MFM2P - Practice Exam
Trigonometry & Measurement: Level 1 & 2
A1. State the value of sin A in the following right triangle.
A2. Convert 5 cubic yards to cubic feet.
A3. Solve for the unknown side.
A4. Solve for θ.
A5. Solve for the unknown side.
A6. Convert 30 centimetres into inches.
A7. A flag pole casts a shadow that is 6m long. At the same time Duane (who is 1.3m tall) casts a shadow that is 3m long. Determine the height of the flag pole.
Trigonometry & Measurement: Level 3
B. Ronnie is flying a kite.
In the table below there are steps that could be used to determine the height of the kite.
a) Select the correct steps (as few of these as possible) and list them in order (just the letter will do)
____, then ____, then ____, then ____ then ____ ....
A / Use your calculator to find cosine of the angle and multiply by 40.B / Use cos A =
C / Use sin A =
D / Measure the angle A
E / Use cos B =
F / Use your calculator to find sine of the angle and multiply by 40.
G / Measure the angle B
H / Use sin B =
b) Explain your choices and why you put them in this order.
Trigonometry & Measurement: Level 4
C. The silo in the picture is used on a farm to store grain. It is made of a cylinder with a half-sphere on top.
a) The diameter of the base is 5.6 m. The height of the cylinder is 14 m. Determine the total volume inside the silo.
b) A train box car, in the shape of a rectangular prism, filled with grain is set to be delivered to the silo. The box car has dimensions 16 yards by 5 yards by 5 yards. Will the grain fit in the silo? Justify your answer.
Linear Systems: Level 1 & 2
D1. Solve
D2. Given x + 2y = 9, determine x when y = -3.
D3. Calculate the slope of the line from ( 5 , 0 ) to ( 9 , 8 )
D4. Solve the following system of equations algebraically: and
D5. Solve the following system of equations by graphing: and
Linear Systems: Level 3
E. Three different systems of equations are listed below.
System A/ System B
/ System C
a) Choose ONE of the systems and explain why one method (substitution, elimination or graphing) is better than the others to find the point of intersection.
b) Solve one system using the method of your choice
Linear Systems: Level 4
F. After eating a lot of chocolate over the holidays Jill has decided to join a gym. There are two gyms within walking distance from her house. Muscles R Us charges $50 per month for unlimited use of their facilities and Gyminy Fitness charges $10 per month as well as $5 per visit.
a) Write an equation to represent the cost per month for each gym where C is the total cost per month in dollars and n is the total number of visits per month.
b) After how many months will the cost at each gym be the same? Justify your answer. You may use a graph, a table or the equations.
c) If Jill decides she is going to go to the gym 12 times per month which gym should she join? Explain.
d) If Jill can only afford $40 per month which gym is her best choice? Explain.
e) Explain what the point of intersection tells you about charges at the two gyms.
Quadratics: Level 1 & 2
G1. Expand and simplify (x – 4)(3x + 1)
G2. Factor the following: a) x2 – 36 b) x2 + 6x + 8
G4. State the x and y intercepts of the relation
G5. State the following for the quadratic equation below:
y-intercept: ______
x-intercepts: ______
vertex: ______
axis of symmetry: ______
max or min? ______
Quadratics: Level 3
H. A student did an experiment of rolling a can up a ramp. Using a motion detector and a graphing calculator, the student recorded the motion of the can until it returned to its starting position. The graph of distance from the starting position versus time is shown below.
a) Explain the meaning of the vertex in this case.
b) Interpret the meaning of the x-intercepts in terms of the experiment.
c) Describe how the graph would change if you gave the can a harder push.
Quadratics: Level 4
I. Karly used her graphing calculator to make graphs of three parabolas.
a)/ b)
/ c)
She used the three relations below to make the graphs. Match the equation to its graph. Justify your choices.
1. 2. 3.
MFM2P Sample Exam
Answer Section
PROBLEM
1. ANS:
PTS: 1 REF: Measurement and Trigonometry
2. ANS:
5 x 3 x 3 x 3 = 135 cubic feet
PTS: 1
3. ANS:
20
PTS: 1
4. ANS:
b) 1 yard = 0.914 4 meter
16 x .9144 = 14.6304
5 x .9144 = 4.572
Yes, you will have enough space, since 305.8 is less than 390.8
PTS: 1
5. ANS:
G then H and then F OR D then B and then A
PTS: 1
6. ANS:
20
PTS: 1
7. ANS:
PTS: 1 REF: Knowledge and Understanding TOP: quadratics
8. ANS:
PTS: 1
9. ANS:
PTS: 1
10. ANS:
A) (2,2)
B) (1,-1)
C) (2, -3)
PTS: 1
11. ANS:
a) C = 50, C = 10 + 5n
b) (8, 50)
c) She should choose Muscles R Us to save $20
d) Gyminy Fitness is her only choice since it will allow her 6 visits while Muscles R Us is too expensive.
e) For 8 visits a month the two gyms charge the same amount ($50)
PTS: 1
12. ANS:
1. The zeros are 4 and -2, and the direction of opening is up. If you expand out the equation we obtain so our y-intercept is -8. Therefore the correct graph is b).
2. The direction of opening is down and the y-intercept is 8. If we factor we obtain so our zeros are 4 and -2. Therefore the correct graph is a).
3. The direction of opening is up and the y-intercept is -8. If we factor we obtain so our zeros are -4 and 2. Therefore the correct graph is c).
PTS: 1 REF: Communication TOP: Quadratics
13. ANS:
a) The vertex is the the point where the can has finished rolling up the ramp and is just about to roll down.
b) The x-intercepts represent when the can is closest to the CBR.
c) The graph might be taller and narrower, with vertex at a higher distance up the ramp, and returning down the ramp more quickly.
PTS: 1 OBJ: Communication KEY: Quadratics