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 least common multiple of 78 and 102.
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3.
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Determine the least common multiple of 48, 72, and 108.
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4.
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One neighbour cuts his lawn every 8 days. Another neighbour cuts her lawn every
10 days. Suppose both neighbours cut their lawns today. How many days will pass before both
neighbours cut their lawns on the same day again?
a. | 80 days | b. | 60 days | c. | 2 days | d. | 40
days |
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5.
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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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6.
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Factor the binomial  .
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7.
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Simplify the expression  , then factor.
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8.
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Identify the greatest common factor of the terms in the trinomial  .
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9.
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Factor the trinomial  .
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10.
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Factor the trinomial  .
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11.
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Simplify the expression  , then factor.
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12.
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Expand and simplify: 
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13.
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Factor: 
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14.
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Factor: 
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15.
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Factor: 
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16.
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Factor: 
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17.
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Factor: 
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18.
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Find an integer to replace “ so that this
trinomial is a perfect square. 
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19.
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Factor: 
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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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Bill and Betty do chores at home. Bill mows the lawn every 8 days, and Betty
bathes the dog every 14 days. Suppose Bill and Betty do their chores today. How many days will pass
before they both do their chores on the same day again?
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23.
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Factor the binomial  .
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24.
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Factor: 
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25.
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Problem
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26.
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a) A student says the prime factors of 13 are 1
and 13. Is the student correct? Explain.
b) List all the prime
numbers between 120 and 140. How do you know they are prime numbers?
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27.
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Chris completes one lap of a go-cart track every 40 s. D’Arcy completes
one lap of the same track every 50 s. Suppose Chris and D’Arcy cross the starting line at the
same time. How many seconds will pass before they cross the starting line at the same time again? How
many laps will Chris have completed in that time? How many laps will D’Arcy have completed in
that time?
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28.
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a) Here are a
student’s solutions for factoring polynomials. Identify the errors in each solution. Write a
correct solution.
i) Factor:  Solution:  ii) Factor: 
Solution:  b) What should the
student have done to check her work?
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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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Factor. Explain your steps. 
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