Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Write the prime factorization of 630.
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2.
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Determine the greatest common factor of 280 and 360.
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3.
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A developer wants to subdivide a rectangular plot of land measuring 600 m by 750
m into congruent square lots. What is the side length of the largest possible square?
a. | 75 m | b. | 30 m | c. | 150 m | d. | 50 m |
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4.
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There are 16 male students and 20 female students in a Grade 10 math class. The
teacher wants to divide the class into groups with the same number of males and the same number of
females in each group. What is the greatest number of groups the teacher can make?
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5.
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A fruit grower wants to plant 64 apple seedlings and 108 pear seedlings in rows.
Each row is to have the same number of each type of seedling. What is the greatest number of rows the
grower can plant?
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6.
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Factor the binomial  .
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7.
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Factor the binomial  .
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8.
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Factor the trinomial  .
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9.
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Factor the trinomial  .
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10.
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Simplify the expression  , then factor.
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11.
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Factor the trinomial  .
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12.
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Factor the trinomial  .
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13.
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Factor: 
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14.
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Which set of algebra tiles represents  ?
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15.
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Expand and simplify: 
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16.
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Factor: 
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17.
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Expand and simplify: 
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18.
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Factor: 
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19.
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Find an integer to replace “ so that this
trinomial is a perfect square. 
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20.
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Factor: 
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Short Answer
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21.
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A builder wants to cover a wall measuring 9 ft. by 15 ft. with square pieces of
plywood.
a) What is the side length of the largest square that could be used to cover the wall?
Assume the squares cannot be cut.
b) How many square pieces of
plywood would be needed?
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22.
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Factor: 
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23.
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24.
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Factor fully: 
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25.
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The area of a square is represented by the trinomial  . Determine an
expression for the perimeter of the square.
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Problem
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26.
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A square is drawn inside a circle with radius  . a)
Write an expression for the area of the shaded region. b)
Factor the expression. 
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27.
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The area of a shape is given by the expression  . a)
Factor the expression. b)
Use both forms of the expression to determine the area of the shape
when  cm and  cm. What do you notice?
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28.
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This composite object is formed by a cone with a hemisphere on top. A formula
for the volume of this object is:   a)
Factor this formula. b) Use both
forms of the formula to calculate the volume of this composite object with radius 4 cm and height 10
cm.
c) Which formula to do you prefer to use? Why?
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29.
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A student is asked to find an integer to replace “ so that  can be factored. The student said the only possible integer
is  . Is the student correct? Explain.
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30.
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Find the area of the rectangle. 
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