CMC Tutoring
Review
Problem
1. Sheila plans to place crown moulding along the top of each wall in her family room. A total of 554 in. of
moulding is required. The moulding costs $1.59/ft. and is sold in 8-ft. lengths. What is the cost of the crown
moulding, before taxes?
2. Jaymee is 4 ft. 5 in. tall.
a) What is Jaymee’s height in centimetres? Write a proportion to determine your answer.
b) Use mental math and estimation to justify that the answer is reasonable.
3. Three wooden blocks need to be painted. The first block is a right rectangular pyramid with base dimensions
1.5 cm by 2.5 cm and a height of 2.0 cm . The second block is a right square pyramid with a base length of
2.8 cm and a height of 2.0 cm. The third block is a right cone with a height of 2.0 cm and a base diameter of
3.6 cm. Which block requires the most paint? Which block requires the least paint? Sketch diagrams to help
explain your answer.
4. The angle between one longer side of a rectangle and a diagonal is 37°. One shorter side of the rectangle is
6.2 cm.
a) Sketch and label the rectangle.
b) What is the length of the rectangle to the nearest tenth of a centimetre?
5. A boat was docked 30.0 m from the base of a cliff. A sailor used a clinometer to sight the top of the cliff. The
angle between the horizontal and the line of sight was 74°. The sailor held the clinometer 1.5 m above the
surface of the water. Determine the height of the cliff to the nearest tenth of a metre.
6. Sue used a clinometer to sight the top of a tall building from a point 160.0 m from the base of the building.
The angle shown on the protractor was 46°. Sue held the clinometer 1.8 m above the ground. Determine the
height of the building to the nearest tenth of a metre.
7. Factor. Check by expanding.
8z 2  112z  360
8. Use decomposition to factor 81y 2  36y  4. Explain your steps.
9. Without evaluating, which power has the least value: 7 155 , 49 78 , or 343 53 ?
Explain your strategy.
10. Determine the value of k when the equations 3kx  7y  10  0 and 2x  y  7  0 represent lines that are:
a) parallel
b) perpendicular
11. In a piggy bank, the number of nickels is 8 more than one-half the number of quarters. The value of the coins
is $21.85.
a) Create a linear system to model the situation.
b) If the number of quarters is 78, determine the number of nickels.
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Name: ________________________
ID: A
12. a) Write a linear system to model this situation:
The coin box of a vending machine contains $23.75 in quarters and loonies. There are 35 coins in all.
b) Use a graph to solve this problem:
How many of each coin are there in the coin box?
13. Use a substitution strategy to solve the following problem.
Vivian invested a total of $5600 in two bonds. She invested in one bond at 2% per annum and in another bond
at 5% per annum. In one year, the interest earned on each bond was the same. How much did Vivian invest in
each bond?
14. Use an elimination strategy to solve this linear system. Verify the solution.
20x  35y  705
10x  5y  195
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