MATH 9 YEAR END REVIEW
Name: ____________________ ______________________
Block: _____
You may use your toolkits to help you with this review, but you will not be able to use them
to write your final exam.
There is an answer key at the end of the booklet. Please mark your work after each
section, then indicate any questions you need to review in the table below.
Note that there is no Chapter 9 in this review package since it was the last chapter we
completed.
Unit
1 – Square Roots and Surface
Area
2 – Powers and Exponent
Laws
Page
#
1
2
3 – Rational Numbers
3
4 – Linear Relations
4
5 - Polynomials
5
6 – Linear Equations and
Inequalities
7 – Similarity and
Transformations
8 – Circle Geometry
6
7
8
Questions I need to review
Math 9
Year End Review
Unit 1 – Square Roots and Surface Area
1. (T / F) A number is a perfect
square if it is made by
multiplying the same number
by itself.
2. Circle the numbers that are
perfect squares:
1, 2, 3, 4, 5, 6, 7, 8, 9
3. Find the value of each
square root.
1
(a)
(b) 0.16
25
4. Calculate the number whose
square root is:
12
(a) 0.7
(b)
17
5. Which of the following are
perfect squares?
4
2
, 0.016 ,
, 0.09 , 0.0121
49
13
6. Estimate:
7. (a) How do you find the surface area of a
rectangular prism?
(b) How do you find the surface area of a
triangular prism?
(a)
65
4
(b)
0.8
8. (a) What is the formula for surface area of a
cylinder?
(b) How does the formula change if one end is
missing from the cylinder? Both ends?
9. This object is built with 1-cm cubes. Find its
surface area.
10. Find the surface area of:
11. Calculate the surface area of this composite
object:
12. Calculate the surface area of this composite
object:
1
Math 9
Year End Review
Unit 2 – Powers and Exponent Laws
1. What is the difference
between 23 and 32?
2. Which of the following are
equal? –32, (–32), – (3)2, (–3)2
3. Evaluate:
(a) –(–3)4
(b) (–5)6
(c) –42
(d) (–4)2
(e) –70
(f) (–7)0
4. Evaluate: [3 x (–2)3 – 4]2
5. Evaluate: 72 – (–4)3 x 40 + 32
6. Why do (–4)2 and –42 give
different answers?
7. When powers are multiplied,
what do you do with the
exponents?
8. When powers are divided,
what do you do with the
exponents?
9. When powers are raised to
an exponent, what do you do
with the exponents?
_________________________
_________________________
________________________
mx x my = m ---------
mx ÷ my = m ---------
(mx)y = m ----------
10. Express as a single power,
then evaluate:
11. Simplify, then evaluate:
12. A student answered the
following skill-testing question
to try to win a prize:
(a) (–3)6 ÷ (–3)2 x (–3)4
4
(a) (–2) x (–2)
2
(–4)3 – (–2)4 ÷ 22 + 52 x 70
(b) 664 ÷ 661
(b)
813  (8 7 ) 2
815  8 9
The student’s answer was 5.
Did they win the prize?
c) (42)3
2
Math 9
Year End Review
Unit 3 – Rational Numbers
1. Which of the following are
NOT rational numbers? Why?
2
3.1,  1.25 , –3.225, π,  ,
3
0.3 , 9 , 2
2. (T / F) Converting rational
numbers to the same form is a
good idea when you are trying
to compare them.
3. Order the following from
least to greatest.
7
24
–4, –3.6,  , –1, 
7
2
4. (a) (T / F) A common
denominator is required to add
or subtract fractions.
5. Evaluate:
6. Evaluate:
(a) –8.38 + (–1.93)
(a) (–14.6)(2.5)
(b) (T / F) You add or subtract
the denominators when adding
or subtracting fractions.
(b) – 4.5 – (–13.7)
(b) (–8.64) ÷ (–2.7)
(c) 
3 2

4 3
3  2 

(c)   8  2 
4  15 

(d) 3
5 
2
  2 
6 
3
(d)  3
(c) (T / F) A common
denominator is required to
multiply or divide fractions.
(d) (T / F) It is a good idea to
convert mixed numbers to
improper fractions first before
doing any operations.
8. Evaluate:
7. (T / F) Following BEDMAS is
only needed some of the time.
(a) (–2.1)(18.5) – 6.8 ÷ 4
(b) [–7.2 – (–9.1)] ÷ 0.5 + (–0.8)
1
2
2
5
3
9. Evaluate:
 7 1  3  1
(a)       

 8  5  10  4
1  6 
1  2

(b)   7    1    
3
55
2

 
 7
10. During the month of July, Bruce earned $225 cutting lawns and $89.25 weeding flower beds. He
spent $223.94 on an MP3 player and purchased 3 DVDs at $22.39 each.
(a) Write an addition statement for Bruce’s balance at the end of July.
(b) What is Bruce’s balance?
3
Math 9
Year End Review
Unit 4 – Linear Relations
1. The pattern in this table
continues:
Term #, n Term value, v
1
5
2
7
3
9
4
11
Write an equation that
relates v to n.
2. Use your answer from
question 1:
4. Does each equation
describe a vertical line,
horizontal line, or oblique
line? How do you know?
5. Carl is cycling across
Canada. This graph shows the
distance he covers in 10 days.
3. Create a table of values for
y = 3x – 2 and graph the data.
(a) Determine the value of the
24th term.
(b) Which term number has a
value of 233?
6. Match each equation with a graph
below.
(a) x + 2y = 5
(b) 2x + y = 5
(a) 2x = 5
(c) 2x – y = 5
(b) y + 2 = –1
(a) Estimate how many days it
will take him to cycle 700 km.
(c) x + y = 3
(b) Predict how far Carl will
cycle in 13 days.
(c) In answering (b), were you
interpolating or extrapolating?
4
Math 9
Year End Review
Unit 5 – Polynomials
1. Match each letter to the appropriate
description:
A. Variable:
an unknown quantity represented by a
letter.
B. Term:
a product of letters and/or numbers
including single variables or
constants.
C. Binomial: an expression with two terms.
D. Monomial: an expression with one term.
E. Constant: a number on its own that does not
change.
F. Trinomial: an expression with three terms.
G. Polynomial: an expression made up of any
number of terms.
H. Coefficient: a number in front of a variable that
does not change.
I. Degree:
the highest sum of the exponents in a
single term.
2. (a) Simplify and write your answer as a polynomial. Recall that white tiles are positive and shaded
tiles are negative.
(i) What is the 3 called in 3x4 + 5? _____
(ii) What is the x called in 3x4 + 5? _____
(iii) What is the 5 called in 3x4 + 5? _____
(iv) What is 3x4 called in 3x4 + 5? _____
(v) 3x2, 4y2 – 7y and 2x2 + 2x all have the
same what? _____
(vi) 2y is an example of what? _____
(vii) 3x4 + 5 is an example of what? _____
(viii) x + y + z is an example of what? _____
(ix) 3x4 + 5 and x + y + z are examples of
what? _____
(b) Which of the following can be represented by the same set of algebra tiles and are therefore
equivalent?
7x – 4 + 3x2
-7x + 4 + 3x2
3x2 + 4 – 7x
3x2 – 7x + 4
3.
(a) (T / F) 3x + 4x2 = 7x3
4. Simplify each polynomial:
(a) 2a – 4 – 9a + 5
(b) (T / F) 3x – 8x – 2x2 + 4x2 = -5x + 2x2
(c) (T / F) Like terms have the same variable and
the same exponents.
(b) 4m2 – 3n2 + 2m – 3n + 2m2 + n2
5. Add or subtract:
6. Determine each product or quotient:
(a) (3s2 – 2s + 6) + (7s2 – 4s – 3)
(a) 9(3s2 – 7s + 4)
(b) 7m(3m – 9)
(b) (2 – 5x + 8x2) – (5x2 + 3x – 4)
(c)
(c) (–8x2 + 7x + 9) – (6x2 – 5x + 2)
35  49w 2  56w
7
(d) (–12d2 + 18d) ÷ (–6d)
5
Math 9
Year End Review
Unit 6 – Linear Equations and Inequalities
1. Solve for x:
2. Solve for x:
3. Solve for x:
4. Solve each equation:
(a) 9x = 7.2
(b)  2.7 
(c) 6.5s – 2.7 = –30
(d)
5. Solve each equation:
6. Solve:
(a) 22 – 7d = –8 – 2d
(a) 6(n – 8.2) = –18.6
a
4
c
 0.2  5.8
4
(b) 2(t – 8) = 4(2t – 19)
(b) 3.8v – 17.84 = 4.2v
7. (a) (T / F) To eliminate fractions, multiply both
sides by the lowest common denominator.
(b) Solve:  8 
(c) Solve:
72
c
m 2m 1

 2
3
5
2
9. Write an inequality to represent each of the
following:
(a)
8. (a) (T / F) When an inequality is multiplied or
divided by a negative number, the direction of the
inequality changes.
(b) Solve: 7m + 23 ≤ 6m – 15
(c) Solve: 6.5 – 0.2t > 8
10. Daphne will sell her video game system for
$120 to Surinder. She also offers to sell him
video games for $15 each. Surinder has saved
$210. How many video games can he buy from
Daphne? Write and solve an inequality.
(b)
6
Math 9
Year End Review
Unit 7 – Similarity and Transformations
1. Determine the scale factor. The original image
is on the left.
2. A drawing of a bedbug is 2.2 cm long. The
actual size is 0.95 cm. Determine the scale
factor.
3. A hockey rink measures 60 m by 26 m. A
model of a hockey rink measures 1.5 m by 0.65
m.
(a) What is the scale factor?
4. Bobbi wants to determine the height of a
building. When Bobbi’s shadow is 2.5 m long, the
shadow of the building is 12 m long. Bobbi is 1.7
m tall. What is the height of the building to the
nearest tenth of a metre?
(b) A hockey goal is 1.8 m by 1.2 m. What are
the dimensions of a goal on the model hockey
rink?
5. Are these two triangles similar? How do you
know?
6. Describe the location of each line of symmetry
to make each polygon a reflection of the shaded
polygon.
A)
B)
C)
7. For the following shape:
8. For the following shape:
(a) How many lines of symmetry?
(a) How many lines of symmetry?
(b) Order of rotational symmetry?
(b) Order of rotational symmetry?
(c) Angle of rotational symmetry?
(c) Angle of rotational symmetry?
7
Math 9
Year End Review
Unit 8 – Circle Geometry
1. What is the value of xº? How do you know?
2. Point G is a point of tangency and O is the
centre of the circle. Determine the length of GH
to the nearest tenth of a centimeter.
3. Find the measures of xº and yº.
4. How far from the centre of this circle is a chord
18 cm long?
5. Find the value of x:
6. Why does angle x equal 120º?
7. Find the measures of bº and cº.
8. Which angle(s) measure 90º? How do you
know?
8
Math 9
Year End Review
ANSWER KEY
Unit 1 – Square Roots and Surface Area (p.1)
1. T
2. 1, 4, 9
3. (a)
1
5
(b) 0.4
5.
4
49
, 0.09, 0.0121
144
289
4. (a) 0.49 (b)
6. (a) 4 (b) 0.89 or 0.9
7. (a) Add up the areas of all the faces (top/bottom,
left/right, front/back)
(b) Add the areas of the two triangles ( bh each) and
2
the three rectangles (l x w each)
8. (a) 2πr2 + 2πrh
(b) one end missing: πr2 + 2πrh
(c) Both ends missing: 2πrh
9. 24 cm2 10. 36 m2 11. 72 cm2 12. 155.2 cm2
Unit 3 – Rational Numbers (p.3)
1. π and
2. T
2
3. –4, –3.6,
7

2
,
24

7
, –1
or
1
2
4. (a) T (b) F (c) F (d) T
1
12
5. (a) –10.31 (b) 9.2 (c)

6. (a) –36.5 (b) 3.2 (c)
56
3
(d)

6
5
or

or
(d)
18
13
2
6
2
3
1
1
5
7. F 8. (a) –40.55 (b) 3
9. (a)
11

24
(b)
121

20
or
1
6
20
10. (a) 225 + 89.25 + (–223.94) + 3(–22.39)
(b) $23.14
Unit 5 – Polynomials (p.5)
1. (i) H (ii) A (iii) E (iv) B (v) I (vi) D (vii) C
(viii) F (ix) G
2. (a) 3x2 – 4x + 9
3. (a) F (b) T (c) T
4. (a) –7a + 1 (b) 6m2 + 2m – 3n – 2n2
5. (a) 10s2 – 6s + 3 (b) 3x2 – 8x + 6
(c) –14x2 + 12x – 7
6. (a) 27s2 – 63s + 36
(b) 21m2 – 63m
2
2
(c) –5 + 7w + 8w or 7w + 8w – 5
(d) 2d – 3
Unit 7 – Similarity and Transformations (p.7)
1. SF = 3 2. SF = 2.3
3. (a) SF = 0.025
(b) 0.045 m by 0.03 m (or 4.5 cm by 3 cm)
4. 8.2 m
5. No. Angles and ratios of corresponding sides
are different.
6. A) vertical line through 5 on x-axis
B) horizontal line through 3 on y-axis
C) oblique line through (0,0) and (5,5)
7. (a) 4 (b) 4 (c) 90º
8. (a) 0 (b) 3 (c) 120º
Unit 2 – Powers and Exponent Laws (p.2)
1. 23 = 2 x 2 x 2 = 8 but 32 = 3 x 3 = 9
2. –32, – (3)2, and (–32) all equal –9. (–3)2 equals 9
(positive).
3. (a) –81 (b) –15625 (c) –16 (d) 16 (e) –1
(f) 1
4. 784
5. 122
6. (–4)2 = (–4)( –4) = 16 but –42 = -(4)(4) = –16
7. add them; mx+y
8. subtract them; mx-y
9. multiply them; mxy
10. (a) (–2)6 = 64 (b) 63 = 216 (c) 46 = 4096
11. (a) (–3)8 = 6561 (b) 83 = 512
12. No, the answer is –43.
Unit 4 – Linear Relations (p.4)
1. v = 2n + 3
2. (a) 51 (b) 115
3. x y
–1 –5
0 –2
1 1
2 4
3 7
4. (a) vertical line (x = 2.5)
(b) horizontal line (y = –3)
(c) oblique line (y = -x + 3)
5. (a) approx. 5.5 days (b) approx. 1600 km
(c) extrapolating
Unit 6 – Linear Equations and Inequalities (p.6)
1. x = 3
2. x = 2
3. x = 3
4. (a) x = 0.8 (b) a = -10.8
(c) s = -4.2 (d) c = 24
5. (a) d = 6 (b) v = -44.6
6. (a) n = 5.1 (b) t = 10
7. (a) T (b) c = -9 (c) m =
75
22
or
3
9
22
8. (a) T (b) m ≤ -38 (c) t < -7.5
9. (a) x < 1 (b) x ≥ 3
10. 120 + 15g ≤ 210; g ≤ 6
Unit 8 – Circle Geometry (p.8)
1. 90º. It is a tangent line meeting a radius at the point of
tangency.
2. 15.0 cm
3. x = 46º y = 33º
4. x = 10.1 cm
5. 19.6
6. Angle x is a central angle on the same arc as the 60º
inscribed angle, so it is twice the measure of the
inscribed angle.
7. b = 44º; c = 43º
8. Angles w and z. They are inscribed angles on a
semicircle.
9