Mixed Review Math 10C
A MIXED BAG
113. Michelle and Pierre both want to buy guitars. Michelle has already saved $60,
and plans to save $5 per week until she can buy the guitar. Pierre has $25, and plans to save $12 per week. How many weeks will pass before Michelle and Pierre have the same amount of money?
114. Supplementary angles are angles that have a sum of 180°. If and are
supplementary, and is 32° greater than , what are the values of and
?
115. The sum of two numbers is 66 and their difference is 18. What are the
numbers?
116. Three times one number added to another number is 39. Twice the first
number minus the other is 6. What are the numbers?
117. Jessica has designed a storage cabinet to store her CDs and DVDs. The
cabinet door can be closed. The cabinet is a right rectangular prism that is 1 m wide, 60 cm deep and 2.4 m high. Determine the volume of the cabinet to the nearest tenth of a cubic metre.
118. The pyramid of Khufu is a right pyramid with a square base. One side of the
base is 230 m; the slant height is 186 m. Determine the surface area of the pyramid, including the base, to the nearest square metre.
119. Jennifer has designed a stone sculpture composed of a square-based right
pyramid and a right rectangular prism. The pyramid’s base has sides 25 cm long and the pyramid has a slant height of 18 cm. The rectangular prism is 30 cm wide, 20 cm deep, and 40 cm high. Calculate the total exposed surface area of the sculpture.
120. The volume of a right rectangular prism is 56 cm3. Determine three
121. Christina received a gift in the mail. The gift was shipped in the gift box shown. Calculate the largest volume that the gift box can hold, to the nearest cubic centimetre.
122. A sphere has a radius of 8 in. Determine the volume of the sphere to the
nearest cubic inch.
123. A rubber hockey puck has a radius of 3.7 cm and a thickness of 2.6 cm. What
is the volume of rubber needed to make the puck, to the nearest cubic centimetre?
124. A water storage tank has a right cylindrical base and a domed top. The base
has a diameter of 10 m and a height of 12 m. The top is half a sphere with the same diameter as the cylindrical base.
a) Determine the volume of the tank.
b) How many litres will the tank hold, to the nearest hundred litres?
125. A conical paper cup for holding popcorn has a radius of 3 in. and a height of 6 in. How much paper, to the nearest square inch, is used to make the cup?
126. A conical pile of road salt has a radius of 10 ft and a height of 14 ft. What is the volume of road salt in the pile, to the nearest cubic foot?
127. A right cone with a volume of 120 cm3 just fits inside a right cylindrical
container. What is the volume of the container?
128. A baseball has a diameter of 7.4 cm. How much leather is needed to cover it,
to the nearest square centimetre?
129. A right cylindrical bird feeder needs painting. It has a diameter of 8 in. and a height of 12 in. Three circles, each with a radius 1.5 in., have been cut from the lateral surface of the cylinder in order for the birds to feed. Determine the area of the feeder that needs to be painted, to the nearest tenth of a square inch.
130. Explain how doubling the length of the sides of a square-based right pyramid
affects the volume of the pyramid.
132. A field is 65 m long by 45 m wide. Petra walks diagonally across the field. What angle, with respect to the width of the field, does Petra’s path make? Answer to the nearest degree.
133. The side adjacent to the 74° angle in a right triangle is 6 cm long. How long is the hypotenuse, to the nearest tenth of a centimetre?
134. The side opposite from the 50° angle in a right triangle is 6 cm long. Determine the length of the hypotenuse.
136. Solve . Express each measurement to the nearest whole unit.
137. During take-off, a plane must rise at least 20 m during the first 1.5 km of flight to successfully clear the runway.
What is the minimum angle the plane must make with the ground for a safe take-off, to the nearest hundredth of a degree?
138. Explain why the primary trigonometric ratios depend only on the given angle
and not the size of the legs and hypotenuse of a right triangle.
139. A wooden cabinet for china is 54 in. wide, 18 in. deep, and 58.5 in. high. The front is completely glass. What is the surface area of the exterior part of the cabinet that is not glass? Express your answer to the nearest square inch.
140. A sheet music cabinet is 1.4 m wide, 45 cm deep, and 1.5 m high. What is the
surface area of the cabinet, not including the open front? Express your answer to the nearest tenth of a square metre.
141. Baylor is creating a rectangular garden in his yard. The length of the garden
142. State whether each of the following is a perfect square, a perfect cube, both, or neither. Explain your answer.
a) 121
b) 216
c) 64
d) 250
143. A brace in the shape of a right triangle is used to support the side of a
building while it is under construction. If the brace is 4 m high and 3 m wide, what is the diagonal length of the brace?
144. What is the volume of this right rectangular prism?
145. What is the edge length of a cube that has the same volume as this right
146. Simplify using the exponent laws. Express your answer using positive exponents only.
147. Simplify the expression , showing all steps. Express your
answer using only positive exponents.
148. What is the simplified form of the expression , using only positive
exponents? Show all steps.
149. The exact value of the edge length of a cube is cm. What is the volume
of the cube?
150. Identify the irrational numbers in this set. Order all the numbers from least to greatest.
, , , , ,
151. Convert each mixed radical to an equivalent entire radical.
a) b)
c)
153. What is the fully factored form of the expression x3 – x2 – 2x?
154. What product does the diagram below represent?
155. Write and simplify an expression that represents the surface area of a cube
with an edge measuring (x + 1) units.
156. Write and simplify an expression that represents the volume of a cube with
an edge measuring x + 1 units.
157. Factor 15a5 – 5a2.
158. What are the factors of the expression 18a4c3 – 27a2c4 + 9a3c?
159. What is the greatest common factor of x4 and x7?
160. Use algebra tiles or a diagram to factor the trinomial 2x2 + 7x + 6.
161. Factor the trinomial 3x2 + 24x + 45.
162. What is the factored form of 8x2 – 6x – 9?
163. What are the factors of x2 – 16x + 64?
164. Factor 4x2 – 36.
165. Determine two values of k so that km2 – 25 can be factored as a difference of
squares.
166. a) Write y = 7x8 – 1792 in factored form.
b) State the values of x that satisfy y = 0.
1 2 3 4 5 6 7 8 9 t (s)
3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51
d (m)
168. Create a correctly labelled speed-time graph for the following scenario:
A snowmobiler accelerates for 15 s until he reaches a speed of 10 m/s. The snowmobiler stays at that speed for 5 min and then takes 60 s to slow down until he stops. He slows at a constant rate.
169. The following set of points represents a relation. Graph the relation and explain how you know it is either linear or non-linear.
{(–2, 7), (–1, 5), (1, 1), (4, –5)}
170. Following are two pairs of equivalent representations. Match the pairs.
A One number is three times a number plus four.
1 2 3 4 5 6 –1
–2 –3 –4 –5
–6 x
3 6 9 12 15
–3
–6
–9
–12
–15
y
C
Dy = 3x + 4
171. Given f(x) = –3x + 7, determine f(–3).
172. What are the domain and range of the relation y = 2(x – 5)2 + 8? Express
your answer using set notation.
173. Express the domain and range of the relation represented by the following
174. A relation is given by the formula d = 4.5t + 3.1.
a) If the domain of the relation is [0, 40], what is the range?
b) Sketch the relation.
175. A rock falls from the top of a 137-m cliff. The rock lands on the ground 5.3 s later. What is the domain of the relation that models the rock’s path?
176. a) Determine if the relation y = –2x2 – 3 is a function and justify your answer.
b) What are the domain and range of this relation?
177. Classify the slope of each line segment as positive, negative, zero, or undefined. Justify your answers.
A B C D H J K L
1 2 3 4 5 6 7 8 9
–1 –2 –3 –4 –5 –6 –7 –8 –9 x 1 2 3 4 5 6 7 8 9 –1 –2 –3 –4 –5 –6 –7 –8 –9 y
178. A graph of Marina’s college fund is shown below, where S represents her
1 2 3 4 5 6 7 8 9 10 t 250 500 750 1000 1250 1500 1750 2000 2250 2500 2750 3000 3250 3500 3750 4000 4250 S
a) What is the slope of this line?
b) What does the slope represent?
179. The cost of renting a car can be modelled by the function C(d) = 19.99 + 0.27d, where C(d) is the total cost in dollars and d is the distance driven, in kilometres.
a) Explain the significance of the number 0.27 to the cost of renting a car.
b) Explain how the graph of this linear relation would change if the 0.27 value were changed to 0.29.
180. What is the x-intercept of each line, given the slope and the y-intercept?
a) slope: –5, y-intercept: 20
b) slope: 3, y-intercept: –12
c) slope: –6, y-intercept: –9
181. Determine the slope and y-intercept of the line y = –2x + 2. Then, graph the line.
182. What is the slope-intercept form of the equation of the line with slope – and
y-intercept 5?
183. What are the x-intercept and y-intercept of the line 3x – 4y – 12 = 0?
185. Write the equation of the line that passes through points (2, 3) and (4, 5).
186. Determine an equation of the line that passes through points (–1, –2) and (3,
4).
187. Determine whether line T with equation y = 5x + 10 is parallel to line U with equation y = 4x + 10. Justify your answer.
188. Determine the equation of the line perpendicular to y = –2x + 5 at the y -intercept. Sketch both lines on the same grid to confirm your answer.
189. What is the equation of the line that is perpendicular to the line –2x + 3y + 6 = 0 and that passes through (3, –1)?
190. Explain how you can determine whether two lines are parallel without
graphing.
191. Explain how the elimination method can be used to solve a system of linear
equations.
192. A line has the equation 3x + 4y – 12 = 0. Determine the equations of a line that is parallel to and a line that is perpendicular to this line.
193. Graph the linear system y = x – 3 and x + y = 9 and determine the solution.
194. Solve the following linear system graphically.
y = 3 3x – y = 3
195. Determine the point of intersection of the lines and y = –x + 3 by
graphing.
196. Graphically determine the number of solutions for the following linear
system.
y = 6x – 3
12x – 2y – 6 = 0
197. Determine the number of solutions for the linear system by graphing.
4x – 2y = –6
y = 2x – 3
198. Write the equation of a line that is parallel to the line 2x + 4y = 8. Express your answer in slope-intercept form.
200. The ordered pairs (1, 3) and (–2, –9) are both solutions to the linear system y
= 4x – 1 and 8x – 2y = 2. Explain how this is possible.
201. Solve the linear system using the substitution method.
2(x – 4) + y = 6 3x – 2(y – 3) = 13
202. The ordered pair (2, -1) is the solution to the linear system ax + by = –7 and 2ax – 3by = 1. What values of a and b make this statement true?
203. Three times one number added to another number is 39. Twice the first
number minus the other is 6. What are the numbers?
204. To solve the following linear system by elimination, Brent first multiplied each equation by 10. Explain why he did this step.
0.3x – 0.5y = 1.2 0.7x – 0.2y = –0.1
205. Explain how you would solve the system 3x + 2y = 5 and 4x + 5y = 11 using the method of elimination.
206. Explain why these two linear systems are equivalent.
System 1
x – 2y = 5 2x + 2y = 6
System 2 3x – 6y = 15
x + y = 3
207. Explain why you might not use the substitution method to solve the following
system of linear equations. 3x + 4y = 10
2x + 5y = 9
208. Is (3, –5) the solution to the following linear system? Explain your answer. 2x + 5y = –19
6y – 8x = 54
209. Choose a method to solve this system of linear equations, and explain your
reasoning.
x + y = 4
y = 2x + 4
210. Which method would you choose to solve the linear system? Explain your
reasoning and then solve using your method. 3x – y = 8
211. Use the elimination method to solve the system of linear equations. 3x + y = –2
2x – y = –3
212. Solve the linear system using a method of your choice.
2x + y = –1 8x + 3y = –7
213. Solve the system of linear equations using the elimination method.
–3x + 4y = 3 5x – 2y = 2
214. Solve the system of linear equations using the substitution method.
