### Review Semester I Final

```The following diagram shows a triangle
with sides 5 cm, 7 cm, 8 cm.
7
5
diagram not to scale
Determine if this could be a right triangle.
8
No, it could not.
The diagram shows a rectangular prism 22.5 cm
by 40 cm by 30 cm.
H
E
G
F
40 cm
D
C
30 cm
A
22.5 cm
B
Calculate the length of [AC].
37.5 cm
x = 1.28 m
4.70 m
The following diagram shows a carton in the shape
of a cube 8 cm long on each side:
(a) The longest rod that will fit on the bottom of the carton
would go from E to G. Find the length l of this rod.
= 11.3 cm
(b) Find the length L of the longest rod that would fit
inside the carton.
= 13.9 cm
B
C
D
A
F
B
G
H
A square garden with sides 100 m is divided into
two triangular plots by a fence along one diagonal.
a) What is the length of the fence in meters?
141 m
b) If the fence costs \$15.50 per meter, what is the
total cost?
\$2186
In the diagram below, PQRS is the square base of a solid
right pyramid with vertex V. The sides of the square are 8
cm, and the height VG is 12 cm. M is the midpoint of [QR].
Diagram not to scale
(a) Write down the length of [GM].
= 4 cm
(b) Calculate the length of [VM].
V
P
Q
G
S
8 cm
8 cm
M
R
= 12.6 cm
Two ships B and C leave a port A at the same time.
Ship B travels in a direction 067 at a constant
speed of 36 km/h. Ship C travels in a direction
157 at a constant speed of 28 km/h.
Find the distance between them after 2 hours.
91.2 km
Find the value of any unknown.
x  29  5.39cm
y  45  6.71cm
A sailing ship sails 46 km North and then 74 km
East.
How far is the ship from its starting point?
= 87.1 km
Simplify
a)
(4x3y5)3
 64x y
9 15
7
4
x y
b) 2 6
x y
5
x
 2
y
Simplify
6
 2c  64c
a)     6
d
 d 
6
 2x 
b)  3 
 y 
2
2
6
y
 4
4x
Solve for x:
5(x + 2) – 2(3 – 2x) = 3
1
x
9
Solve for x:
x(2x + 1) – 2(x + 1) = 2x(x – 1)
x=2
Solve for x:
4x  7 5  x

11
2
41
x
19
Solve for x:
5
11

4x
12
15
x
11
Solve for x:
2x  5
 4
x 1
1
 x
6
Solve for x.
4x = 8
3
x
2
Solve for x.
9
x 2
1

3
3
x
2
solve by elimination
2x + 7y = 2
3x + 5y = -8
(-6, 2)
solve by substitution
5x – y = -11
4x + 12y = 4
(-2, 1)
A caterer is planning a party for 232 people.
•The customer has \$808 to spend.
•A \$32 pan of pasta feeds 8 people and a \$36 sandwich
tray feeds 12 people.
•How many pans of pasta and how many sandwich
trays should the caterer make?
p = no. of pans of pasta
w = no. of trays of sandwiches
32p + 36w = 808
p = 14
8p + 12w = 232
w = 10
14 pans of pasta
10 sandwich trays
The bill for 3 Big Macs and 2 Cokes is 59 Bsf.
The bill for 7 Big Macs and 8 Cokes is 161 Bsf.
What would be the bill for 2 Big Macs and 1
Coke? b = cost of 1 Big Mac
c = cost of 1 Coke
3b + 2c = 59
b = 15 Bsf
7b + 8c = 161
c = 7 Bsf
2 Big Macs and 1 Coke would cost
37 Bsf.
Your family is planning a 10 day trip to Florida. You
estimate that it will cost \$350 per day in Orlando and
\$310 per day in Miami. Your total budget for the 10
days is \$3220. How many days should you spend in
each location?
m = no. of days in Miami
d = no. of days in Orlando
m + d = 10
m=7
350d + 310m = 3220
d=3
7 days in Miami
3 days in Orlando
George is 10 years older than Jane.
Three years ago Jane was ¾ as old as
George. How old is George now?
George is 43 years old.
Write as powers of 2, 3, or 5
1
a)
4
=2-2
1
b)
x
27
=3-3x
5
c) 125  5
=5-2
Solve for x.
1
x1
 32
2
4
x
5
Find the equation of the line that goes
through the points (-3, 6) and (-2, 4).
y = -2x
Write the equation, in standard form, of the
line that passes through (-2, 5) and (3, 1)
4 x  5 y  17
Write the equation of the line, in standard form,
with slope  3 and containing the point (4, -1).
4
3x + 4y = 8
Given that M is the midpoint of PT, find the
coordinates of T if P is (6, -2) and M is  4,  11 

T is (2, -9)
2
Find the midpoint of the line segment
AB given A(-5, -3) and B(9, 3)
(2, 0)
Find the distance between (2, -4)
and (-5, -1)
Find the negative value of b given that the
distance between (-2, 5) and (3, b) is 61
-1 = b
A line passes through the point (-5, -7)
and has a slope of 10. Write the
equation for this line in slope-intercept
form.
y = 10x + 43
Graph x + 2y = 4
Write the equation of the graph below.
Graph x = -2
Graph 3x – 5y = 15
by finding the x- and y-intercepts
x-intercept: y-intercept:
3x – 5(0) = 15 3(0) – 5y = 15
x=5
y = -3
8
6
4
2
(5, 0)
(0, -3)
-8 -7 -6 -5 -4 -3 -2 -1
-2
-4
-6
-8
1 2 3 4 5 6 7 8
Graph the line with slope 0 and containing
the point (3, -5)
Use technology to find the point of
intersection of 5x – y = -11 and
4x + 12y = 4.
(-2, 1)
Write the equation, in standard form, of the
line containing the point (-1, 3) and parallel
to the line 3x + 7y = 70.
3x + 7y = 70
3
y   x  10
7
3
m
7
3 x  7 y  18
Write the standard form of the equation of the
line perpendicular to x – 6y + 30 = 0
and passing through the point (5, 3)
6x + y = 33
Use the distance formula to determine if
triangle ABC is scalene, isosceles or
equilateral.
A(2, 1) B(3, -2) C(5, 2).
isosceles
AB  10
BC  20
AC  10
Formulae you will need to know:
•
•
•
•
•
Distance
Midpoint
Slope
Slope-intercept
Pythagorean theorem
45
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