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Grade 9 Academic Math Review
I should be able to:
✔
✔
✔
✔
relate their understanding of inverse operations to squaring and taking
the square root, and apply inverse operations to simplify expressions and
solve equations
solve first-degree equations, including equations with fractional
coefficients,
rearrange formulas involving variables in the first degree, with and
without substitution
solve problems that can be modelled with first-degree equations, and
compare algebraic methods to other solution methods.
Unit 3 - Equations
2
a) Write an equation that models the number of magazines John can
afford.
1
Solve.
a)
x5=9
b)
b) Solve the equation.
f −7=3
3
Vocabulary
c) 3h=15
d)
A triangle has angle measures that are related as follows.
➔ The largest angle is twelve times the smallest angle
➔ the middle angle is 5 times the smallest angle
K
=3
4
Find the measure of the angles.
e)
2x5=11
f)
3y−5=−8
4
g)
i)
k)
Correction Notes for Equations Unit Test
John has $23.65 to spend on a book and magazines. The book costs
$5.95. The magazines cost $2.95 each.
m)
104f =−34
5x2=12
−64u=−3
−3r7=−5r −3
h)
−5m−3=12
j) 3p8=5
l)
Find the root of each equation.
a)
1
 x3=5
2
b)
b−5
=3
7
c)
2
6= m−1
3
d)
−5=
e)
4=
5r 7
3
f)
1
 p5=2p−3
3
g)
1
3q15= q−5
2
h)
2b5
=3
4
3d4
3
5x4=2x13
n) 2a5=6a9
➔
➔
o)
3b−7=b5
p)
5n8=8n−10
➔
➔
➔
q)
4a −2−a=6a3−7a
r)
−7d3=−3d11
Complete a formal check for h)
LS =
RS =
5
Find the solution to each equation
a)
 x−5  x 4
=
3
4
b)
d) One number is twenty four times another. If the sum of the two
numbers is 25, then find both numbers.
2
3
 y−2=  y1
4
3
Two friends are collecting pop-can tabs. Natasha has 250 more pop-can
11 tabs than Krysten. Together they have collected 880 pop can tabs. How
many tabs has each friend collected?
e) One number is three more than four times
another. If the sum of the two numbers is 23, then
find both numbers.
c)
b5  b−3
=
3
5
d)
3
1
 v2=  v−3
5
2
12 Justin and Kieran both participated in a walk-a-thon to raise money for
a charity. Justin raised $20 more than Kieran. How much money did
they each raise.
f) One number is six more than six times another. If the difference of
the two numbers is –41, what are the two numbers?
6
Rearrange each formula to isolate the variable indicated
a) motion
F =ma
for m
8
b) voltage
V = IR
for I
The total of three cousins' ages is 8. Suresh is half as old as Hakima
and 4 years older than Saad. How old are the cousins?
13 Jack is selling used computer. He is paid $15/h plus a 5% commission
on sales. What dollar amount must Jack make to earn $1000 in a 40-h
work week.
c)areaof a circle
d)Perimeter of a rectangle
A = ∏r2
P = 2l + 2w
for r
for w
9
Adila sells T-shirts at a rock concert. She earns $8.00 per hour plus
$0.50 for each T-shirt she sells.
a) How much will Adila earn in a 4 hour shift if she sells 35 T-shirts?
e) Linear Relations
y = mx + b
14
for x
b) How many T-shirts must Adila sell to earn $80 in a 6 hour shift?
7
Alicia and Wayne are both collecting coins. Alicia has three times as
many coins as Wayne. Together they have 712 coins. How many coins
do they each have?
a) The sum of three consecutive integers is 24. Find the
three consecutive integers?
10 Ramesh sells hot dogs at a baseball game. He earns $8.50 per hour
plus $0.35 for each hotdog he sells.
b) The sum of three EVEN integers is 42. What are the
three EVEN integers?
a) How much will Ramesh earn in a 4 hour shift if he sells 52 hotdogs.
The length of the banquet hall where John works is double its width.
15 The area of the banquet hall is 200 m2.
b) How many hotdogs must Ramesh sell to earn $103 in an 8-h shift.
c) The sum of three ODD integers is –33. What are the three ODD
integers?
c) How many hotdogs must Ramesh sell to earn $79 in
an 6-h shift.
a) find the length and the width of the banquet hall
b) How much shorter would it be for John to walk across
the diagonal of the banquet hall instead of around the the
perimeter (2 sides)