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:   -3 and 9? -27
    
2.   Add:   12 and -10? 2
    
3.   Divide:   12 and 3? 4
    
4.   Substract:   -17 and 4? -21
    
5.   Calculate: |-6 · 10 + 10| 50
    
6.   Simplify the following expressions:
  • -7x – 19 – 5 -24-7x
        
  • 19x – 20y + 1 – 10x 1+9x-20y
        
  • -10 + -9y + -12y + -14z + -17z -10-21y-31z
        
  • x-17 × x12 × x-15 × y-7 x-20 × y-7
        
  • x3
    x13
    x-10
        
  • (3x4)8 6561x32
        
7.   Which of the following expressions show the associative property?
  • ( x + y ) + z = x + ( y + z )
  • -3 + -1 = -1 + -3
  • ( 6 + 8 ) × 5 = 5 × ( 6 + 8 )
  • 6 + 8u + 5
A
    
8.   Which properties are illustrated by the following three expressions?
  • -13 + -2 × 4 = -2 × 4 + -13
  • ( 15 × 14 ) × 9 = 15 × ( 14 × 9 )
  • (-6 + x) × 1 = 1 × (-6 + x)
  • Associative property of addition, Identity property of addition and Distributive property
  • Identity property of multiplication, Commutative property of addition and Associative property of addition
  • Commutative property of addition, Associative property of multiplication and Commutative property of multiplication
  • Associative property of multiplication, Distributive property and Associative property of addition
C
    
9.   Solve the following equations for x:
  • -40 = -39 + x x = -1
        
  • 12
    27
    = -
    4
    9
    x x = -1
        
  • -78 = 2x – 90 x = 6
        
  • fx – e = -a x = (e-a)/f
        
10.   Solve the following inequalities. Then graph a) on the number line
  • -25x – -31 < 6 x > 1
        
  • x ≠ -349
  • -15 ≥ x ≥ -25
  • 33
    3
    x ≤ -11 x ≤ -1
        
11.   Convert the following numbers into scientific notation:
  • 0.00000186 1.86 × 10-6
        
  • 626000000 6.26 × 108
        
12.   Add the following polynomials:
  • 5z9 + -4z8 + 11z4 + -2z3  and  -7z9 + 9z4 + 10z3
    -2z9 + -4z8 + 20z4 + 8z3
        
  • -10z19 + -6z3 + 6z1  and  2z19 + -15z3 + -11z1 -8z19 + -21z3 + -5z1
        
13.   Multiply the following polynomials and simplify:
  • (3x5 + 10x4 + 10x3)(7x5 + 6x)
    21x10 + 70x9 + 70x8 + 18x6 + 60x5 + 60x4
        
  • (7x3 + 10x2)(1x5 + 3x4 + 4x)
    7x8 + 31x7 + 30x6 + 28x4 + 40x3
        
14.   Divide:
  • x3 - x2 - 8x + 31 / x - 1
    (x2 - 8) with a remainder of 23
        
15.   Find the greatest common factor of the following terms:
  • 45, 90, 48
    3
        
  • 40x6y7, 70x10y7
    10x6y7
        
16.   Factor the following polynomials:
  • 18x5 + 27x4 + 4x3
    18x3(x +
    1
    6
    )(x +
    4
    3
    )
        
  • x2 + 8x + 12
    (x + 2)(x + 6)
        
  • x8 - 6x7 - 27x6
    x6(x - 9)(x + 3)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -2
    and
    -6


        
  • x =
    0
    ,
    9

    and
    -3
        
18.   You have 4 CDs. How many different ways can you listen to them?
  • 24
        
19.   Use the following data to construct a box and whiskers plot:
  • 6, 20, 4, 12, 22, 26, 21, 16, 37, 35
        
20.   Suppose you toss a coin and spin a spinner numbered 1 through 10
  • What is the probability of getting heads and 6?
    5.00%
        
  • What is the probability of getting heads and an even number?
    25%
        
  • What is the probability of getting tails and a multiple of 5?
    10%
        
  • What is the probability of getting heads and a prime number?
    20%
        
  • What is the probability of not heads and not 10?
    45%
        
  • 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 = -7
    x - y = -20
    A(-13.5,6.5)
        
  • 9x - 10y = -2
    4x + 5y = -13

    B(-1.65,-1.28)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • (x + 9)3
    (x + 9)7
    1
    (x + 9)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 - 18x = -65
    x1 = 13,   x2 = 5
        
24.   Convert the following repeating decimal into a fraction:
  • x = 0.319
    319
    999
        
25.   Solve the following equation:
  • 4 -
    x - 10
    = -3
    x = 59
        
26.   Rationalize the denominator of each fraction below:
  • 35
    21
    - 5
    -
    35
    21
    + 175
    4
        
27.   Use a trigonometric ratio to find x:
x = 25.00 cm
    
28.   The sum of two consecutive even integers is 50. What are the integers? (Hint: use 2x as the first even integer)
a=24, b=26
    
29.   After you leave your house, you walk 9 blocks north and 12 blocks east. How far are you from your house?
  • I am
    15
    blocks from my house.
        
30.   Each side of a square is lengthened by 6 m. This makes the area of the square 121m2. What is the original length of a side of the square?
  • 5 m
        


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:   -3 and -9? 27
    
2.   Add:   20 and -15? 5
    
3.   Divide:   1 and -1? -1
    
4.   Substract:   8 and 4? 4
    
5.   Calculate: |-15 + -3 · 9| 42
    
6.   Simplify the following expressions:
  • -19 – 19 – -12x -38+12x
        
  • -7y + -15x + 6x + -17y -9x-24y
        
  • -20z – 1 + 12x + 1y – 19 + -20z -20+12x+1y-40z
        
  • x16 × y6 x16 × y6
        
  • x5
    x-8
    x13
        
  • (5x)10 9765625x10
        
7.   Which of the following expressions show the associative property?
  • 4( 3 + 4 ) = 4×3 + 4×4
  • ( 8 + 6 ) + 9 = 8 + ( 6 + 9 )
  • 7 + 2q + 9
  • -10 × 1 = -10
B
    
8.   Which properties are illustrated by the following three expressions?
  • (h + i) × 4 = 4 × (h + i)
  • v + ( w + x ) = ( v + w ) + x
  • y + -5 × 2 = -5 × 2 + y
  • Identity property of multiplication, Associative property of addition and Commutative property of multiplication
  • Identity property of multiplication, Distributive property and Associative property of multiplication
  • Commutative property of addition, Commutative property of multiplication and Identity property of addition
  • Commutative property of multiplication, Associative property of addition and Commutative property of addition
D
    
9.   Solve the following equations for x:
  • x – -2 = 1 x = -1
        
  • -
    1
    17
    x = -
    22
    17
    x = 22
        
  • -65 = -18x + 79 x = 8
        
  • -ax – e = -bx x = e/(-a+b)
        
10.   Solve the following inequalities. Then graph a) on the number line
  • 18x + -30 > 24 x > 3
        
  • x ≠ 469
  • 94 > x ≥ 16
  • -
    24
    4
    x >
    12
    2
    x < -1
        
11.   Convert the following numbers into scientific notation:
  • 0.0000267 2.67 × 10-5
        
  • 313000000000 3.13 × 1011
        
12.   Add the following polynomials:
  • -10z8 + 7z7 + 11z6 + -2z1  and  8z9 + -13z8 + -5z7 + -13z5
    8z9 + -23z8 + 2z7 + 11z6 + -13z5 + -2z1
        
  • -5z11 + 13z3 + -12z2 + -3z2 + 15  and  6z16 + 13z11 + 6z8 + 11z2 6z16 + 8z11 + 6z8 + 13z3 + -4z2 + 15
        
13.   Multiply the following polynomials and simplify:
  • 10x4(7x4 + 6x2 + x)
    70x8 + 60x6 + 10x5
        
  • (8x5 + 5x2)(1x5 + x4)
    8x10 + 8x9 + 5x7 + 5x6
        
14.   Divide:
  • 20x3 + 4x2 + 25x + 5 / 5x + 1
    4x2 + 5
        
15.   Find the greatest common factor of the following terms:
  • 96, 42, 36
    6
        
  • 50x3y, 45xy4
    5xy
        
16.   Factor the following polynomials:
  • 64x5 - 24x4 - 4x3
    64x3(x -
    1
    2
    )(x +
    1
    8
    )
        
  • x2 - x - 90
    (x + 9)(x - 10)
        
  • x9 + 10x8 + 16x7
    x7(x + 2)(x + 8)
        
17.   For question 16, exercises b) and c), solve for x:
  • x =
    -9
    and
    10


        
  • x =
    0
    ,
    -2

    and
    -8
        
18.   You are seating 7 people on 7 chairs. How many different ways can those people sit?
  • 5040
        
19.   Use the following data to construct a box and whiskers plot:
  • 27, 36, 33, 22, 4, 12, 21, 20, 24, 9
        
20.   A bag contains 4 blue balls, 3 red balls, and 5 white balls.
You pick a ball from the bag and return it to the bag.
What is the probability of picking:
  • A white ball?
    41.67%
        
  • A blue ball or red ball?
    58.33%
        
  • Two red balls?
    6.25%
        
  • A blue ball and a white ball?
    13.89%
        
21.   Solve and graph the following systems of linear equations:
  • x + y = 3
    x - y = 4
    A(3.5,-0.5)
        
  • 8x - 6y = -14
    10x + 7y = -3

    B(-1,1)
        
22.   Write the following fractions in simplest form:
  • 22x6y7z4
    44x7y9z2
    z2
    2xy2
        
  • (x + 7)
    (x2 + 14x + 49)
    1
    x + 7
        
23.   Solve the equation below in two different ways. First, solve it using the quadratic formula. Secondly, solve it by completing the square.
  • x2 + 2x = 24
    x1 = 4,   x2 = -6
        
24.   Convert the following repeating decimal into a fraction:
  • x = 3.411
    3070
    900
        
25.   Solve the following equation:
  • -
    11
    x
    = -14
    x =
    121
    196
        
26.   Rationalize the denominator of each fraction below:
  • 9
    7
    10
    14
    9
    2
    20
        
27.   Use a trigonometric ratio to find x:
x = 28.28 cm
    
28.   The sum of two consecutive even integers is 26. What are the integers? (Hint: use 2x as the first even integer)
a=12, b=14
    
29.   After you leave your house, you walk 8 blocks east and 15 blocks south. How far are you from your house?
  • I am
    17
    blocks from my house.
        
30.   The length of a rectangle is 8 less than 4 times the width. What are the dimensions of the rectangle if the area is 252ft2?
  • width = 9,  length = 28
        


To print this algebra practice test, click here.



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