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:   -11 and -14? 154
    
2.   Add:   20 and -17? 3
    
3.   Divide:   -3 and 3? -1
    
4.   Substract:   2 and -10? 12
    
5.   Calculate: |19 + -10 · 1 + 12| 21
    
6.   Simplify the following expressions:
  • 8x – -20x – 19 -19+28x
        
  • 8y – 20y – -1 + -20x 1-20x-12y
        
  • -4z + -9z + -4x + 17 – 19y 17-4x-19y-13z
        
  • y10 × y-2 × x-1 x-1 × y8
        
  • x-15
    x-6
    x-9
        
  • (4x5)6 4096x30
        
7.   Which of the following expressions show the associative property?
  • ( m × n ) × 2 = m × ( n × 2 )
  • k × ( l + 9 ) = kl + 9l
  • 3 × 1 = 3
  • ( -2 × 4 ) + -1 = -1 + ( -2 × 4 )
A
    
8.   Which properties are illustrated by the following three expressions?
  • -4 + -15 × -17 = -15 × -17 + -4
  • 0 + c + d = c + d
  • 11 × ( 6 × -9 ) = ( 11 × 6 ) × -9
  • Associative property of addition, Distributive property and Associative property of multiplication
  • Commutative property of addition, Identity property of addition and Associative property of multiplication
  • Commutative property of addition, Distributive property and Identity property of multiplication
  • Distributive property, Commutative property of addition and Commutative property of multiplication
B
    
9.   Solve the following equations for x:
  • -20 = -4 · x x = 5
        
  • 3
    29
    x =
    6
    29
    x = 2
        
  • 23 = -34x – 79 x = -3
        
  • -e = -a – fx x = (e-a)/f
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -6x – -8 ≤ 32 x ≥ -4
        
  • x ≠ 721
  • -92 ≤ x ≥ -61
  • -
    39
    3
    x < -26 x > 2
        
11.   Convert the following numbers into scientific notation:
  • 0.000256 2.56 × 10-4
        
  • 7460000000 7.46 × 109
        
12.   Add the following polynomials:
  • 1z10 + -12z4 + -8z3 + 14z1  and  -8z10 + -15z4 + 4z3 + 4z2 + -14
    -7z10 + -27z4 + -4z3 + 4z2 + 14z1 + -14
        
  • -11z16 + -12z15 + -2z4 + 3  and  5z16 + -11z15 + -14z2 + 8 -6z16 + -23z15 + -2z4 + -14z2 + 11
        
13.   Multiply the following polynomials and simplify:
  • (10x4 + 4x + 5)-9
    -90x4 - 36x - 45
        
  • (2x - 6)(6x5 + 4x4)
    12x6 - 28x5 - 24x4
        
14.   Divide:
  • 15x2 - 2x - 1 / 3x - 1
    5x + 1
        
15.   Find the greatest common factor of the following terms:
  • 75, 30, 96
    3
        
  • 50y3, 30y7, 36x8y6
    2y3
        
16.   Factor the following polynomials:
  • 12x5 - 56x4 + 59x3
    12x3(x -
    14 +
    19
    6
    )(x -
    14 -
    19
    6
    )
        
  • x2 - 14x + 40
    (x - 10)(x - 4)
        
  • x9 - 27x8 + 182x7
    x7(x - 14)(x - 13)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    10
    and
    4


        
  • x =
    0
    ,
    14

    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:
  • 33, 11, 31, 28, 4, 36, 24
        
20.   Suppose you toss a coin and spin a spinner numbered 1 through 8
  • What is the probability of getting heads and 8?
    6.25%
        
  • What is the probability of getting heads and an odd number?
    25%
        
  • What is the probability of getting tails 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 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 = 7
    x - y = 6
    A(6.5,0.5)
        
  • 2x - 6y = 16
    6x + 12y = 18

    B(5,-1)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • (x + 2)4
    (x + 2)2
    (x + 2)2
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • -7x - 78 = -x2
    x1 = 13,   x2 = -6
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.79
    720
    900
        
25.   Solve the following equation:
  • -12
    x
    + 6 = 7
    x
    - 13
    x = 1
        
26.   Rationalize the denominator of each fraction below:
  • 21
    14 +
    14
    42 - 3
    14
    26
        
27.   Use a trigonometric ratio to find x:
x = 41.01 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 south. 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 3ft2. What are the dimensions of the rectangle?
  • width = 1,  length = 3
        


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:   -18 and -3? 54
    
2.   Add:   9 and 20? 29
    
3.   Divide:   -7 and -1? 7
    
4.   Substract:   -17 and 17? -34
    
5.   Calculate: |8 + -20 · 18 + -7| 359
    
6.   Simplify the following expressions:
  • 20 – 3x + 14x 20+11x
        
  • -16y – -16y – 12x + 12y -12x+12y
        
  • -9y + 16z + 19y – -4z + 6y – 11z 16y+9z
        
  • y7 × x-13 x-13 × y7
        
  • x-2
    x17
    x-19
        
  • (3x)2 9x2
        
7.   Which of the following expressions show the associative property?
  • a + b = b + a
  • -5 × 1 = -5
  • ( x + y ) × 6 = 6 × ( y + x )
  • ( x × y ) × z = x × ( y × z )
D
    
8.   Which properties are illustrated by the following three expressions?
  • o + ( p + q ) = ( o + p ) + q
  • (h + i) × 1 = h + i
  • x + y + z + 0 = x + y + z
  • Associative property of addition, Identity property of multiplication and Identity property of addition
  • Commutative property of addition, Commutative property of multiplication and Distributive property
  • Commutative property of multiplication, Commutative property of addition and Associative property of multiplication
  • Commutative property of addition, Distributive property and Identity property of multiplication
A
    
9.   Solve the following equations for x:
  • x + 57 = -86 x = -143
        
  • 26
    10
    = -
    1
    10
    x x = -26
        
  • -29 – -22x = -51 x = -1
        
  • ax = f – e x = (f-e)/a
        
10.   Solve the following inequalities. Then graph a) on the number line
  • x – 20 > -37 x > -17
        
  • x ≠ -514
  • 22 < x > -11
  • -
    36
    18
    x >
    36
    3
    x < -6
        
11.   Convert the following numbers into scientific notation:
  • 0.000000000653 6.53 × 10-10
        
  • 31100000 3.11 × 107
        
12.   Add the following polynomials:
  • -6z8 + 15z7 + 10z4 + 7z2 + 12z1  and  -2z10 + -10z7 + -3z2 + -14z1
    -2z10 + -6z8 + 5z7 + 10z4 + 4z2 + -2z1
        
  • 4z13 + -12z8 + -9z6  and  2z13 + -4z8 + -5z7 + -3z6 + -13 6z13 + -16z8 + -5z7 + -12z6 + -13
        
13.   Multiply the following polynomials and simplify:
  • (7x5 + 3x + 10)(10x5 + 9x4 + 8x2)
    70x10 + 63x9 + 56x7 + 30x6 + 127x5 + 90x4 + 24x3 + 80x2
        
  • (7x5 + 8x4 - 1)(10x4 + 3x2 - 9)
    70x9 + 80x8 + 21x7 + 24x6 - 63x5 - 82x4 - 3x2 + 9
        
14.   Divide:
  • 4x3 + 36x2 - 8x - 42 / x + 9
    (4x2 - 8) with a remainder of 30
        
15.   Find the greatest common factor of the following terms:
  • 63, 90
    9
        
  • 48x5, 60x4y5
    12x4
        
16.   Factor the following polynomials:
  • 45x5 - 54x4 - 72x3
    45x3(x +
    4
    5
    )(x - 2)
        
  • x2 - x - 72
    (x + 8)(x - 9)
        
  • x5 + 8x4 - 84x3
    x3(x + 14)(x - 6)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -8
    and
    9


        
  • x =
    0
    ,
    -14

    and
    6
        
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:
  • 19, 10, 22, 39, 35, 17, 23, 12
        
20.   Suppose you toss a coin and spin a spinner numbered 1 through 15
  • What is the probability of getting tails and 15?
    3.33%
        
  • What is the probability of getting tails and an odd number?
    23.33%
        
  • What is the probability of getting tails and a multiple of 3?
    16.67%
        
  • What is the probability of getting heads and a prime number?
    20%
        
  • What is the probability of not tails and not 14?
    46.67%
        
  • 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 - 6y = -16
    7x + 10y = 13

    B(-1.58,2.4)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • (x + 4)4
    (x + 4)
    (x + 4)3
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • -11x = x2 + 18
    x1 = -2,   x2 = -9
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.3953
    3950
    9990
        
25.   Solve the following equation:
  • -20 +
    x + 6
    = 20
    x = 1594
        
26.   Rationalize the denominator of each fraction below:
  • 10
    15
    21
    20
    5
    3
    21
        
27.   Use a trigonometric ratio to find x:
x = 40.00 cm
    
28.   The sum of two consecutive even integers is 54. What are the integers? (Hint: use 2x as the first even integer)
a=26, b=28
    
29.   After you leave your house, you walk 6 blocks south and 8 blocks east. How far are you from your house?
  • I am
    10
    blocks from my house.
        
30.   Each side of a square is decreased by 7 ft. The area of the newly created square is 361ft2. What was the original length of one side of the square?
  • 26 ft
        


To print this algebra practice test, click here.



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