 9x + -1 = -1 + 9x
• ( x × y ) + 8 = 8 + ( y × x )
• ( m + n ) + 4 = m + ( n + 4 )
• 3 × ( y + 9 + 7 ) = 3×y + 3×9 + 3×7
C

8.   Which properties are illustrated by the following three expressions?
• 13 × ( 7 × 18 ) = ( 13 × 7 ) × 18
• 9 + ( -17 + -5 ) = ( 9 + -17 ) + -5
• ( y + 0 ) × x = y × x + 0 × x
• Associative property of multiplication, Associative property of addition and Distributive property
• Commutative property of multiplication, Identity property of addition and Identity property of multiplication
• Commutative property of addition, Identity property of multiplication and Associative property of multiplication
• Associative property of multiplication, Associative property of addition and Commutative property of addition
A

9.   Solve the following equations for x:
• x – -95 = -10 x = -105

• -
1
3
x =
17
3
x = -17

• 98 = 74 + -24x x = -1

• bx + e = f x = (-e+f)/b

10.   Solve the following inequalities. Then graph a) on the number line
• 25x + -9 > -34 x > -1

• x ≠ -342
• -53 < x > 53
• 39
13
x ≤ 3 x ≤ 1

11.   Convert the following numbers into scientific notation:
• 0.0000711 7.11 × 10-5

• 6730000 6.73 × 106

• -15z9 + 14z4 + -10z3 + -2z2 + 6  and  -13z6 + 4z4 + -7z3 + 13z2 + 10z1
-15z9 + -13z6 + 18z4 + -17z3 + 11z2 + 10z1 + 6

• 11z7 + 8z6 + -8z1  and  -4z7 + 15z6 + -1z2 + -12z1 + 6 7z7 + 23z6 + -1z2 + -20z1 + 6

13.   Multiply the following polynomials and simplify:
• (7x5 + 5x2)(10x3 + 3x2 + 9x)
70x8 + 21x7 + 63x6 + 50x5 + 15x4 + 45x3

• (5x4 + 7x2 + 4)(3x4 + 5x3 + 8)
15x8 + 25x7 + 21x6 + 35x5 + 52x4 + 20x3 + 56x2 + 32

14.   Divide:
• 5x2 + 41x + 42 / x + 7
5x + 6

15.   Find the greatest common factor of the following terms:
• 78, 21, 75
3

• 72x2y10, 60x3y2, 99xy9
3xy2

16.   Factor the following polynomials:
• 18x3 - 90x2 + 54x
18x(x -
5 +
13
2
)(x -
5 -
13
2
)

• x2 - 13x + 30
(x - 10)(x - 3)

• x7 + 9x6 - 70x5
x5(x + 14)(x - 5)

17.   For question 16, exercises b) and c), solve for x:
• x =
10
and
3

• x =
0
,
-14

and
5

18.   You are seating 3 people on 3 chairs. How many different ways can those people sit?
• 6

19.   Use the following data to construct a box and whiskers plot:
• 14, 7, 6, 39, 25, 17, 22, 12, 34 20.   Suppose you toss a coin and spin a spinner numbered 1 through 8
• What is the probability of getting tails and 7?
6.25%

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

• What is the probability of getting tails and a multiple of 2?
25%

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

• What is the probability of not tails and not 6?
43.75%

• 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 = 4
x - y = -11
A(-3.5,7.5)

• 3x - 6y = -14
10x + 10y = 6

B(-1.16,1.76)

22.   Write the following fractions in simplest form:
• 11x4y10
44xy
x3y9
4

• (x + 4)
(x2 + 8x + 16)
1
x + 4

23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
• x2 + 3x = -2
x1 = -2,   x2 = -1

24.   Convert the following repeating decimal into a fraction:
• x = 3.13
310
99

25.   Solve the following equation:
• 14
x
= 13
x =
196
169

26.   Rationalize the denominator of each fraction below:
• 7
30
7
30
1

27.   Use a trigonometric ratio to find x: x = 34.64 cm

28.   The sum of two consecutive odd integers is 60. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=29, b=31

29.   After you leave your house, you walk 8 blocks west and 15 blocks south. How far are you from your house?
• I am
17
blocks from my house.

30.   A rectangle has a length 3 ft greater than its width. The area of the rectangle is 108ft2. What are the length and width of the rectangle?
• width = 9,  length = 12

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