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.

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

x = 1.28 m

4.70 m

= 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

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

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

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.

29 5.39x cm

45 6.71y cm

A sailing ship sails 46 km North and then 74 km East.How far is the ship from its starting point?

= 87.1 km

7 4

2 6)

x yb

x ya) (4x3y5)3 9 1564x y

5

2

x

y

Simplify

22

3

2)

xb

y

62

)c

ad

6

6

64c

d

6

44

y

x

Simplify

Solve for x:5(x + 2) – 2(3 – 2x) = 3

1

9x

Solve for x:x(2x + 1) – 2(x + 1) = 2x(x – 1)

x = 2

Solve for x: 4 7 5

11 2

x x

41

19x

Solve for x: 5 11

4 12x

15

11x

Solve for x: 2 54

1

x

x

1

6x

4x = 8

3

2x

Solve for x.

2 19

3x

3

2x

Solve for x.

2x + 7y = 2

3x + 5y = -8

solve by elimination

(-6, 2)

(-2, 1)

5x – y = -11 4x + 12y = 4

solve by substitution

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

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

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

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)

4a 1

)27x

b5) 125 5c =2-2 =3-3x =5-2

1132

2x

5

4x

Solve for x.

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 5 17x y

4

3

Write the equation of the line, in standard form,

with slope and containing the point (4, -1).

3x + 4y = 8

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)

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: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

Graph the line with slope 0 and containing the point (3, -5)

(-2, 1)

Use technology to find the point of intersection of 5x – y = -11 and 4x + 12y = 4.

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

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

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

Formulae you will need to know:

• Distance• Midpoint• Slope• Slope-intercept• Pythagorean theorem