Courses

Hints for improving exam questions:
 * Start with the answer instead of the question
 * Ask for similariities and differences
 * Leave the values of the problem somewhat open
 * Solve the problem in multiple ways
 * Justify solution using another representation/model
 * Make connections to...

Please post your edited exam questions for your course group in the appropriate section below:


 * MBF3C Questions**:

Given triangle PRQ, where side q=11cm, side p=10cm angle R=90, angle Q=35, find side r. || Revised Question 1 - Solve for the length of side r using one method, and verify using a different method. - Is a right triangle with sides measuring 9cm, 10cm and 11cm possible? Verify your answer. (or, is it possible if the hypotenuse is 9 cm?) || Given the data: 1, 1, 2, 2, 2, 3, 4, 4 - Find the mean. || Revised Question 2 - Given the data 1, 1, 2, 2, 2, 3, ?, ? - Find the missing values which would give a mean of 2.5 - Give a set of 6 different numbers which give a mean of 2.5 || Graph the value of a $1000 investment compounded at 6%/a compounded annually for 10 years. || Revised Question 3 - How do different percentages and compounding periods effect the graphs of $1000 invested with compounded interest? || Find the present value of $1000 a week for 20 years. Assume 4%/a compounded weekly. || Revised Question 4 - Would you rather win $1 000 000 today or $1000/week for life? Justify your answer. Which costs the lottery more money? ||
 * Original Question 1
 * Original Question 2
 * Original Question 3
 * Original Queston 4


 * MCF3M Questions**

Evaluate the following: 32 to the power of 2/5 || Revised Question 1 - Give an example of a power with a base of 32 that gives an answer of 4 || Given f(x)=3x^2-4x+2, determine f(4) || - What is the difference between 32 to the 2/5 and 32 to the 5/2 - Write a power that has the same value as 32 to the 2/5
 * Original Question 1
 * Original Question 2

Revised Question 2 ||
 * 1) 1. State the difference between f(x)=4 and f(4) using the function notation f(x) = 3x^2-4x+2
 * 2) 2. Determine the equation of function such that f(4)=32, using function notation?
 * 3) 3. What does any f(4) mean in terms of graph of f(x)?
 * Original Question 3

Factor 6b^2-3ab+12b || Write a trinomial with degree two that has 3b as the greatest common factor. ||
 * Original Queston 4 || Revised Question 4 ||


 * MCR3U Questions**

Given Triangle ABC, a=13cm,b=9cm and c= 16cm. Determine the value of angle A. || Revised Question 1 Determine possible dimensions of a scalene triangle that must contain an angle with a measure of 35 degrees. || Find the sum of the series 3 + 9 + 27 + .........+6561 || Revised Question 2 How is finding the sum of 3 + 9 + 27 + ....+ 6561 similar to finding the sum of 3 + 9 +16 + .......+597? How is it different? || Solve the following equation using the most appropriate method x^2-10x+34=0 || Revised Question 3 Find the x-intercepts of the function f(x)=x^2-10x+34 algebraically. Compare these results when trying to find the x-intercepts using "Zero Operation" on your graphing calculator. || Expectation 3.2 - make and describe connections between compound interest and geometric sequence
 * Original Question 1
 * Original Question 2
 * Original Question 3
 * Original Queston 4 || Revised Question 4 ||
 * Use an example to describe the relationship between compound interest and geometric sequence.


 * MAP4C Questions**

How much will Adam need to invest in an annuity per month to make $6000 in 5 years with an interest rate of 5.2%/a compounded monthly? || Revised Question 1 Adam currently has $3000 in his account. Is it possible for Adam to double his investment in 5 years? Explain. || Jack deposits $550 every month into an account earning interest at 6%, compounded monthly. How much will he have in 3 years? || Revised Question 2 Jack is saving to buy a $20 000 car in 3 years. He deposits $550 every month into an account earning interest at 6%, compounded monthly. Will he have enough money to buy the car? ||
 * Original Question 1
 * Original Question 2
 * Original Question 3 || Revised Question 3 ||
 * Original Queston 4 || Revised Question 4 ||


 * MDM4U Questions**


 * Original Question 1

If the P(A) = 0.4, P(B) = 0.5, and the P(A and B) = 0.2, find the P(A or B). || Revised Question 1 If P(A) = 0.4 and P(A or B) = 0.7, what are the possible range of values for P(B) and P(A and B)? Does it depend on the sets A and B being mutually exclusive or not? ||
 * //Process Focus: Reflecting//**
 * Original Question 2

Using the Normal Distribution X~N(7, 2.2 ^ 2), find the percent of data that is within the given interval: 3 < X < 6. || Revised Question 2

If the percent of data that is within 3 < X < 6 is 29.13%, find X~N(mu, sigma squared). || Given points A(1,5,-7) and B(3,0,1), determine the magnitude of vector AB. || Revised Question 3 A vector AB has a magnitude of the square root of 93. Determine the possible components of vector AB. Determine possible coordinates for points A and B. ||
 * Original Question 3
 * Original Queston 4 || Revised Question 4 ||

**//__Process Questions (Day 3)__ Strand B: Probability Distributions : Expectation 1.1//**
//Question #1:// Describe the similarities and the differences between the binomial and hypergeometric distributions.

//Question #2:// Calculate the probabilities associated with the following probability distribution: _**without** using technology. Using technology justifiy your solution.

__//Question #3://__ Describe how the shape of a distribution changes when its parameters are changed.


 * MHF4U Questions **

Factor x ⁴ +5x³-8x²-48x fully. || Revised Question 1 The sum of all the x-intercepts of a quartic polynomail function is -5. What might be a polynomail function in expanded form that satisfies this criteria? Justify your answer. || Determine the zeros of the function f(x)=3(x²-25)(4x²+4x+1) || Revised Question 2 Given the function f(x)=3(x²-25)(4x²+4x+1), which graph best represents the above function and justify your answer. (I am unable to post the graphs but the idea is there) OR What is a possible equation for the bolded graph? || Find fog(x) and gof(x) if f(x) = 2x + 3 and g(x) = 1/( 3x + 5) || Revised Question 3 Investigate algebraically and verify numerically whether fog(x)=gof(x) || Find the intersection, if any, of the line For the lines L(1) and L(2) with equations a. Are L(1) and L(2) skew lines? (R&P) b. Draw two parallel planes, one containing first line and the other, the second line.(R&P) c. Find a common normal to the planes.(C) d. Find the Cartesian equation of the planes.(C) e. Find the distance from origin to the planes and the distance between the planes.(R&P) f. Find the shortest distance between the lines L(1) and L(2).(C) g. Draw a line segment PQ having P on L(1), Q on L(2) and the length the shortest distance between L(1) and L(2) and prove that PQ is perpendicular on both lines.(R, R&P) h. Find the coordinates of P and Q.(R&P) i. Find the distance PQ. Is it the shortest distance between the lines? j. Explain how could be determined if two lines in three-dimensional space are intersecting without solving a system.(R) k. If one car is on the first line, 2 km from P, at a speed of 60 km/h and another car is on the 2nd line, 5 km from from Q at a speed of 80 km/h, find the rate of separation after 10 minutes. (R&P) l. How many cases are to consider for previous question.(Rep)  || The position of an object is given by the equation s(t) = (t^2 - 3)e^(1-t) where t>=0. When is the velocity of the object zero and when is it positive? || Revised Question 2 The velocity of an object is given by the equation v(t) = (-t^2 + 2t + 3) e^(1-t). a. Find the degree of a polynomial P(t) such that the derivative of P(t)e^(t^2-3) is v(t). (R&P) b. Find a possible equation for s(t), the position function.(ST&CS) || Determine the angle ß, [0,90º], to the nearest tenth of a degree, between the planes 2x+3y-z+9=0 and x+2y+4=0 || Revised Question 3 (Reasoning/Proving) : Verify that the planes 2x+3y-z+9=0 and x+2y+4=0 are not perpendicular (Problem Solving): Determine the equations of any two planes that have an acute angle of intersection. Justify your solution algebraically || Find the absolute maximum and minimum values of the function f(x)=x^3-5x^2+3x+7, x E [1,5] || Revised Question 4 f(x)=Ax^3+Bx^2+Cx+D,1<=x<=5 such that: Critical numbers are 1/3, 3 Absolute max at (5, 22) Absolute min at (3, -2) xE (-1, 6] || Determine the intervals of increase/decrease for the function f(x) = x^3 -- 6x^2 || Revised Question 5 1. Given that f(x) is increasing on the intervals (negative infinity, x), (y, positive inifinity) and decreasing on (x, y), determine a possible equation for f(x) (reasoning) 2. What conditions cause a function to change from increasing to decreasing (or vice versa) (connecting) 3. Create a function that has two intervals of increase and one interval of decrease. Justify your answer mathematically. (reasoning) || Determine the point(s) on the curve where the tangent line is perpendicular to the line x--2y=1 || Revised Question 6 What type of real-life problem would require you to determine a perpendicular to a given line? Justify your answer. (reasoning/communication || Determine the derivative of f(x) = x^5/15 -- 2x || Revised Question 7 When do you need the derivative of a function? Give an example of a function whose derivative is f(x) = x^3 +2x (reasoning, communication) ||
 * Original Question 1
 * Original Question 2
 * Original Question 3
 * MCV4U Questions **
 * Original Question 1
 * r ** = (1, 2, 2) + s (4, 3, 2) and the line
 * r ** = (1, 0, -3) + t (4, -6, -1) || Revised Question 1
 * r ** = (1, 2, 2) + s (4, 3, 2) and
 * r ** = (1, 0, -3) + t (4, -6, -1) answer to the following questions.
 * Original Question 2
 * Original Question 3
 * Original Queston 4
 * 1) 1 (Representing/Connecting): Draw a function that has an absolute max of 22, an absolute min of -2 and lies in the domain -3<x<=10
 * 2) 2 (Reasoning): Find the values of A, B, C, D of
 * 3 : Given the graph, determine (if any), the absolute max/min over the interval
 * Original Question 5
 * Original Question 6
 * Original Question 7

Original Question 8 Given points A(1,5,-7) and B(3,0,1), determine the magnitude of vector AB. ||

Revised Question 8 A vector AB has a magnitude of the square root of 93. Determine the possible components of vector AB. Determine possible coordinates for points A and B. ||

Expectation 2.5 - Solve problems arising from real-world applications

Q1 - How can police officers determine how fast cars are travelling before an accident occurs? What would be the most important pieces of info required?

Q2 - A ferris wheel rotates at a constant rate (mapping out a sinusoidal function). When will your carriage be moving at its greatest velocity? Show support for your answer.

__MCV4U1 - Expectation 4.3__ State whether the normals to the following planes are collinear, coplanar or neither. You must show work/explain to recieve marks. 2x-2y+z=6 4x-2y-7z=3 5x-4y-2z=11