Math Proficiency Practice Test #1

Answers are available at the end of the practice test.

Note: These practice questions, as yet, are not in interactive form. You will need to work and record your answers on paper. If you save your scratch paper with the work on it and bring it when you come for help at the Math Skills Center, we will be better able to help you find any mistakes, incorrect steps, etc.

1.  Write 29,049 in expanded form.
        a)  20,000 + 9000 + 400 + 90
        b)  2000 + 900 + 40 + 9
        c)  20,000 + 900 + 40 + 9
        d)  20,000 + 9000 + 40 + 9

2.  Evaluate   (3²)(5²)(7) 
        a)  1280
        b)  1575
        c)  420
        d)  1050

3.  A clothing manufacturer produces and boxes 225 shirts each hour.  Five shirts are put in each box for shipment.  How many boxes can be filled in 8 hours?
        a)  375 boxes
        b)  350 boxes
        c)  45 boxes
        d)  360 boxes

4.  Simplify:  3  +  2 ( 12  -  2 )  ÷  4
        a)  10
        b)  9
        c)  12
        d)  8

5.  Write the numbers in order from smallest to largest:  -(-1) ,  |-8| ,  |0| , - |2|
    a)  -(-1),  |0|,  -|2| , |-8|
    b)  -|2|, -(-1), |0|, |-8|
    c)  |0|,  -(-1), -|2|, |-8|
    d)  -|2|, |0|, -(-1), |-8|

6.  Evaluate  -x + y  when x = -9 and y = -7
    a)  -16
    b)  16
    c)  -2
    d)  2

7.  The high temperature for the day was 11^o C.  The low temperature was -5^o C.  Find the difference between the high and low temperatures for the day.
    a)  16^o C
    b)  6^o C
    c)  -6^o C
    d)  -16^o C

8.  Evaluate  (-2a + c) ÷ d  when a = 1, c = 4, and d = -2.
    a)  3
    b)  -3
    c)  -1
    d)  1

9.  5  5/8   -   3  5/6
    a)  2  5/24
    b)  1  19/24
    c)  1  11/24
    d)  9  11/24

10.  A developer purchases 27½ acres of land and plans to set aside 2½ acres for an entranceway to a housing development to be built on the property.  Each house will be built on a 1¼ acre lot of land.  How many houses does the developer plan to build on the property?
    a)  20 houses
    b)  22 houses
    c)  11 houses
    d)  8 houses

11.  Evaluate  0.6p when p = 5.4
    a)  3.24
    b)  3.04
    c)  30.4
    d)  32.4

12.  Use the formula  M = S - C ,  where M is the   markup on a consumer product, S is the selling price, and C is the cost of the product to the seller, to find the markup on a product that cost the seller $20.82 and whose selling price is $59.34,
    a)  $80.16
    b)  $38.52
    c)  $79.16
    d)  $39.52

13.  Convert 9/20  to a decimal.
    a)  .45
    b)  .22
    c)  .920
    d)  2.22

14.  Write 240% as a decimal.
    a)  24
    b)  2.4
    c)  .240
    d)  .00240

15.  Write 0.035 as a percent.
    a)  0.35%
    b)  350%
    c)  3.5%
    d)  35%

16.  Simplify:   -2x - 3 ( 2 - 4x )
    a)  -14x + 6
    b)  -10x + 6
    c)  10x - 6
    d)  -14x - 6

17.  Find the perimeter of a rectangle whose width is 5 ft. and whose length is 8½ ft.
    a)  13½ ft.
    b)  26 ft.
    c)  27 ft.
    d)  42½ ft

18..  Translate  "twelve less than one-third of y"  into a variable expression.
    a)  12  -  (1/3)y
    b)  (1/3)y  -  12
    c)  (y - 12)  ÷  1/3
    d)  (1/3) y   ·   -12

19.  Find 150% of 120.
    a)  80
    b)  125
    c)  150
    d)  180

20.  A student answered 12 of the 80 questions on a test incorrectly.  What percent of the answers were incorrect?
    a)  10%
    b)  15%
    c)  20%
    d)  85%

21.  A department store has 150 employees and must hire an additional 30% for the holiday season.  What is the total number of employees needed for the holiday season?
    a)  45
    b)  195
    c)  205
    d)  450

22.  Solve:   5x + 4  =  -2x - 10
    a)  14/3
    b)  -2
    c)  2
    d)  -1

23.  Solve  2b - 3 ( b - 2 )  =  -4
    a)  -2
    b)  2
    c)  10
    d)  -10

24.  Solve:  4x - 10  >  2x
    a)  x < 5
    b)  x < -5
    c)  x > -5
    d)  x > 5

25.  Which point has coordinates ( -1 , -3 )?
                           
    a)  A
    b)  B
    c)  C
    d)  D

26.  Name the coordinates of the point indicated on the graph:
                        .
a)  ( -2 , -2 )
b)  ( -2 , -1 )
c)  (-1 , 2 )
d)  ( 2 , -1 )

27.  Graph:  2x + 5y  =  10
    a)
   
b)
      
c)

d)
   

28.  Graph  x + 3y  =  -3
a) 

b)

c)

d)

29.  Graph:   x  =  4
a)

b)

c)

d)

30.  Solve this system of equations:    -2x + 4y  = -10
                                                          2x   - 5y  = 11
    a)  x  =  1 , y  =  -2
    b)  x  =  8 , y  =  -1
    c)  x  =  -3 , y  =  -1
    d)  x  =  3 , y  =  -1

31.  ( 5x² - 3x + 7 )  -  ( -x³ + 2x² - 4 ) =
    a)  x³ - 3x - 3
    b)  x³ + 3x² + 3x - 3
    c)  x³ + 3x² - 3x + 11
    d)  -x³ + 3x² + 3x - 11

32.  ( 4 a² b³ ) ( -2 a³ b⁴ ) =
    a)  -8 a⁵ b⁷
    b)  2 a⁶ b¹²
    c)  6 a³ b
    d)  6 a⁵ b⁷  

33.  Simplify:  ( -2 x³ y² )³  
   a)   8 x⁹ y⁶
    b)  -8 x⁹ y⁶
    c)  -8 x⁶ y³
    d)  -8 x⁶ y⁵

34.  Multiply:  ( 2x - y ) ( 3x + 4y)
    a)  6x² + 5xy + 4y²
    b)  6x² + 5xy - 4y²
    c)  6x² - 5xy - 4y²
    d)  6x² - 5xy + 4y²

35.  Simplify:  ( x + 3y )²
   a)   x² + 9y²
    b)  2x + 6y
    c)  x² + 9xy + 9y²
    d)  x² + 6xy + 9y²

36.  Simplify:
                       
a)  3x² - 2x + 3
b)  x² + 2x - 3
c)  x² + 2x + 3
d)  x² - 2x + 3

37.  Write  363,400,000 in scientific notation.
    a)  3.634 x 10^-8
    b)  3.634 x 10⁸
    c)  3634 x 10⁵
    d)  400,000,000

38.  Factor:  a² - 4a - 21
    a)  ( a + 7 ) ( a + 3 )
    b)  ( a - 7 ) ( a + 3 )
    c)  ( a + 7 ) ( a - 3 )
    d)  ( a - 7 ) ( a - 3 )

39.  Solve:  x² + 2x - 15  =  0
    a)  x = 5 and x = 3
    b)  x = -5 and x = -3
    c)  x = -5 and x = 3
    d)  x = 5 and x = -3

40.  The length of a rectangle is 3 inches more than the width.  The area is 180 square inches.  Find the length of the rectangle.
    a)  12 inches
    b)  13 inches
    c)  15 inches
    d)  18 inches

41.  Nine ceramic tiles are required to tile a 4-square-foot area.  At   this rate, how many tiles are required to tile a 308-square-foot area?
    a)  600 tiles
    b)  625 tiles
    c)  650 tiles
    d)  693 tiles

42.  A stock investment of 400 shares pays a dividend of $320.  At this rate, how many additional shares must one own to earn a dividend of $500?
    a)  225 shares
    b)  275 shares
    c)  350 shares
    d)  625 shares

43.  Two triangles, ABC and DEF, are similar.  Find side DE.  Round to the nearest tenth.

    a)  20.7 ft.
    b)  21.8 ft.
    c)  22.5 ft.
    d)  23.4 ft.

End of Practice Exam #1

Click here for the answer page.

Questions, comments, corrections? Send them to Marilyn Creed.