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The following diagram shows a triangle with sides 5 cm, 7 cm, 8 cm.
5 7
8
diagram not to scale
Determine if this could be a right triangle.
No, it could not.
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The diagram shows a rectangular prism 22.5 cm by 40 cm by 30 cm.
Calculate the length of [AC].
37.5 cm
H G
E F
A B
D C
40 cm
30 cm
22.5 cm
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x = 1.28 m
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4.70 m
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= 11.3 cm
The following diagram shows a carton in the shape of a cube 8 cm long on each side:
B C
B H
AD
GF
(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.
(b) Find the length L of the longest rod that would fit inside the carton. = 13.9 cm
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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?
b) If the fence costs $15.50 per meter, what is the total cost?
141 m
$2186
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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].
(b) Calculate the length of [VM].
V
P
G
Q
M
RS 8 cm
8 cm
= 4 cm
= 12.6 cm
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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
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Find the value of any unknown.
29 5.39x cm
45 6.71y cm
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A sailing ship sails 46 km North and then 74 km East.How far is the ship from its starting point?
= 87.1 km
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7 4
2 6)
x yb
x ya) (4x3y5)3 9 1564x y
5
2
x
y
Simplify
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22
3
2)
xb
y
62
)c
ad
6
6
64c
d
6
44
y
x
Simplify
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Solve for x:5(x + 2) – 2(3 – 2x) = 3
1
9x
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Solve for x:x(2x + 1) – 2(x + 1) = 2x(x – 1)
x = 2
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Solve for x: 4 7 5
11 2
x x
41
19x
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Solve for x: 5 11
4 12x
15
11x
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Solve for x: 2 54
1
x
x
1
6x
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4x = 8
3
2x
Solve for x.
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2 19
3x
3
2x
Solve for x.
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2x + 7y = 2
3x + 5y = -8
solve by elimination
(-6, 2)
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(-2, 1)
5x – y = -11 4x + 12y = 4
solve by substitution
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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 = 14
w = 10
32p + 36w = 808
8p + 12w = 232
14 pans of pasta
10 sandwich trays
p = no. of pans of pastaw = no. of trays of sandwiches
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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 = 15 Bsf
c = 7 Bsf
3b + 2c = 59
7b + 8c = 161
2 Big Macs and 1 Coke would cost 37 Bsf.
b = cost of 1 Big Macc = cost of 1 Coke
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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 = 7
d = 3
m + d = 10
350d + 310m = 3220
7 days in Miami
3 days in Orlando
m = no. of days in Miamid = no. of days in Orlando
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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.
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Write as powers of 2, 3, or 5
1)
4a 1
)27x
b5) 125 5c =2-2 =3-3x =5-2
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1132
2x
5
4x
Solve for x.
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Find the equation of the line that goes through the points (-3, 6) and (-2, 4).
y = -2x
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Write the equation, in standard form, of the line that passes through (-2, 5) and (3, 1)
4 5 17x y
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4
3
Write the equation of the line, in standard form,
with slope and containing the point (4, -1).
3x + 4y = 8
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Given that M is the midpoint of PT, find the coordinates of T if P is (6, -2) and M is 11
4,2
T is (2, -9)
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Find the midpoint of the line segment AB given A(-5, -3) and B(9, 3)
(2, 0)
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Find the distance between (2, -4) and (-5, -1)
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Find the negative value of b given that the distance between (-2, 5) and (3, b) is 61
-1 = b
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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
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Graph x + 2y = 4
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Write the equation of the graph below.
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Graph x = -2
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Graph 3x – 5y = 15 by finding the x- and y-intercepts
x-intercept:3x – 5(0) = 15 x = 5
(5, 0) -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8
-8
-6
-4
-2
2
4
6
8
(0, -3)
y-intercept: 3(0) – 5y = 15 y = -3
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Graph the line with slope 0 and containing the point (3, -5)
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(-2, 1)
Use technology to find the point of intersection of 5x – y = -11 and 4x + 12y = 4.
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Write the equation, in standard form, of the line containing the point (-1, 3) and parallel to the line 3x + 7y = 70.
3x + 7y = 703
107
y x
3 7 18x y
3
7m
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Write the standard form of the equation of the line perpendicular to x – 6y + 30 = 0and passing through the point (5, 3)
6x + y = 33
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Use the distance formula to determine if triangle ABC is scalene, isosceles or equilateral. A(2, 1) B(3, -2) C(5, 2). isosceles
10AB
20BC
10AC
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Formulae you will need to know:
• Distance• Midpoint• Slope• Slope-intercept• Pythagorean theorem