Algebra test generator



Name _____________________                                        Date:_____________________


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

                           

Solve the following problems:

Important instructions

(or click here to generate a new test)
1.   Multiply:   1 and -8? -8
    
2.   Add:   -18 and -10? -28
    
3.   Divide:   13 and -13? -1
    
4.   Substract:   5 and -16? 21
    
5.   Calculate: |4 · 11 + 20 · 17| 384
    
6.   Simplify the following expressions:
  • 19x + -11x + 7x 15x
        
  • -11y – 12y + 18x + -7y 18x-30y
        
  • 13x – -12 – -3z – 11 + 13y 1+13x+13y+3z
        
  • x10 × x-5 x5
        
  • x19
    x8
    x11
        
  • (9x3)4 6561x12
        
7.   Which of the following expressions show the associative property?
  • ( 2 + 3 ) + 4 = 2 + ( 3 + 4 )
  • a + b = b + a
  • o × ( p + 8 ) = op + 8p
  • ( m × n ) + 8 = 8 + ( m × n )
A
    
8.   Which properties are illustrated by the following three expressions?
  • (x + y + z) × 1 = x + y + z
  • 5 + 10z = 10z + 5
  • -7 + ( -8 + 1 ) = ( -7 + -8 ) + 1
  • Commutative property of addition, Associative property of multiplication and Distributive property
  • Commutative property of addition, Commutative property of multiplication and Associative property of addition
  • Identity property of addition, Distributive property and Identity property of multiplication
  • Identity property of multiplication, Commutative property of addition and Associative property of addition
D
    
9.   Solve the following equations for x:
  • -51 = x · -17 x = 3
        
  • -
    10
    20
    x = -
    10
    20
    x = 1
        
  • 38x + -27 = -65 x = -1
        
  • ax = d x = d/a
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -12x + 12 ≤ -12 x ≥ 2
        
  • x ≠ -898
  • 36 ≥ x ≥ 14
  • 36
    3
    x > -
    24
    2
    x > -1
        
11.   Convert the following numbers into scientific notation:
  • 0.00000965 9.65 × 10-6
        
  • 1830000000 1.83 × 109
        
12.   Add the following polynomials:
  • -11z7 + -5z4  and  -3z7 + 8z6 + 9z3
    -14z7 + 8z6 + -5z4 + 9z3
        
  • 5z13 + -15z7 + -9z1  and  10z13 + -1z12 + 1z3 + -2z1 15z13 + -1z12 + -15z7 + 1z3 + -11z1
        
13.   Multiply the following polynomials and simplify:
  • (5x3 - 6)(10x5 - 3)
    50x8 - 60x5 - 15x3 + 18
        
  • (4x5 + 9x3)(1x2 + 10x)
    4x7 + 40x6 + 9x5 + 90x4
        
14.   Divide:
  • 8x3 + 20x2 - 14x - 32 / 2x + 5
    (4x2 - 7) with a remainder of 3
        
15.   Find the greatest common factor of the following terms:
  • 72, 40
    8
        
  • 26y8, 88x9y3
    2y3
        
16.   Factor the following polynomials:
  • 42x4 - 70x3 - 28x2
    42x2(x +
    1
    3
    )(x - 2)
        
  • x2 - 3x + 2
    (x - 2)(x - 1)
        
  • x6 - 12x5 - 45x4
    x4(x + 3)(x - 15)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    2
    and
    1


        
  • x =
    0
    ,
    -3

    and
    15
        
18.   You can purchase your ice cream in a cup or a cone. Orders can be one or two scoops. Flavors can be chocolate, vanilla, strawberry or peach. How many choices do you have?
  • 16
        
19.   Use the following data to construct a box and whiskers plot:
  • 33, 38, 12, 11, 7, 15, 28
        
20.   Suppose you toss a coin and spin a spinner numbered 1 through 17
  • What is the probability of getting heads and 5?
    2.94%
        
  • What is the probability of getting heads and an odd number?
    23.53%
        
  • What is the probability of getting heads and a multiple of 7?
    5.88%
        
  • What is the probability of getting tails and a prime number?
    20.59%
        
  • What is the probability of not heads and not 5?
    47.06%
        
  • 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 = 5
    x - y = -4
    A(0.5,4.5)
        
  • 8x - 9y = 20
    5x + 9y = -5

    B(1.15,-1.2)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • x5 - 12x4 + 35x3
    x2(x - 7)
    x(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.
  • 56 = x2 - 10x
    x1 = -4,   x2 = 14
        
24.   Convert the following repeating decimal into a fraction:
  • x = 9.30
    921
    99
        
25.   Solve the following equation:
  • -1 +
    2x - 5
    = 10
    x = 63
        
26.   Rationalize the denominator of each fraction below:
  • 6
    15
    21
    21
    2
    35
    49
        
27.   Use a trigonometric ratio to find x:
x = 22.52 cm
    
28.   The sum of two consecutive odd integers is 24. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=11, b=13
    
29.   After you leave your house, you walk 15 blocks east and 8 blocks north. How far are you from your house?
  • I am
    17
    blocks from my house.
        
30.   The sides of a square are increased by 2 ft. The area of the newly created square is 361ft2. What was the original length of one side of the square?
  • 17 ft
        


To print this algebra practice test, click here.



Name _____________________                                        Date:_____________________


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

                           

Solve the following problems:

Important instructions

(or click here to generate a new test)
1.   Multiply:   17 and -5? -85
    
2.   Add:   -5 and -2? -7
    
3.   Divide:   11 and -1? -11
    
4.   Substract:   8 and 13? -5
    
5.   Calculate: |7 + 2 · -19 + -5| 36
    
6.   Simplify the following expressions:
  • -2x + 20 – 7 13-2x
        
  • 18x + 20 – -16y – 19 1+18x+16y
        
  • -10 + -6 + 20y + 2y + 8x + 3z -16+8x+22y+3z
        
  • x-19 × x13 x-6
        
  • x10
    x-10
    x20
        
  • (10x5)2 100x10
        
7.   Which of the following expressions show the associative property?
  • ( m × n ) + 2 = 2 + ( m × n )
  • ( 9 + 8 ) + 7 = 9 + ( 8 + 7 )
  • 8 × 1 = 8
  • d × ( e + 9 ) = de + 9e
B
    
8.   Which properties are illustrated by the following three expressions?
  • 79 + 74 = 79 + 74
  • 93 + 0 = 93
  • (m + n + o) × 1 = m + n + o
  • Associative property of addition, Commutative property of addition and Associative property of multiplication
  • Commutative property of addition, Identity property of addition and Identity property of multiplication
  • Commutative property of addition, Associative property of addition and Identity property of addition
  • Distributive property, Commutative property of addition and Associative property of multiplication
B
    
9.   Solve the following equations for x:
  • 91 = -x + -65 x = -156
        
  • 28
    30
    = -
    28
    30
    x x = -1
        
  • 100 + 196x = -96 x = -1
        
  • g = -bx + e x = (-g+e)/b
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -x – 37 < 6 x > -43
        
  • x ≠ 128
  • -11 > x > -22
  • -2x > 14 x < -7
        
11.   Convert the following numbers into scientific notation:
  • 0.000000326 3.26 × 10-7
        
  • 45200 4.52 × 104
        
12.   Add the following polynomials:
  • 1z7 + -8z6 + 11z4 + -5z3  and  5z6 + 9z4 + -11z3
    1z7 + -3z6 + 20z4 + -16z3
        
  • 2z15 + 9z13 + 1z11 + 15z5 + 2z3  and  -13z16 + 5z11 + 9z5 + -12z3 -13z16 + 2z15 + 9z13 + 6z11 + 24z5 + -10z3
        
13.   Multiply the following polynomials and simplify:
  • (8x - 9)-4
    -32x + 36
        
  • (3x5 + x4 + 6x2)(10x5 + 2)
    30x10 + 10x9 + 60x7 + 6x5 + 2x4 + 12x2
        
14.   Divide:
  • 3x3 + 10x2 + 12x + 40 / 3x + 10
    x2 + 4
        
15.   Find the greatest common factor of the following terms:
  • 90, 60, 10
    10
        
  • 84x4y9, 24x7y4, 65x9y2
    x4y2
        
16.   Factor the following polynomials:
  • 8x5 + 32x4 + 26x3
    8x3(x -
    -4 +
    3
    2
    )(x -
    -4 -
    3
    2
    )
        
  • x2 + 11x + 30
    (x + 6)(x + 5)
        
  • x6 + 4x5 - 21x4
    x4(x + 7)(x - 3)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -6
    and
    -5


        
  • x =
    0
    ,
    -7

    and
    3
        
18.   You can purchase your ice cream in a cup or a cone. Orders can be one, two, or three scoops. Flavors can be chocolate, vanilla, strawberry or peach. How many choices do you have?
  • 24
        
19.   Use the following data to construct a box and whiskers plot:
  • 12, 30, 13, 3, 15, 31, 20
        
20.   Suppose you toss a coin and spin a spinner numbered 1 through 14
  • What is the probability of getting tails and 10?
    3.57%
        
  • What is the probability of getting tails and an even number?
    25%
        
  • What is the probability of getting tails and a multiple of 3?
    14.29%
        
  • What is the probability of getting heads and a prime number?
    21.43%
        
  • What is the probability of not heads and not 14?
    46.43%
        
  • 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 = 17
    x - y = -8
    A(4.5,12.5)
        
  • x - 7y = -13
    3x + 10y = -13

    B(-7.13,0.84)
        
22.   Write the following fractions in simplest form:
  • 30x8y6
    15x9y2
    2y4
    x
        
  • (x2 - 10x + 25)
    (x - 5)
    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 = 21x + 90
    x1 = -15,   x2 = -6
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.339
    336
    990
        
25.   Solve the following equation:
  • 9 -
    x - 9
    = -18
    x = 738
        
26.   Rationalize the denominator of each fraction below:
  • 10
    14
    + 9
    -
    10
    14
    - 90
    67
        
27.   Use a trigonometric ratio to find x:
x = 24.04 cm
    
28.   The sum of two consecutive odd integers is 16. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=7, b=9
    
29.   After you leave your house, you walk 8 blocks east and 6 blocks south. How far are you from your house?
  • I am
    10
    blocks from my house.
        
30.   The length of a rectangle is 9 less than 3 times the width. What are the dimensions of the rectangle if the area is 390ft2?
  • width = 13,  length = 30
        


To print this algebra practice test, click here.



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