Grade 9 Math – Review Sheet
UNITS 1) NUMERACY (CH. 1)
2) RELATIONSHIPS (CH. 2)
3) POWERS AND ROOTS (CH. 5)
4) ALGEBRA (CH. 6, 7)
5) SLOPES AND LINES (CH. 3, 4, 8)
6) MEASUREMENT (CH. 10)
7) GEOMETRY (CH. 11)
8) STATISTICS (CH. 9)
1.
a) Define the following number sets: N, I, Q.
b) List the following number sets:
i) All multiples of 8 Between -35 and 14.
ii) All “proper” fractions with denominator less than 6.
2.
Evaluate the Following Expressions in Simplest Form:
a) 12 + (-13) – (-6)
c)
b)
d)
e)
f)
3.
Change these to Decimals:
4.
Change these to fractions in lowest terms:
5.
Graph these on a number line: -3, 0.2,
6.
Find:
7.
Simplify:
8.
“Crazy David’s” is having a sale on stereos. What would you pay for a $399 stereo if it is being
sold at a 30% discount, including 15% sales tax?
9.
3 “Ex – Teenagers” find that the product of their ages is 17710. How old are they?
10.
Illustrate, on a number line, the “difference” between -11 and -3, and write the corresponding
“equation”.
11.
A rectangular lawn has dimensions 24m by 30m. A 6m strip is cut from the outside. What
percent of the lawn has been cut?
12.
A pump removes ¼ of the air from a vacuum chamber with every stroke. What fraction of the
air remains after 3 strokes?
a) 60% of $2000
a)
b)
c)
a) 0.35
b) -1.24
d)
c)
d) 0.0013
,
b) 0.5% of $400
a)
b)
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Grade 9 Math – Review Sheet
13.
The graph gives the total distance travelled by a falling
object, in metres, during a 4 second fall. Determine:
a) The distsance fallen after 1s? 2s?
b) Approximately how long did it take to fall 30m?
c) How far did it fall during the last 2s?
d) What was the average speed of the object:
i) During the first 2 seconds?
ii) For the whole fall>
14.
The graph gives the distance from a wall during an 8s
walk wit ha CBR (in metres).
a) Describe the motion “verbally”!
b) How fast was the person walking toward the wall?
15.
2.5kg of peanuts cost $12.25.
a) How much will 8.2kg cost?
b) How many kilograms can you purchase for $34.50?
c) Draw a graph to show the cost of any amount of peanuts (up to 10kg).
16.
Evaluate these in standard form (exact answers):
17.
a) 25
c) (-2)3
e) 2-3
g) (-6)0
i)
b) 50
d) 3-2
f) (-4)-2
h) -60
j)
Write in simplest form (Answers may be left in exponential form):
a)
c)
e)
g)
b)
d)
f)
h)
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i)
Grade 9 Math – Review Sheet
18.
Write in standard form:
a)
19.
b)
c)
Write in scientific notation:
a) 311 000 000 000
20.
Explain why we define
21.
Evaluate:
b) 0.000 000 0412
c)
and
.
a)
c)
e)
g)
b)
d)
f)
h)
22.
State Pythagorean Theorem.
23.
Find the unknown side in each of the following triangles:
a)
b)
c)
24.
A rectangle has length 5cm and width
25.
“Alpha Centauri” is approximately 4 light years from our solar system. If light travels at
, how many kilometers away is Alpha Centauri?
26.
One water molecule has a mass of about
molecules in Lake Superior, which holds about
27.
Simplify:
a)
b)
cm. How long is its diagonal?
c)
Page 3
. Calculate the number of water
of water.
d)
Grade 9 Math – Review Sheet
28.
A box has dimensions 3m by 4m by 5m. Find the length of its main diagonal. (Upper vertex to
opposite lower vertex)
29.
Use the letters a, b, and c to state the distributive property for multiplication over addition.
30.
Use distributive property to show why
31.
Simplify:
32.
Solve the following equations by inspection:
a)
33.
b)
.
c)
d)
Solve for x:
a)
e)
i)
b)
f)
j)
c)
g)
k)
d)
h)
34.
Show that -2 is a root of
.
35.
Solve the following problems with the aid of suitable algebraic models.
a) Steve paid a library fine of $1.60 using nickels, dimes, and quarters. The number of nickels
was 2 more than the number of dimes, and the number of quarters was 2 less than the
number of dimes. How many of each were there?
b) Sam’s age is twice Jennie’s age. Three years ago the sum of their ages was 45. How old is
Jennie today?
c) One of the equal sides of an isosceles triangle is 3m less than twice its base. The perimeter
is 44,. Find the lengths of the sides.
d) How many milliliters of 50% acid solution must be mixed wit h30% solution to produce
100mL of 45% solution?
e) A garden is 20m by 25m. It is surrounded by a walkway whose outside perimeter is 114m.
What is the (uniform) width of the walkway?
f) A can left a service centre on Highway 401 and drove east at 80km/h. Fifteen minutes later,
a second car left the same service centre and drove east at 100km/h. How long did it take
the first car to be overtaken by the second car?
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Grade 9 Math – Review Sheet
g) Candy A costs $7.50/kg and Candy B costs $5.00/kg. How many kilograms of each should
be used to obtain 10kg of a mixture worth $6.00/kg?
h) A freight train travelling 60km/h takes 1 hr longer than a passenger train travelling at
80km/hr for a trip between 2 stations. Find the distance between the stations.
36.
For the polynomial
, state:
b) The degree of the 2nd term.
D) the degree of the polynomial.
a) The number of terms.
c) The coefficient of the 2nd term.
37.
Simplify the following polynomial expressions:
a)
b)
c)
d)
e)
38.
Simplify:
a)
d)
f)
b)
e)
g)
c)
39.
Factor:
a)
b)
c)
d)
40.
Draw a diagram to show why
41.
Simplify, then factor:
42.
Write
e)
f)
.
:
a) As a trinomial.
b) As a product of 2 binomials.
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Grade 9 Math – Review Sheet
43.
Graph the following functions:
a)
b)
c)
d)
e)
f)
44.
In question 43:
a) Which of these relations are linear?
b) Which of the lines can be graphed by finding its x-intercepts and y-intercepts?
45.
On a set of co-ordinate axes, draw a line through the given point, with the given slope:
46.
a)
b)
c)
d)
e)
f)
Find the slope of each of the following lines.
a) The line on A(3, 2) and B(10, 4).
b) The line on C(-6, 1) and D(2, -3).
c) The line with x-intercept 4 and y-intercept 5.
d) The line
.
e) The line
f) The line parallel to
.
.
g) The line perpendicular to
47.
.
Find the equations of each of the following lines. Write your answer in the form
or
:
a) The line on (-2, 1) with slope -1.
b) The line on (3, 2) and (0, -2).
c) The line with slope
and x-intercept 5.
d) The line parallel to
e) The line on (-2, -2), perpendicular to
with y-intercept -1.
.
48.
a) Find the point of intersection of
and
(Graphically).
b) Find the equation of the line which passes through this point, parallel to the y-axis.
49.
How do you find the perimeter of:
a) Any polygons?
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b) Any Circle?
Grade 9 Math – Review Sheet
50.
Match each of the following formulas wit ha labeled diagram:
51.
Find the Perimeter and area of each of the following figures:
a)
b)
d)
c)
e)
f)
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Grade 9 Math – Review Sheet
52.
a)
Find the volume of each of the following figures:
b)
c)
d)
53.
An open-topped box has a square base, and a volume of 4000cm3.
a) Find the dimensions of 4 such boxes.
b) Find the surface area of each of your boxes.
c) Find the surface area of the box whose dimensions are
.
d) Find a formula for surface area in terms of x. (Remember, the volume is always
4000cm3).
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Grade 9 Math – Review Sheet
54.
Find the unknown angles in the following diagrams:
a)
b)
c)
d)
e)
f)
g)
h)
i)
55.
Using Ruler and compasses, show that the right bisectors of the 3 sides of 2 different triangles
are concurrent (pass through the same point), and show that this point is the centre of a circle which
passes through the 3 vertices of the triangle.
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Grade 9 Math – Review Sheet
ANSWERS:
1.
a) N  {1, 2,3,...}
b) I  {..., 2, 1,0,1, 2,...}
c) Q   | a, b  I , b  0
a
b


1
24
2.
a) 5
b) -14
c) 
3.
a) 0.875
b) 0.26
c) 0.857142
4.
a)
7
20
b) 
31
25
6.
a) $1200
b) $2
7.
a)
11
4
b) 
8.
$321.20
9.
22, 23, 35
c)
1
3
d) -1
e)
1
3
f) 
1
2
d) -3.4
d)
13
10000
5.
4
47
10.
11.
70%
12.
27
64
13.
a) 5m
14.
a) Start 2m from wall, walk 1m towards the wall in 2s. Stand still for 3s. Walk 3m away from
wall for 3s.
b)
b) 20m
c) 60m
d) 10m/s, 20m/s
1
m/s
2
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Grade 9 Math – Review Sheet
15.
a) $40.18
b) 7kg
16.
a) 32
b) 1
c) -8
d)
1
16
g) 1
h) -1
i)
a) 420
b) 7-2
c) 5-1
d) 522
f) 2-12
g) 9000
h) 512
i)
f)
17.
1
9
1
16
e)
1
8
j) 16
e) 63
9
4
18.
a) 64100000
b) 0.00031
c) 0.000027
19.
11
a) 3.1110
9
b) 4.12 10
8
c) 4 10
20.
a0  a n  a0 n  a n
an
a  n  1
a
0
21.
a) 30
b) 31
g) 8-3
h) 2
22.
c 2  a 2  b2
23.
a) 17
b) 24
d)
4
5
d)
16
9
c) 6
31cm
24.
25.
150868224000000 km
26.
4 1041 molecules
27.
a)
28.
c) 9
an  an  ann  a0  1
1
 an  n
a
169
81
b) 4
c) 45
50
29.
a(b + c) = ab + ac
30.
6a + 4a = a(6 + 4) = 10a
31.
5x + y + 6
Page 11
e) 9
f) 3
Grade 9 Math – Review Sheet
32.
a) 6
33.
a)
8
5
g) 18
b) 3
c)  11
d) 25
b) 21
c) 45
d) -7
e) 1
h) 6
i) -21
j) 9
k) 2
34.
If x = -2, then -8 + 4 + 10 – 6 = 0, and thus, -2 is a root.
35.
a) 7 nickels, 5 dimes, 3 quarters
b) Jennie is 18 years old
c) 75 mL of 50% and 25mL of 30%
d) 10m, 17m, 17m
e) 3m
f) 1 hr
g) 4kg of A and 6kg of B
h) 240km
36.
a) 4
37.
a) 7 x2  5x  2
b) -12
c) 3
b)  y  3
38.
5
a) 7a 2
b) 20x
2
g) -6a – 4b + 5b
39.
a) 6(2x + 3)
e) 2 r  r  h 
d) 4
c) 8a  18
6 3
c) 12a b
b) x2(x + 8)
f)  2 x  y  a  4
7  2 x 2  5 x  1
42.
a) 6x2  x  35
d) 2x3  11x2  7 x  4
4
d) 3a
c) 5a(5a – 8b)
40.
41.
f) 2
b)  2 x  5 3x  7 
Page 12
e) 4mp
e) 5n2  24n 16
f) 4a + 3b
d) 3x(3x2 + 4x + 5)
Grade 9 Math – Review Sheet
43.
44.
a) All but y2 = 4x.
b)
a), b), and d)
45.
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Grade 9 Math – Review Sheet
2
7
b) 
1
2
c) 
5
4
46.
a)
47.
a) x  y  1  0
e) 5x  4 y  2  0
48.
a)
b) x = -3
49.
a) P = sum of the sides
b) P  2 r
b) 4x  3 y  6  0
d)
3
2
c) x  2 y  5  0
50.
Page 14
e) 
2
5
f) 0
d) 3x  2 y  2  0
g)
7
3
Grade 9 Math – Review Sheet
51.
a) P = 60, A = 150
b) P = 30, A = 40
c) P  10  2 8 , A = 16
d) P  12 , A  36
e) P  13  7  20  10, A  17
9
2
f) P    17, A  36 
52.
a) 40
1
2
81

8
b) 18
c) 144
d) 180 3
53.
b) Use A  2hl  2hw  2lw , for your sample.
c)
A  4 xy  x 2
d)
x 2 y  4000
4000
y  2
x
 4000 
 A  4x  2   x2
 x 
16000
A
 x2
x
Page 15
e)
2500
3
Grade 9 Math – Review Sheet
54.
a) x = 35, y = 75
d) x= 110
g) x = 130
b) x= 108
e) x = 93
h) x = 50
c) x = 30
f) x = 55
i) x = 15
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