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:   -12 and -17? 204
    
2.   Add:   -4 and 3? -1
    
3.   Divide:   15 and -5? -3
    
4.   Substract:   4 and -2? 6
    
5.   Calculate: |11 · -7 + -3| 80
    
6.   Simplify the following expressions:
  • -9 + -10x – 9 -18-10x
        
  • -4 – 8y + -10x – 19 -23-10x-8y
        
  • 17x – 7z – -3y – -7x + 2x 26x+3y-7z
        
  • x-11 × y1 × x19 × y-10 x8 × y-9
        
  • x-3
    x2
    x-5
        
  • (8x4)7 2097152x28
        
7.   Which of the following expressions show the associative property?
  • -10 × 1 = -10
  • ( x × y ) × z = x × ( y × z )
  • ( 5 + 3 ) × 1 = 1 × ( 5 + 3 )
  • r × ( s + 8 ) = rs + 8s
B
    
8.   Which properties are illustrated by the following three expressions?
  • -9 × 14 = -9 × 14
  • 0 + a + b + c = a + b + c
  • (u + v + w) × 1 = u + v + w
  • Commutative property of multiplication, Identity property of addition and Identity property of multiplication
  • Associative property of multiplication, Commutative property of multiplication and Commutative property of addition
  • Associative property of multiplication, Commutative property of addition and Distributive property
  • Associative property of addition, Commutative property of addition and Associative property of multiplication
A
    
9.   Solve the following equations for x:
  • -5 = -x + -56 x = -51
        
  • 1
    7
    x = -
    13
    7
    x = -13
        
  • -11x + 33 = -99 x = 12
        
  • -c = -b + gx x = (-c+b)/g
        
10.   Solve the following inequalities. Then graph a) on the number line
  • 39x + -5 < 34 x < 1
        
  • x ≠ -299
  • 64 ≥ x ≤ -38
  • -
    35
    7
    x < 35 x > -7
        
11.   Convert the following numbers into scientific notation:
  • 0.0000000760 7.6 × 10-8
        
  • 593000000 5.93 × 108
        
12.   Add the following polynomials:
  • -13z9 + 1z6 + -9z4 + -11z3 + -9  and  -10z6 + -8z4 + 4z3 + -13z2
    -13z9 + -9z6 + -17z4 + -7z3 + -13z2 + -9
        
  • 8z16 + 7z12 + -6z9 + 10z5 + 13z4  and  1z16 + -14z10 + 4z5 + 13z4 9z16 + 7z12 + -14z10 + -6z9 + 14z5 + 26z4
        
13.   Multiply the following polynomials and simplify:
  • 8x5(2x3 - 2)
    16x8 - 16x5
        
  • (3x5 + 10x4)(7x2 - 7)
    21x7 + 70x6 - 21x5 - 70x4
        
14.   Divide:
  • 15x3 - 12x2 - 15x + 20 / 5x - 4
    (3x2 - 3) with a remainder of 8
        
15.   Find the greatest common factor of the following terms:
  • 49, 28, 100
    1
        
  • 33xy8, 30y3
    3y3
        
16.   Factor the following polynomials:
  • 14x4 + 12x3 - 2x2
    14x2(x + 1)(x -
    1
    7
    )
        
  • x2 - 5x - 24
    (x - 8)(x + 3)
        
  • x4 + 18x3 + 65x2
    x2(x + 5)(x + 13)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    8
    and
    -3


        
  • x =
    0
    ,
    -5

    and
    -13
        
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:
  • 6, 30, 3, 8, 19, 24, 16, 15, 5, 18
        
20.   Suppose you toss a coin and spin a spinner numbered 1 through 4
  • What is the probability of getting tails and 1?
    12.50%
        
  • What is the probability of getting heads and an even number?
    25%
        
  • What is the probability of getting heads and a multiple of 2?
    25%
        
  • What is the probability of getting tails and a prime number?
    25%
        
  • What is the probability of not heads and not 2?
    37.5%
        
  • 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 = 5
    x - y = -2
    A(1.5,3.5)
        
  • 8x - 4y = -7
    3x + 5y = 15

    B(0.48,2.71)
        
22.   Write the following fractions in simplest form:
  • 16x10y3
    8x4y5
    2x6
    y2
        
  • x3(x + 9)
    x3 + 3x2 - 54x
    x2
    (x - 6)
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • -10 = x2 + 11x
    x1 = -1,   x2 = -10
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.14
    14
    99
        
25.   Solve the following equation:
  • 11
    x
    - 20 = 2
    x
    - 2
    x = 4
        
26.   Rationalize the denominator of each fraction below:
  • 35
    20
    7
    5
    2
        
27.   Use a trigonometric ratio to find x:
x = 36.00 cm
    
28.   The sum of two consecutive odd integers is 48. What are the integers? (Hint: use 2x+1 as the first odd integer)
a=23, b=25
    
29.   After you leave your house, you walk 12 blocks north and 5 blocks east. How far are you from your house?
  • I am
    13
    blocks from my house.
        
30.   The sides of a square are increased by 10 ft. The area of the newly created square is 324ft2. What was the original length of one side of the square?
  • 8 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:   -5 and 8? -40
    
2.   Add:   19 and -15? 4
    
3.   Divide:   -12 and -2? 6
    
4.   Substract:   10 and -11? 21
    
5.   Calculate: |14 + -16 · 1 + 7| 5
    
6.   Simplify the following expressions:
  • -3x + -17 + -5x -17-8x
        
  • 16y + 1x – 4y + 17 17+1x+12y
        
  • -6x – -16y + -12y + 18x + 5z + -4z 12x+4y+1z
        
  • y18 × y3 × x0 x0 × y21
        
  • x6
    x-9
    x15
        
  • (10x4)8 100000000x32
        
7.   Which of the following expressions show the associative property?
  • ( 4 + 5 ) + 2 = 4 + ( 5 + 2 )
  • ( 6 × 4 ) + 1 = 1 + ( 6 × 4 )
  • 2( 7 + 7 ) = 2×7 + 2×7
  • 4 + 6c + 9
A
    
8.   Which properties are illustrated by the following three expressions?
  • o × ( p × q ) = ( o × p ) × q
  • -79 + 0 = -79
  • (t + u + v) × 1 = t + u + v
  • Distributive property, Commutative property of addition and Associative property of addition
  • Commutative property of addition, Associative property of addition and Associative property of multiplication
  • Identity property of addition, Associative property of multiplication and Commutative property of multiplication
  • Associative property of multiplication, Identity property of addition and Identity property of multiplication
D
    
9.   Solve the following equations for x:
  • -10 = x + 28 x = -38
        
  • 4
    28
    x = -
    8
    28
    x = -2
        
  • 10 = 53x – -63 x = -1
        
  • -g = ex x = -g/e
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -11x + -24 > -13 x < -1
        
  • x ≠ -160
  • -82 ≤ x ≤ -54
  • -
    16
    8
    x ≥ -
    8
    2
    x ≤ 2
        
11.   Convert the following numbers into scientific notation:
  • 0.0000751 7.51 × 10-5
        
  • 69400000000 6.94 × 1010
        
12.   Add the following polynomials:
  • 2z10 + -13z7 + 12z3 + -6z1 + -15  and  6z10 + 15z3 + -11z1 + 10
    8z10 + -13z7 + 27z3 + -17z1 + -5
        
  • -5z19 + -10z17 + 9z9 + -14z7 + -14z3  and  -8z17 + -4z16 + 7z3 -5z19 + -18z17 + -4z16 + 9z9 + -14z7 + -7z3
        
13.   Multiply the following polynomials and simplify:
  • (2x4 + 2x3 - 9)2x
    4x5 + 4x4 - 18x
        
  • (6x - 3)(1x5 + 8x3 - 10)
    6x6 - 3x5 + 48x4 - 24x3 - 60x + 30
        
14.   Divide:
  • 4x3 - 2x2 + 16x - 8 / 4x - 2
    x2 + 4
        
15.   Find the greatest common factor of the following terms:
  • 49, 72, 75
    1
        
  • 50x5y7, 100x10y
    50x5y
        
16.   Factor the following polynomials:
  • 56x3 + 32x2 + 4x
    56x(x -
    -4 +
    2
    14
    )(x -
    -4 -
    2
    14
    )
        
  • x2 + 4x - 45
    (x - 5)(x + 9)
        
  • x5 + 11x4 - 12x3
    x3(x + 12)(x - 1)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    5
    and
    -9


        
  • x =
    0
    ,
    -12

    and
    1
        
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 or vanilla. How many choices do you have?
  • 12
        
19.   Use the following data to construct a box and whiskers plot:
  • 31, 34, 19, 20, 38, 28, 26, 21
        
20.   A bag contains 4 blue balls, 3 red balls, and 2 white balls.
You pick a ball from the bag and return it to the bag.
What is the probability of picking:
  • A white ball?
    22.22%
        
  • A blue ball or red ball?
    77.78%
        
  • Two red balls?
    11.11%
        
  • A blue ball and a white ball?
    9.88%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = -7
    x - y = 4
    A(-1.5,-5.5)
        
  • x - 8y = -11
    8x + 6y = 16

    B(0.89,1.49)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • x(x - 9)
    x7 - 10x6 + 9x5
    1
    x4(x - 1)
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • -10x = x2 - 75
    x1 = -15,   x2 = 5
        
24.   Convert the following repeating decimal into a fraction:
  • x = 8.545
    8460
    990
        
25.   Solve the following equation:
  • -6
    x
    + 10 = -3
    x
    + 7
    x = 1
        
26.   Rationalize the denominator of each fraction below:
  • 35
    9
    35
    3
        
27.   Use a trigonometric ratio to find x:
x = 23.09 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 8 blocks north 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 3 m less than its length. The area of the rectangle is 4m2. What are the dimensions of the rectangle?
  • width = 1,  length = 4
        


To print this algebra practice test, click here.



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