1. The following diagram shows a triangle with sides 5 cm, 7 cm, 8 cm.
diagram not to scale
Determine if this could be a right triangle.
No, it could not.

2. The diagram shows a rectangular prism 22.5 cm by 40 cm by 30 cm.
H G E F
A B D C
40 cm
30 cm
22.5 cm
Calculate the length of [AC].
37.5 cm

3. x = 1.28 m

4. 4.70 m

5. The following diagram shows a carton in the shape of a cube 8 cm long on each side:
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.
= 11.3 cm
= 13.9 cm

6. A square garden with sides 100 m is divided into two triangular plots by a fence along one diagonal.
What is the length of the fence in meters?
If the fence costs $15.50 per meter, what is the total cost?
141 m
$2186
Math 1 text, page 102, #10

7. Write down the length of [GM]. (b) Calculate the length of [VM].
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
Write down the length of [GM].
(b) Calculate the length of [VM]. V P G Q M R S
8 cm
= 4 cm
= 12.6 cm

8. Two ships B and C leave a port A at the same time
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
Studies text, page 101 #8

9. Find the value of any unknown.
Math 3 text, page 85 #6b

10. = 87.1 km A sailing ship sails 46 km North and then 74 km East.
How far is the ship from its starting point?
= 87.1 km
SL text, page 206 #4

11. Simplify
a) (4x3y5)3

12. Simplify

13. Solve for x:
5(x + 2) – 2(3 – 2x) = 3

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

15. Solve for x:

16. Solve for x:

17. Solve for x:

18. Solve for x.
4x = 8

19. Solve for x.

20. solve by elimination
2x + 7y = 2
3x + 5y = -8
(-6, 2)

21. solve by substitution
5x – y = -11
4x + 12y = 4
(-2, 1)

22. p = 14 32p + 36w = 808 w = 10 8p + 12w = 232 14 pans of pasta
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
8p + 12w = 232
p = 14
w = 10
14 pans of pasta
10 sandwich trays

23. 2 Big Macs and 1 Coke would cost 37 Bsf.
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
7b + 8c = 161
b = 15 Bsf
c = 7 Bsf
2 Big Macs and 1 Coke would cost 37 Bsf.

24. m = 7 m + d = 10 d = 3 350d + 310m = 3220 7 days in Miami
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 $ How many days should you spend in each location?
m = no. of days in Miami
d = no. of days in Orlando
m + d = 10
350d + 310m = 3220
m = 7
d = 3
7 days in Miami
3 days in Orlando

25. George is 10 years older than Jane
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.

26. Write as powers of 2, 3, or 5
=2-2
=3-3x
=5-2

27. Solve for x.

28. Find the equation of the line that goes through the points (-3, 6) and (-2, 4).
y = -2x

29. Write the equation, in standard form, of the line that passes through (-2, 5) and (3, 1)

30. Write the equation of the line, in standard form, with slope and containing the point (4, -1).
3x + 4y = 8

31. Given that M is the midpoint of PT, find the coordinates of T if P is (6, -2) and M is
T is (2, -9)

32. Find the midpoint of the line segment AB given A(-5, -3) and B(9, 3)
(2, 0)

33. Find the distance between (2, -4) and (-5, -1)

34. Find the negative value of b given that the distance between (-2, 5) and (3, b) is

35. A line passes through the point (-5, -7) and has a slope of 10
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

36. Graph x + 2y = 4

37. Write the equation of the graph below.

38. Graph x = -2

39. by finding the x- and y-intercepts
Graph 3x – 5y = 15
by finding the x- and y-intercepts
x-intercept:
3x – 5(0) = 15
x = 5
y-intercept:
3(0) – 5y = 15
y = -3
(0, -3)
(5, 0)

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

41. Use technology to find the point of intersection of 5x – y = -11 and
(-2, 1)

42. 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

43. 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

44. Use the distance formula to determine if triangle ABC is scalene, isosceles or equilateral.

45. Formulae you will need to know:
Distance
Midpoint
Slope
Slope-intercept
Pythagorean theorem