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Midterm Practice Examination

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G r a d e 1 1 a p p l i e d M a t h e M a t i c s

Midterm Practice Examination

Name: ___________________________________

Student Number: ___________________________

Attending q Non-Attending q

Phone Number: ____________________________

Address: _________________________________

__________________________________________

__________________________________________

InstructionsThe midterm examination is based on Modules 1 to 4 of the Grade 11 Applied Mathematics course. It is worth 20% of your final mark in this course.

TimeYou will have a maximum of 2.5 hours to complete the midterm examination.

Notes You are allowed to bring the following to the examination: pens/pencils (2 or 3 of each), metric and imperial rulers, a graphing and/or scientific calculator, and your Midterm Exam Resource Sheet. Your Midterm Exam Resource Sheet must be handed in with the examination. Graphing technology (either computer software or a graphing calculator) is required to complete this examination.

Show all calculations and formulas used. Use all decimal places in your calculations and round the final answers to the correct number of decimal places. Include units where appropriate. Clearly state your final answer. Final answers without supporting calculations or explanations will not be awarded full marks. Indicate equations and/or keystrokes used in calculations.

When using graphing technology, include a screenshot or printout of graphs or sketch the image and indicate the window settings (maximum and minimum x- and y-values), increments, and axis labels, including units.

For Marker’s Use Only

Date: _______________________________

Midterm Mark: _____ /100 = ________ %

Comments:

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Answer all questions to the best of your ability. Show all your work.

Module 1: Quadratic Functions (37 marks)

1. How many x-intercepts will a quadratic function have if the vertex coordinates are (8, 9) and the function equation is y = x2 - 16x + 73? Explain. (2 marks)

2. A quadratic function has vertex coordinates at (3, 0). How many x-intercepts will the quadratic function have? Explain. (2 marks)

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3. Sketch the following features of a quadratic function.a) The axis of symmetry equation is x = 3.b) The coordinates of the vertex are (3, -3).c) The x-intercepts are 0 and 6.

Then sketch the corresponding quadratic function. (4 marks)

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4. The x-intercepts of the quadratic function y = -1.5x2 - 2x + 3 are -2.23 and 0.90.a) What are the roots of the equation -1.5x2 - 2x + 3 = 0? (1 mark)

b) What is the relationship between the x-intercepts of a function and the roots of the corresponding equation? (1 mark)

5. Use a grapher to determine the x-intercepts, to two decimal places, of the graph of the quadratic function given below. Include a sketch of your graph with intercepts labelled. (3 marks) y = -4x2 + 7x + 7

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6. Write a possible quadratic equation in factored form that has the same x-intercepts and opens in the same direction as the graph below. (3 marks)

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7. Draw three separate quadratic functions with the characteristics given. (3 marks)a) The function has two x-intercepts and opens up.b) The function has no x-intercepts and opens up.c) The function has one x-intercept and opens down.

a)

b)

c)

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8. Consider the quadratic function y x x=− − +

12

5 32 , with axis of symmetry equation

x = -5.

a) Determine the vertex coordinates. (2 marks)

b) Determine the maximum and minimum values (if they exist). (1 mark)

c) Determine the domain. (1 mark)

d) Determine the range. (1 mark)

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9. Create a table of values and sketch a graph of the quadratic function y = x2 - 2x + 3. (3 marks)

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10. Sketch a graph of the following quadratic function using the intercepts. Include the coordinates of the intercepts and vertex on your graph. (3 marks)

y = 3(x - 2)(x)

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11. An outdoor fenced chicken coop with three sections is to be built attached to a pre-existing barn, as shown. No fence is needed against the barn. Determine the dimensions of the chicken coop with the greatest area that can be enclosed using 650 feet of fencing, by completing the following.

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a) If 650 feet of fencing is to be used to create four widths, w, and one length, determine an expression for the length in terms of w. (1 mark)

b) Determine a quadratic function model to define area in terms of width. (2 marks)

c) Using a graphing utility, find the coordinates of the vertex of the quadratic function and interpret their meaning. (2 marks)

d) Determine the dimensions of the pen with the largest area. (2 marks)

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Module 3: Reasoning to Solve Problems (28 marks)

1. Determine a conjecture that could be made about the sum of a multiple of 4 and a multiple of 6. Use at least two examples to help you develop your conjecture. (3 marks)

2. Jordyn arrives at her first pre-calculus mathematics class in Grade 11. She realizes that there is only one other girl in the class, and the other members of the class are male. Jordyn then attends her first home economics class and notices that the majority of the class is female. State two possible conjectures Jordyn can make about the gender of students attending pre-calculus and home economics classes. (2 marks)

3. If possible, find a counter-example to the following conjectures.a) The sum of a multiple of 5 and a multiple of 6 will be an odd number. (1 mark)

b) All cars consume gasoline. (1 mark)

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4. Consider the following number trick. Pick a number. Subtract 1. Multiply the result by 3. Add 12. Divide the result by 3. Add 5. Subtract your original number.

a) Make a conjecture about the result of the above number trick and provide two examples to support your conjecture. (2 marks)

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b) Prove that this number trick will always result in the conjecture you made in (a). (4 marks)

5. Determine whether the following scenarios represent inductive or deductive reasoning. (2 marks) a) Ms Newton told her class that if they receive an A on the final exam, then they will

earn a final grade of A in the course. Britney receives an A on the final exam and expects to earn a final grade of A in the course.

b) It has rained for the past three days. Brayden assumes it will rain again tomorrow.

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6. Use inductive reasoning to determine the next three terms in each of the following patterns. (3 marks)a) 1, 2, 3, 2, 4, 6, 4, 8, 12, . . .

b)

7. Explain why the following proofs are invalid. (4 marks) a) All parallelograms are quadrilaterals. Figure ABCD is a quadrilateral. Therefore,

figure ABCD is a parallelogram.

b) Dylan is trying to prove that a number trick always results in the value of 5. Let x be the number. Pick a number. x + 3 Add 3. 2x + 6 Multiply by 2. 2x + 10 Add 4. 2x + 5 Divide by 2. x + 5 Subtract the original number.

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8. Consider the following image made up of 17 toothpicks. Remove 6 toothpicks to leave two squares. (2 marks)

9. Prove that the sum of a multiple of 3 and a multiple of 6 is a multiple of 3. (4 marks)

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Module 4: Geometry of Angles and Triangles (35 marks)

1. Determine if the following sets of lines are parallel. Explain your answers. (4 marks)a)

b)

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2. Find the indicated angle(s) in each of the diagrams below and state the property or rule you used to determine these angles. (6 marks)a) (1 mark)

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b) (1 mark)

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c) (2 marks)

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d) (2 marks)

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3. For each diagram below, state the measurement of Ðx and the property that allows you to determine it. (6 marks) a)

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4. If the sum of the interior angles of a polygon is 4680°, how many sides does the polygon have? (2 marks)

5. If a polygon has 17 sides, what is the sum of the interior angles? (2 marks)

6. Determine the size of the missing exterior angle in the polygon below. (2 marks)

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7. Determine the size of the missing interior angle in the polygon below. (2 marks)

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8. Prove that Angle 3 and Angle 5 have a sum of 180° in the diagram below, given that lines l and m are parallel. In other words, prove that same side interior angles sum to 180°. (4 marks)

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9. A school wants to plant a new flower garden in the shape of a parallelogram, as displayed by the diagram below. The flower garden will be divided into four sections.

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a) Explain how the school could find the measurements of all the indicated angles without using a protractor. (1 mark)

b) Determine the measurements of angles a and b. (2 marks)

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10. Find the value of the angles labelled with a letter in the diagram below and state the property or rule you used to determine these angles. (4 marks)

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