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 11? 121

2.   Add:   2 and 20? 22

3.   Divide:   -16 and -4? 4

4.   Substract:   6 and -16? 22

5.   Calculate: |-12 · 11 + -13| 145

6.   Simplify the following expressions:
• -2 + -3x – 1 -3-3x

• 14y + 20x – 10y – 20x 4y

• -3 – 6y – 18z + 9x – 5x – -16 13+4x-6y-18z

• x15 × y-9 × x1 x16 × y-9

• x7
x-9
x16

• (8x)8 16777216x8

7.   Which of the following expressions show the associative property?
• ( m × n ) + 3 = 3 + ( m × n )
• ( m × n ) × p = m × ( n × p )
• 5 × ( y + 8 + 4 ) = 5×y + 5×8 + 5×4
• 3( 9 + 6 ) = 3×9 + 3×6
B

8.   Which properties are illustrated by the following three expressions?
• -20 × ( -4 × -5 ) = ( -20 × -4 ) × -5
• -10 × 10 = -10 × 10
• x × ( y + 0 ) = x × y + x × 0
• Associative property of multiplication, Identity property of multiplication and Commutative property of multiplication
• Associative property of multiplication, Associative property of addition and Distributive property
• Distributive property, Associative property of addition and Commutative property of addition
• Associative property of multiplication, Commutative property of multiplication and Distributive property
D

9.   Solve the following equations for x:
• 92 = -77 + -x x = -169

• 23
19
=
23
19
x x = 1

• -10x – -39 = 49 x = -1

• b = -gx x = -b/g

10.   Solve the following inequalities. Then graph a) on the number line
• 26x + -29 ≤ -3 x ≤ 1

• x ≠ 899
• -52 ≥ x < 36
• -
18
9
x < -
28
2
x > 7

11.   Convert the following numbers into scientific notation:
• 0.00000000285 2.85 × 10-9

• 46900 4.69 × 104

• 11z8 + -7z2  and  8z8 + 9z5
19z8 + 9z5 + -7z2

• 12z10 + -10z7 + 3z3 + 1z1 + 11z1  and  10z16 + 12z7 + 1z3 + 8z1 10z16 + 12z10 + 2z7 + 4z3 + 20z1

13.   Multiply the following polynomials and simplify:
• (1x4 + 6x3 + 8x2)(3x4 + 7x3 + 5)
3x8 + 25x7 + 66x6 + 56x5 + 5x4 + 30x3 + 40x2

• (5x5 + x4)(5x5 + 6x2)
25x10 + 5x9 + 30x7 + 6x6

14.   Divide:
• 5x3 - 8x2 + 40x - 64 / 5x - 8
x2 + 8

15.   Find the greatest common factor of the following terms:
• 63, 36, 42
3

• 36x8y9, 45x7y8, 78x10y4
3x7y4

16.   Factor the following polynomials:
• 54x3 + 42x2 + 5x
54x(x -
-7 +
19
18
)(x -
-7 -
19
18
)

• x2 + 11x + 30
(x + 6)(x + 5)

• x9 - 22x8 + 105x7
x7(x - 7)(x - 15)

17.   For question 16, exercises b) and c), solve for x:
• x =
-6
and
-5

• x =
0
,
7

and
15

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, peach or kiwi. How many choices do you have?
• 40

19.   Use the following data to construct a box and whiskers plot:
• 19, 17, 8, 35, 9, 25, 10, 12, 38

20.   A bag contains 5 blue balls, 6 red balls, and 5 white balls.
You pick a ball from the bag and put it in your pocket.
What is the probability of picking:
• A white ball?
31.25%

• A blue ball or red ball?
68.75%

• Two red balls?
12.50%

• A blue ball and a white ball?
10.42%

21.   Solve and graph the following systems of linear equations:
• x + y = 1
x - y = 14
A(7.5,-6.5)

• 10x - 2y = 18
2x + 6y = 8

B(1.94,0.69)

22.   Write the following fractions in simplest form:
• 22x5y8
11x9y2
2y6
x4

• x5(x + 8)
x4 + 18x3 + 80x2
x3
(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.
• x2 + 35x = -66
x1 = -33,   x2 = -2

24.   Convert the following repeating decimal into a fraction:
• x = 0.3
3
9

25.   Solve the following equation:
• 19
x
+ 5 = 18
x
+ 15
x = 100

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

27.   Use a trigonometric ratio to find x:
x = 32.33 cm

28.   The sum of two consecutive odd integers is 32. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=15, b=17

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

30.   A rectangle has a width that is 2 ft less than its length. The area of the rectangle is 99ft2. What are the dimensions of the rectangle?
• width = 9,  length = 11

Name _____________________                                        Date:_____________________

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

Solve the following problems:

Important instructions

1.   Multiply:   -5 and 10? -50

2.   Add:   8 and -20? -12

3.   Divide:   19 and 1? 19

4.   Substract:   20 and -2? 22

5.   Calculate: |20 + -11 – -9 – -14| 32

6.   Simplify the following expressions:
• 4x + -20 + -2 -22+4x

• -14y + 8x + -11x + -18x -21x-14y

• -2 + -1y – 14x + 19z + -14 + 4 -12-14x-1y+19z

• y11 × y-18 × y-4 y-11

• x18
x6
x12

• (10x3)10 10000000000x30

7.   Which of the following expressions show the associative property?
• ( 6 × 8 ) × 5 = 6 × ( 8 × 5 )
• 0 + 6x = 6x
• ( m × n ) + 2 = 2 + ( m × n )
• ( x × y ) + 4 = 4 + ( y × x )
A

8.   Which properties are illustrated by the following three expressions?
• ( v + w ) × u = v × u + w × u
• 0 + j + k + l = j + k + l
• (a + b + c) × 1 = a + b + c
• Identity property of addition, Associative property of multiplication and Associative property of addition
• Distributive property, Identity property of addition and Identity property of multiplication
• Identity property of addition, Distributive property and Commutative property of multiplication
• Commutative property of multiplication, Associative property of multiplication and Associative property of addition
B

9.   Solve the following equations for x:
• -56 – x = -49 x = -7

• -
16
23
= -
16
23
x x = 1

• 56 = 86 – 10x x = 3

• d – gx = ax x = d/(g+a)

10.   Solve the following inequalities. Then graph a) on the number line
• x + -12 ≥ -8 x ≥ 4

• x ≠ 96
• 99 ≤ x > 33
• -
18
9
x > -20 x < 10

11.   Convert the following numbers into scientific notation:
• 0.000000000896 8.96 × 10-10

• 315000 3.15 × 105

• -1z10 + 12z5 + 10z4  and  -7z10 + -13z5
-8z10 + -1z5 + 10z4

• 15z14 + -13z11 + 14z8 + 1z3  and  -10z14 + 4z3 + -5 5z14 + -13z11 + 14z8 + 5z3 + -5

13.   Multiply the following polynomials and simplify:
• 9x5(3x5 + 3x - 8)
27x10 + 27x6 - 72x5

• (10x3 + 2x2 - 6)(4x3 + 8x)
40x6 + 8x5 + 80x4 - 8x3 - 48x

14.   Divide:
• 2x2 + 15x - 27 / 2x - 3
x + 9

15.   Find the greatest common factor of the following terms:
• 72, 90, 84
6

• 18y5, 35xy10, 70x3y7
y5

16.   Factor the following polynomials:
• 36x5 + 54x4 + 19x3
36x3(x -
-9 +
5
12
)(x -
-9 -
5
12
)

• x2 - x - 6
(x + 2)(x - 3)

• x9 + 3x8 - 10x7
x7(x + 5)(x - 2)

17.   For question 16, exercises b) and c), solve for x:
• x =
-2
and
3

• x =
0
,
-5

and
2

18.   You have 3 pants, 4 shirts, and 5 shoes. How many different ways can you dress?
• 60

19.   Use the following data to construct a box and whiskers plot:
• 37, 34, 3, 20, 2, 10, 4, 30

20.   Suppose you toss a coin and spin a spinner numbered 1 through 5
• What is the probability of getting heads and 4?
10.00%

• What is the probability of getting tails and an even number?
20%

• What is the probability of getting heads and a multiple of 2?
20%

• What is the probability of getting tails and a prime number?
30%

• What is the probability of not heads and not 3?
40%

• 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 = 4
x - y = 3
A(3.5,0.5)

• x - 5y = 3
4x + y = -9

B(-2,-1)

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

• (x - 4)
(x - 4)3
1
(x - 4)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 = 15x + 50
x1 = -5,   x2 = -10

24.   Convert the following repeating decimal into a fraction:
• x = 0.737
664
900

25.   Solve the following equation:
• 6
x
= 9
x =
36
81

26.   Rationalize the denominator of each fraction below:
• 14
6
5 +
7
35
6
- 7
42
9

27.   Use a trigonometric ratio to find x:
x = 20.00 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 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 5 ft. This makes the area of the square 169ft2. What is the original length of a side of the square?
• 8 ft

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