Math 9 Cumulative Exam Review
Name: _________________
Details: The Math 9 Exam is a cumulative exam, meaning it will cover all of the units we have covered in class since September. You will be given the entire 2 hour exam length to complete the exam and be provided calculators, rulers, protractors as well as formulas you have been provided for tests and assignments. To succeed in this exam, it is of great importance that you review your notes, practice review questions, as well as review previous assessments to determine where your studying could be best focused.
The exam is worth 30% of your final grade. To determine what you need on the exam to obtain your ideal mark in the course on the report card, complete the following calculation:
% Needed on the exam to obtain ideal grade
=
( Ideal grade) – (Current grade x 0.70) x 100%
30
Great Resources for Study Preparation in order to Succeed:
1.
Review notes and study material.
2.
Review examples in the Math 9 textbook for areas you had trouble with throughout the year.
3.
Review and recomplete Assignments, Test Review Assignments, Quizzes, and Tests (ignore the answers and see if you can obtain the correct answer).
4.
Complete entire Exam Review package.
5.
Using the website below, which shows each outcome broken down over the year, examples of how to complete the problems, as well as links in each outcome with 5-10 practice questions and feedback: https://ca.ixl.com/standards/alberta/math/grade-9
Your username should be your last name, first initial of first name, then 784. Password: mroulton
Ex: John Smith would be: username: smithj784, password: mroulton
6.
Scheduling time with Mr. Oulton if you are having difficulty (do this well in advance of the Exam date, you cannot expect to review the entire year the day before the Exam). Alternatively if you have quick questions, you can email Mr. Oulton at oultonr@ccrsb.ca
with questions (will reply within 24 hours, usually a lot earlier).

1

2

1.
Use a calculator to help determine the square roots of the following rational numbers ( round to the nearest hundredth where necessary ): a.
√125 = b.
√20 = c.
√2.56
= d.
√
25
4
= e.
√
71
36
=
2.
For the above rational numbers in question 1, which were perfect squares and how do you know?
3.
Define what it means to be a perfect square .
4.
Estimate the following square roots using benchmarks to the nearest tenth (closest perfect square roots above and below the number). a.
√15 ≈ b.
√115 ≈ c.
√57 ≈ d.
√200 ≈
5.
Determine the area of the following shapes (formula sheet attached); don’t forget units!
a.
b. c.
3

6.
In an attempt to wrap a Christmas gift, Sally is trying to use the exact amount of wrapping paper. Calculate the exact amount of wrapping paper it would take to wrap the following rectangular prism box (don’t forget your units!). Hint: How many sides in rectangular prism? Does each side have a matching pair?
7.
Determine how much material would be used to manufacture this Pringles can, not including the plastic cover (remember to subtract the cover area if you calculate the total surface area of the cylinder).
8.
The surface area of the cylinder is 351.68in
2 and the surface area of the rectangular prism is 952in 2 separately. Determine the total surface area of this entire composite object (remember to account for overlap).
4

9.
Calculate the total surface area of this composite figure (cylinder with a rectangular prism).
Surface Area of Rectangular Prism:
Surface Area of Cylinder:
Overlap:
Total Surface Area = Rectangular Prism + Cylinder – Overlap = _________________________
10.
Complete the table below:
Power Base Exponent Repeated Multiplication Standard Form
3 3
-3 2
(-9) 0
-(-9) 0
-7
(-2)
10
(-9)
1
2
2
0
0
(-2) x (-2) x (-2) n/a n/a
49
5

11.
Complete the following questions pertaining to Powers of 10: a.
Write the following numbers in standard form : i.
2 × 10 0
+ 3 × 10
1
+ 5 × 10
2
= ii.
3 × 10 5
+ 9 × 10
3
+ 1 × 10
1
= b.
Write the following numbers using Powers of 10 : i.
3004 = ii.
12 906 =
12.
On day 1 there are 2 cells, on day 2 there are 4 cells, and on day 3 there are 8 cells (they are undergoing mitosis!). Determine how many cells there will be on day 13.
13.
Write the following as single powers ( if possible ) using your exponent laws : a.
(-7) 3 x 5 3 = _____ d.
7 8 ÷ 7 8 = _____ b.
c.
(-4) x (-4) 9 = _____
9 0 x 9 = _____ e.
f.
2
11
= ______
2
6
(-3) 6 ÷ (-3) = ______
6

14.
Simplify the following problems as much as possible (write as a single power ): a.
5 6 x 5 4 = _____ d.
(-6) 8 = _____
5 x 5 2 (-6) 2 x (-6) 4 b.
2 2 x 2 9 = _____ e.
[(-5) 0 ] 2 = ____
2 3 x 2 6
c.
(3) 2 = _____ f.
(5 5 ) 5 = _____
15.
Write the following in simplified form ( as powers ), then evaluate. a.
[(-2) 2 × (-2) 1 ] 2 + [3 × 3 2 × 3 3 ] = _______________ Evaluated: _________ b.
[(5) 2 × (5) 1 ] 0 + [2 × 2 0 × 2 2 ] = _______________ Evaluated: _________
16.
Simplify the following as a Product of Powers, or a Quotient of Powers: a.
(3 2 x 7) 2 = _______ c.
[(-3) x 4 3 ] 2 = ________ b.
(4 2 ÷ 7) 2 = _______ d.
[(-3) 2 ÷ 9] 2 = ________
7

17.
Evaluate (actually solve for an answer) the following questions; show your steps! a.
(3 2 + 5×2) x 2 + 8 0 b.
– (5 7 + 2 12 × 6 3 ) 0 + 2 3
= =
= =
= =
= =
18.
Write the following numbers in order from least to greatest :
1.25 ,
5
3
, 3
1
3
,
−
11
, -0.5 , -0.56
3
______, ______, ______, ______, ______, ______
19.
List four (4) rational numbers between each of the two values on the number lines listed below.
−0.55
−0.54
5
16
5
4
20.
What rational numbers best represent the following letters below?
A _____
B _____
C _____
D _____
8

21.
Complete the following operations without the use of a calculator. Leave the answers as fractions!
a.
−3
5
+
−1
2
= b.
−2
9
+
5
=
9
c.
−2
4
−
−5
= d.
4
1
4
−
1
3
=
e.
3
5
×
12
= f.
3
−7
5
× 6 =
g.
6
2
÷
2
5
= h.
−1
7
÷
9
7
=
22.
The temperature is quickly falling outside. You read the thermometer and notice it is -2°C. If the temperature falls 1.5°C every 5 minutes, what will the temperature be after 20 minutes from your first reading?
23.
You are trying to make sure you have enough Pop for a birthday party. You realize that every party-go-er will want to drink at least 1 glass ( 0.25L
) of Pop. If you buy 5.5L
and there are 25 people at the party, will you have enough pop? Make sure to show your work in order to explain why you do or do not have enough Pop.
9

24.
Complete the following problems (make sure to show your work, leave fractions as fractions ). a)
(
1
2
+
1
3
)
−2
5 b)
−1.5 ÷ (0.5) 2 c)
(
−2
3
−
7
3
) +
−1
4
= = =
= = =
= = =
= = =
25.
Identify the error(s) in each problem and show a correct solution .
a.
−𝟏
𝟔
+
𝟐
𝟑
×
−𝟒
𝟑 b. (−𝟎. 𝟒 + 𝟏. 𝟐) ÷ (𝟎. 𝟐)
𝟐
=
−1
6
+
−2
6
=
0.8 ÷ (0.2)
2
=
−3
= 0.8
÷ (0.4)
6
= 2
10

26.
Complete the problem below building an equation to represent the pattern. a.
Draw Figure 4 using the pattern below:
Figure 1 Figure 2 Figure 3 Figure 4 b.
Complete the table below relating figure number ( f ) and number of squares ( s ). f s
1
2
3
4
5 c.
Write an equation that relates number of squares (s) and figure number ( f ). d.
How many squares does figure number 220 have? Show your work.
27.
Eight times a number, plus two times a number is 24. Let x and y represent these numbers respectively . a.
Write an equation to describe the relation between x and y . ( 2 pts ) x Y b.
Complete the table to the right using your equation .
1
3
11

28.
Using the equation: y = 2x – 3 x a.
Create a table of values: y
-2
-1
0
1
2 b.
Graph the linear relation
(label axis, etc.)
29.
Match one (1) of the equations below to the graph below. Must show your work (verify/prove that this equation is a match to the line graphed below). a.
y = x + 2 b.
y = -4x + 5 c.
y = 2x + 5 d.
y = -3x + 2
Proof (using one of the three strategies):
12

30.
Using the graph, determine the values below. You may need to extrapolate . a.
When x = 2, y = _____ b.
When x = _____, y = -5 c.
When x = -4, y = _____ d.
When x = _____, y = 3
31.
Let c represent number of cats and d represent number of dogs. When an owner has 1 cat , they have 4 dogs . As the number of cats increase by 1 , the number of dogs in the house increases by 4 .
If I have 10 cats , according to this pattern, how many dogs do I have?
32.
Complete the following table using the polynomials indicated:
Expression
-2x 2 – 6x + 9
# of
Terms
Monomial,
Binomial, or
Trinomial
Degree of
Polynomial
Variable Coefficient(s) Constant
Term
-3y + 8y 2
1
2p + 5
13

33.
Simplify the following polynomials by gathering like terms : a) 5x + 20 – 2x 2 + 2x + 9x 2 – 15 b) 5a 2 – 3b 2 + 6ab – 4a 2 +7ab + 3b 2
34.
Add the following polynomials modeled below and write your answer in symbolic notation:
+
Answer : _______________________________________
35.
Complete the operation indicated on the following polynomials. a.
(2 d 2 – 4d + 8 ) + ( –d 2 + 3d + 6) f.
( 4a 2 – 4ab + b 2 ) – ( –2a 2 + 4ab – b 2 ) b.
( 2x + 3x 2 – 3 ) + ( – x 2 – 6x + 9 ) g.
5(2x 2 – 3x + 12) c.
d.
( a 2 – 12ab + 4b 2 ) + ( 5a 2 + 13ab – b 2 )
( 7x 2 – 3x + 1 )
–
(
–3x 2 –5x + 1 ) h.
i.
– 2w ( 5w + 1)
(4x 2 – 8x + 12) ÷ 2 e.
x(2y – 3x + z) j.
(–6a 2 + 16a)
2a
14

36.
Model the following multiplication problems: a.
–2x(3x – 2) b.
3(2y
2
– 3y + 2)
37.
Write statements for the following model: a.
Multiplication statement: b.
Division statement:
38.
Mr. Oulton has made a few errors in his division question, but he just can’t seem to find out where!
Circle where Mr. Oulton made his errors AND show your work for the correct solution .
(8a 2 – 4ab – 8ac)
–2a
= +8a 2 – 4ab –8ac
–2a –2a –2a
=
–
4a 2 –
2b
–
4c
39.
A square window is cut from a wooden door. If the doors length and width is as shown in the diagram, and the square’s width is as shown, determine the polynomial that represents the area of the door (without the window).
15

40.
Using the arrow diagram below: a) Write the linear equation represented: b) Complete the diagram in order to solve for b
41.
Assuming all of the blocks on the pan balance are positive and that it IS in fact balanced: a.
Write the equation represented by the blocks on the pan balance. b.
Solve for the value of x.
42.
The following model represents a linear equation , where the dotted line represents equivalence (=).
Using this model, complete the following ( show your work!) :
a. Write the equation represented ( using variable x ) : b. Solve for x = _____
16

43.
A car rental company offers a choice of vehicles to rent; both options are listed below:
Truck: $40, plus $3 per hour driven.
Car: $20, plus $6 per hour driven.
a.
Determine how many hours must each be driven so that the costs are equal for renting a truck or car. Show ALL of your work!
b.
How many hours must be driven for the cost of renting the car to be greater than the cost of renting the truck?
44.
Solve each of the following equations for the variable indicated THEN verify . a. -6y + 4 = –12 b.
3x + 7 = –4x – 14 𝒔 c.
𝟒
+ 𝟐 = 𝟒
Verify: Verify: Verify:
45.
List four (4) numbers that are solutions for the following inequality: m ≤ –9
17

46.
Graph the following inequality: x ≤ –9
47.
Graph the following inequality: y > 4
48.
Write an inequality statement for the following graph:
49.
Solve the following linear inequalities for the variable indicated using whichever strategy you wish. a. –6p + 6 > –12 b. 𝒙
𝟐
+ 𝟒 ≤ 𝟖 c. 3.7 > –1.3 + 2.4x
50.
For the inequality p – 3 ≤ 2.6
, are the following numbers solutions? Yes or No. a) – 5 b) 6 c) 2.6 d) 5.9 e) 5.6 f) 9
18

51.
Mrs. Gilbert couldn’t remember how to solve an inequality when variables and constants were on both sides. She tried her best, but Mr. Jones said she made 2 errors. Circle these two (2) errors. Provide the correct solution.
2x + 3 < 5 + 4x
2x + 3 + 3 < 5 + 3 + 4x
2x < 8 + 4x
2x – 4x < 8 + 4x – 4x
–2x < 8
–2x ÷ (–2) < 8 ÷ (–2)
x < –4
52.
Define the following terms and provide an example : a.
Corresponding angles b.
Similar Polygons c.
Line of symmetry d.
Scaled diagram
53.
If a photograph had dimensions 4” by 6” what would the new dimensions be if it were scaled by the following scale factors ? a.
3 b. 12 c. 0.25 d. 0.5
19

54.
The statue of liberty casts a shadow that is 157.7ft long at the same time of day that Mr. Stubbert’s shadow is 3.2ft long. If Mr. Stubbert is 6.2ft tall, determine how tall the statue of liberty is, rounding to the nearest tenth . Draw a diagram to assist you .
55.
Using the Amherst Regional High Logos shown to the right, complete the following questions: a.
Determine if this is considered a scale diagram and why. b.
From the smaller image to the larger image, would we expect the scale factor to be bigger than 1 , less than 1 , or equal to 1 ? c.
What would be considered to have a scale factor equal to 1 ?
56.
Are the following considered similar polygons ? Prove why or why not .
20

57.
In each of the cases below, are the triangles similar? Explain why or why not! a. b.
58.
Determine (if any) which rectangle(s) are similar to the shaded rectangle. Show how you know.
59.
Draw the lines of symmetry in each of the images (if there are any). If no lines of symmetry, say “ no lines of symmetry .”
21

60.
Complete the following table:
Order Angle of Rotation Example
2
120°
61.
Determine the distance across the river (length AB) .
(the diagram around point A as a whole)
22

62.
Describe the symmetry in the following object (multiple choice): a.
1 line of symmetry, order 2 rotation b.
2 lines of symmetry, order 4 rotation c.
1 line of symmetry, order 4 rotation d.
2 lines of symmetry, order 2 rotation e.
4 lines of symmetry, order 2 rotation
63.
Reflect the following image in the line y = 3 :
6
5 y
4
3
2
1
1 2 3 4 5 6 7 x
64.
Using the following diagram: a.
Describe the line of reflection (dotted line). b.
Reflect in this oblique line
65.
Complete each transformation using the original shape: a.
Reflect in the line y = 6. b.
Translate R5, U4. c.
Rotate
90° clockwise about point (2,1), i.e. fix point (2,1).
13
12
11
10
9
8
7
6
5
4
3
2
1
–2
6
5
4
3
2
1 y
4
3
2
1
6
5 y
A
1 2 3 4 5 6 7 8 y
A x
1 2 3 4 5 6 x
23
1 2 3 4 5 6 7 8 x

66.
O is the center of the circle and T , Q, M are points of tangency. Determine the value of x in each case.
S
37°
T
P x°
Q x°
O
53°
O
37°
N
O x°
M
67.
O is the center of the circle and A is a tangency point. Determine the value of m to the nearest tenth.
A
25
O m
25
38
68.
Determine the value of the angle indicated in each of the circles below (think about what kind of triangles these are when the radius is the sides).
B
O
A
52°
B v°
C
O
98° a°
Q
P
T
S b° O
18°
24

69.
Point O is the center of the circle. Determine the value of m to the nearest tenth.
70.
Label the major arc CD and the minor arc CD of this circle. m
O
D
C
71.
O is the center of this circle, determine what the relationship is between
D
A z°
133°
O x°
107° y°
B
O
and
F
72.
Point O is the center of the circle. Determine the values of x, y and z in each diagram.
E
.
C
7
B
12
C
A
25

73.
A pedestrian underpass is constructed using a cylindrical pipe of radius 2.6 m. The bottom of the pipe will be filled and paved. The headroom at the centre of the path is 3.9 m.
How wide is the path to the nearest tenth of a metre?
2.6 m
3.9 m
74.
This arc is part of a circle. Explain how you could locate the centre of the original circle.
75.
a. In a circle, can a chord be longer than a diameter of the circle? Explain
b. In a circle, can a chord be shorter than a radius of the circle? Explain.
76.
A circle has diameter 32 cm. How far from the centre of the circle, to the nearest centimeter, is a chord
20 cm long?
26