MPM2D Practice Exam (June 2010) MPM2D June Exam 2010 Grading Guide
Quick Descriptors STUDENT NAME:______** consult Rubric for Full Description of Levels B: Blank School:______R: Remedial 1: Limited 2: Approaching (the expectations) Teacher : ______3: Sufficient (achieved the expectations) 4: Insightful and Thorough (achieved the expectations) *: Communication focus in C and H can be used to modify the overall level
B R 1 2 3 4 A Apps/Comm/K Trig B Apps/Comm/K Trig C* Apps/Comm/K Trig
B R 1 2 3 4 Overall D Apps/Comm/K Analytic Exam E Apps/Comm/K Analytic F* Apps/Comm/K Analytic Overall Task B R 1 2 3 4 G Apps/Comm/K Quads H* Apps/Comm/K Quads I* ** Apps/Comm/K Quads Final Course
Level R All strands 2 strands 1 strands 10% 35% 45%
Level 4 Level 3 Level 2 Level 1 80-100 70-79 60-69 50-59
IMPORTANT: This exam is divided into 9 parts and labeled A to I. Each section contains questions of similar achievement level. Complete the 1st and 2nd section of each of the three overall expectations (Part A & B - Trigonometry, Part D & E - Analytic Geometry and Part G & H -Quadratics). At the end of the exam if time permits, complete the three remaining sections (Part C, F and I). Answer each question to the best of your ability, that may include explaining what you are doing and why.
In the interest of saving paper, this exam does not provide space for graphs and solutions. Please answer your questions on a separate sheet of paper and label each question carefully. Your actual board-wide exam on Wednesday June 17, 2010 @ 8:45 a.m. will provide space for your solutions.
This practice exam is way longer than the actual exam. You will have more than enough time to complete the real exam. This will probably take between 8 and 10 hours to complete.
Page 1 of 9 MPM2D Practice Exam (June 2010)
PART A: Trigonometry (Level 1 & 2)
A1. State the similar triangles. *Note: The diagram is not to scale. *
96 c m K L F
40 c m 24 c m
72 c m H 120 c m 32 c m G
J A2. Using the angle provided, write an equation using a primary trigonometric ratio that could be used to solve for x. *Note: The diagram is not to scale. *
x
47 10 c 81 A3. Given , determine the value of c. Round your answer to one decimal place. sin7 sin69
PART B: Trigonometry (Level 3)
B1. Determine the value of x (round your answer to the nearest cm). *Note: The diagram is not to scale. *
64 37
23 c m 23 c m
x
B2. Brett measures the angle of elevation to the top of a tower to be 10. He then moves 145 m closer to the tower and the new angle of elevation is 30. What is the height of the tower to the nearest meter? Include a labeled diagram with your solution.
bh B3. Determine the area of a triangle ( A ) that has sides measuring 6 cm, 8 cm, with a base of 12 cm. It is 2 not a right triangle. Accurate to the nearest tenth of a unit.
Page 2 of 9 MPM2D Practice Exam (June 2010) PART C: Trigonometry (Level 4)
C1. In the diagram below, EH is parallel to FG. Note that the diagram is not to scale. Determine the length of EF. *Note: The diagram is not to scale. *
E F 15 c m D
18 c m
H 6 c m G
C2. Two straight roads intersect at town B at an angle of 48. The distance from town B to town A is 32 km. The distance from town B to town C is 40 km. A straight road connecting towns A and C is under construction. Currently to travel from towns A to C, you must go through town B. How many kilometres will you save once the new road is open. Round your answer to the nearest kilometre. *Note: The diagram is not to scale. * Town B
Town C
Town A
PART D: Analytic Geometry (Level 1 & 2)
D1. State the number of solutions to the system of equations given below. 4 y x 5 7 4 y x 9 7
D2. Show your work/explain your answer Determine if (-2,4) is a solution to the system defined by:
x 2y 6 4x 3y 5
Page 3 of 9 MPM2D Practice Exam (June 2010)
D3. Given the line segment with end points A(-3, 2) and B(5, -4) determine a) The midpoint of AB y 5
4
3
A 2 1 b) The length of AB –5 –4 –3 –2 –1 1 2 3 4 5 x –1
–2
–3
–4 B –5
D4. A circle has centre (0, 0) and a radius of 10. State the equation of the circle.
D5. Classify quadrilateral ABCD given the following measurements. Justify your choice
mAB mBC mCD mDA d AB d BC dCD d DA 3 11 3 11 3 4 3 4 11 3 11 3
PART E: Analytic Geometry (Level 3)
x 2y 7 E1. Solve the following linear system: 3x 10y 8
E2. Diego correctly modeled the sale of tickets for the school art show with the following linear system. He represented the number of student tickets sold with the variable x, and, the number of adult tickets sold with the variable y.
SCHOOL ART SHOW! SCHOOL ART SHOW! x y 750 Student tickets - $5 each 5x 8y 5100 StudentAdult tickets tickets - -$8 $5 each each Adult tickets - $8 each a) Given the equations, what was the total number of tickets sold?
b) Explain the meaning of the following terms in the equation: 5x 8y 5100
5x: 5100:
E3. Solve the system of equations defined by the two relations below. Justify your solution. y Relation 1: 3x y 6 Relation 2: 8 7 6 5 4 3 2 1
–8 –7 –6 –5 –4 –3 –2 –1–1 1 2 3 4 5 6 7 8 x –2 –3 –4 –5 –6 –7 –8
Page 4 of 9 MPM2D Practice Exam (June 2010) E4. Find the equation of the median for ABC, from the vertex at C. y
10 9 8 7 6 C 5 4 A 3 2 B 1
–2 –1–1 1 2 3 4 5 6 7 8 9 10 x –2
E5. A line, defined by y = 4x – 2, intersects a circle, defined by x 2 + y2 = 16. Choose any point on the line and determine if it is inside, outside or on the circle.
E6. When Ms. Hill goes to visit her friends, she drives 393 km from her home in Ottawa to a lodge near Tamagami (Northern Ontario). She travels at an average speed of 70 km/h along the highway to North Bay and then at 50 km/h on the narrow road from North Bay to Temagami. The whole trip takes 6 h. Determine the distance from Temagami to North Bay.
PART F: Analytic Geometry (Level 4)
F1. Given the following relationships, determine the value of each shape. Solve algebraically using substitution or elimination. + + + + = 10 + + + + = 10 + + = 13 + + = 13
F2. Austin is creating a new product to sell in his “Natural foods” store by combining two products: a pineapple-flavoured mix that sells for $18/kg and a banana-flavoured mix that sells for $10/kg. He is making 80 kg of the new product and will sell it for $12.50/kg. Austin uses the graph shown at right to determine how much of each type he needs to use.
a) Write the equations of the linear relations ) g k (
x i m
a n a n
b) Interpret Austin’s graph as it relates to the problem. a b
f y o 100 s s
a 90
M 80
70
60
50
40 c) How much of each blend will Austin need to use? 30 Be sure to fully support your answer. 20
10
10 20 30 40 50 60 70 80 90 100 x Mass of pineapple mix (kg)
Page 5 of 9 MPM2D Practice Exam (January 2010)
F3. Mr. Godin makes up a test question for his MPM 2D class and shares it with Mr. Lim. Unfortunately, Mr. Godin spilled coffee on the test, so Mr. Lim can only see:
Solve the following system of equations: 5x + 2y = 2 3x –
If Mr. Lim just fills in some numbers at random, discuss how the number he will pick can affect the solution and the way that the problem will probably be solved.
F4. You are asked to solve a system of equations. The first equation is y = 2x – 43. The second equation isn't given to you, only a table of values: x y –6 –11 –3 –9 0 –7 3 –5 6 –3
Discuss (you can use point form) several methods you could use to solve this system. Choose “the best” method and solve the system. State why you think your method was the best.
F5. Three new lampposts are being installed in the parking lot at Osgoode THS. Points A, B, and C are the locations of the new posts. Electricians want to install the power supply at a spot equidistant from all of the new posts. Determine the coordinates of this point.
Map from www.maps.google.com
F6. Four lines intersect to form a quadrilateral we have studied this year (rhombus, parallelogram, rectangle, square). Three of these lines are defined below.
Determine the equation of a fourth line and state the name of the quadrilateral you have created.
Line A: -3x + y – 4 = 0 Line B: 2x + 6y + 12 = 0 Line C: y = 3x – 2 Line D:
Page 6 of 9 MPM2D Practice Exam (January 2010) PART G: Quadratics (Level 1 & 2)
G1. For the graph of the relation below, answer the y following: 5 4 a) What are the coordinates of the vertex? 3 2
1
–5 –4 –3 –2 –1 1 2 3 4 5 x –1
–2
–3
–4
–5
b) What are the x-intercepts for this relation?
c) What is the y-intercept for this graph?
d) State the equation of the axis of symmetry.
e) Fill in the equation for this graph.
1 y= ( x )( x ) 2
G2. Expand: q 32q 5.
G3. Factor 3x2 x 2 using a representation of algebra tiles. 1 2 G4. Describe the transformations applied to y x2 to obtain the parabola y x 6 11. 5 G5. Determine the y-intercept of the relation y (x 4)(x 1) 1 G6. Determine the maximum/minimum value for the quadratic relation y=( x + 1)( x - 5) . Is it a 2 maximum or a minimum? Explain.
PART H: Quadratics (Level 3)
H1. A swimmer diving from a cliff follows a parabolic path defined by the relation h 4.9t 22 20 , where h is the height in metres and t is the time in seconds. a) State the maximum height of the swimmer. b) At what time does the swimmer reach her maximum height?
3 H2. How many zeros does the relation y= -( x - 5)2 + 1 have? Explain how you know. 4 H3. Give an example of a quadratic relation in standard form that cannot be written in factored form. Explain.
H4. Determine the equation for the following parabola in standard form. Show your work.
Page 7 of 9 MPM2D Practice Exam (January 2010)
H5. Find the value(s) of b so that y= x2 + bx +16 only has one zero.
Page 8 of 9 MPM2D Practice Exam (January 2010)
PART I: Quadratics (Level 4)
I1. Solve the equation x(5 x+ 8) + 3 = x (2 x - 4) - 3.
I2. A quadratic relation has the following table. Complete the table.
x y First Second 1 -1 2 3 4 -6 5 -10 6
I3. Find the missing values of b and c in the equation x2+ bx +7 = ( x + c ) 2 + 3.
I4. David and Steven stand on either side of a 2 m tall fence, 20 m apart. If the fence is 17 m from David and the ball reaches a maximum height of 5 m, will the ball reach Steven? The path of the ball can be modeled by a quadratic relation.
I5. Determine the number of zeros of the relation y=4 - ( x - 3)(3 x + 1) . Show your work.
I6. While on the Moon, astronauts throw a ball upwards from atop a platform. The height of the ball is given by the formula h= -0.81 t2 + 15 t + 12 , where h is the height in metres and t is the time in seconds. Tell me enough about the motion of this ball to earn a level 4. Do not forget to explain your thinking.
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