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Released Assessment Questions, 20 16 Grade 9 Assessment of Mathematics, • Academic

For Use with Assistive Technology: ⚪

Listen as your teacher reads the instructions. Some key points are listed below.

Make sure you have the Formula Sheet for reference.

The diagrams in this booklet are not all drawn to scale.

Answering Multiple-Choice Questions: ⚪

Answer all multiple-choice questions. If you fill in more than one answer to a question, or leave a question blank, the question will be scored zero. Incorrect answers will also be scored zero.

Answering Open-Response Questions: ⚪

Do all of your work for each question in the space provided for the question only.

Write your solutions, including all calculations, clearly and completely.

Attention: ⚪

The format of this document differs from that of the actual assessment booklets, as the questions are sorted by strand.

There are more multiple-choice and open-response questions in this document than in a regular booklet.

You are now ready to start.

Multiple-Choice, questions 1 to 8: Question 1: A ball is dropped from a height of 25 metres. The ball’s height, capital H, in metres, after n bounces is represented by the equation below.

Capital H = 25 ([bracket] 1 over 2 [bracket]) to the power of n: ⚪

What is the height of the ball after 4 bounces?

A: 𝟐𝟐𝟐𝟐𝟏𝟏𝟏𝟏

25 over 16, metres: ⚪

B: 𝟐𝟐𝟐𝟐𝟖𝟖

25 over 8, metres: ⚪

C: 𝟐𝟐𝟐𝟐𝟒𝟒

25 over 4, metres: ⚪

D: 𝟐𝟐𝟐𝟐𝟐𝟐

25 over 2, metres: ⚪

Question 2: A cube with a given side length is pictured below.

The length of one side of this face is labelled x. ⚪

Which algebraic expression represents the area of one face of the cube?

A: 2x: ⚪

B: 4x: ⚪

C: x to the power of

2: ⚪

D: x to the power of

3: ⚪

Question 3: A school is planning a car wash to raise 600 dollars.

• There will be 8 teams. ⚪

• Each team will wash 2 cars per hour. ⚪

• The car wash will last 5and a half

𝟏𝟏𝟐𝟐 hours. ⚪

• Each team will take two 15-minute breaks.

How much should the school charge per car to raise exactly 600 dollars?

A: 15 dollars: ⚪

B: 7 dollars and 50 cents: ⚪

C: 6 dollars and 82 cents: ⚪

D: 6 dollars and 25 cents: ⚪

Question 4: Which of the following is equivalent to: ⚪

3, ([bracket] 5x minus 1), ⚪ [bracket] minus 2, ⚪ ([bracket] 3x plus 5) [bracket]?

A: 9x minus 13: ⚪

B: 9x plus 4: ⚪

C: 21x minus 13: ⚪

D: 21x plus 4: ⚪

Question 5: Information about the relationship between the height of a plant and time is shown on the grid below.

The horizontal axis, labelled Number of weeks, n, starts at 0 and every other grid line is labelled in increments of 1, up to 6. The vertical axis, labelled Height in centimetres, capital H, starts at 0 and every other grid line is labelled in increments of 1, up to 7. Five points are shown on the grid. Here are the coordinates for each point: ⚪

1, ⚪ 0 decimal 5: ⚪ 2, ⚪ 1: ⚪ 3, ⚪ 2: ⚪ 4, ⚪ 3 decimal 5: ⚪ 5, ⚪ 6: ⚪

Which table of values shows only information about this relationship?

A:

Number of weeks, 1: ⚪ Height, 2 centimetres: ⚪

Number of weeks, 2: ⚪ Height, 3 centimetres: ⚪ Number of weeks, 6: ⚪ Height, 5 centimetres: ⚪

B:

Number of weeks, 2: ⚪ Height, 1 centimetre: ⚪ Number of weeks, 3: ⚪ Height, 2 centimetres: ⚪

Number of weeks, 5: ⚪ Height, 6 centimetres: ⚪

C:

Number of weeks, 1: ⚪ Height, 1 centimetre: ⚪

Number of weeks, 2: ⚪ Height, 2 centimetres: ⚪ Number of weeks, 4: ⚪ Height, 7 centimetres: ⚪

D:

Number of weeks, 2: ⚪ Height, 1 centimetre: ⚪ Number of weeks, 3: ⚪ Height, 2 centimetres: ⚪

Number of weeks, 4: ⚪ Height, 4 centimetres: ⚪

Question 6: Two golf courses offer student memberships. Information about the linear relationships between the total cost, capital C, in dollars, and the number of games played, n, at these two golf courses is given below.

The horizontal axis, labelled Number of games, n, starts at 0 and every other grid line is labelled in increments of 1, up to 4. The vertical axis, labelled Total cost in dollars, capital C, starts at 0 and every other grid line is labelled in increments of 10, up to 50. A line is drawn on the grid. The co-ordinates of 3 points along this line are: ⚪ 0, ⚪ 10: ⚪ 1, ⚪ 20: ⚪ 2, ⚪ 30: ⚪

Number of games, n, and Total cost, capital C, in dollars. ⚪

Number of games, 3: ⚪ Total cost, 51 dollars: ⚪ Number of games, 5: ⚪ Total cost, 85 dollars: ⚪ Number of games, 9: ⚪ Total cost, 1 hundred 53 dollars: ⚪

Number of games, 12: ⚪ Total cost, 204 dollars: ⚪

Which of the following statements correctly describes the two relationships?

A: They are both direct variations.

B: The first is a direct variation, and the second is a partial variation with an initial value of 17 dollars.

C: The first is a partial variation with an initial value of 10 dollars, and the second is a direct variation.

D: The first is a partial variation with an initial value of 10 dollars, and the second is a partial variation with an initial value of 17 dollars.

Question 7: The graph below represents Joe’s distance from a wall as he walks. ⚪

The horizontal axis, labelled Time in seconds, t, starts at 0 and every other gridline is labelled in increments of 2, up to 8. The vertical axis, labelled Distance from wall in meters, capital D, starts at 0 and every other gridline is labelled in increments of 2 up to 6. Three line segments that are joined are plotted on the graph. The end points of each line segment are: ⚪

0, 2, ⚪ and, 3, 5: ⚪ 3, 5, ⚪ and, 6, 5: ⚪ 6, 5, ⚪ and, 9, 2 decimal 8: ⚪

Which statement could describe Joe’s walk?

A: Joe walks toward the wall, stands still and then walks away from the wall. ⚪

B: Joe walks away from the wall, stands still and then walks toward the wall. ⚪

C: Joe walks toward the wall, stands still and then continues to walk toward the wall. ⚪

D: Joe walks away from the wall, stands still and then continues to walk away from the wall. ⚪

Question 8: Consider the graph below. ⚪

The horizontal axis, labelled n, starts at 0 and every other grid line is labelled in increments of 1, up to 3. The vertical axis, labelled capital P, starts at 0 and every other grid line is labelled in increments of 1, up to 6. A line is drawn on the graph.

Here are the coordinates of two points on the line: ⚪ 0, 6, and, 3, 0: ⚪

Which of the following is an equation representing this graph?

A: capital P = 2n plus 6: ⚪

B: capital P = 1 over 2, 𝟏𝟏𝟐𝟐n plus 6: ⚪

C: capital P = negative 2n plus 6: ⚪

D: capital P = negative 1 over 2, 𝟏𝟏𝟐𝟐n plus 6: ⚪

Open-Response, questions 9 to 14: Question 9: Floored Areas: ⚪

The diagram of the floor shown below has algebraic expressions for the lengths of its sides, in metres.

It is made of a large rectangle where a small rectangular corner is removed from its bottom right corner. The left side of the floor plan, is the width of the large rectangle and it is labelled 7x. The top side of the floor plan is the length of the large rectangle and it is labelled 4x minus 3. Continuing clockwise around the floor plan, from the top right corner of the large rectangle, the next side is labelled 5x. The next side is the top side of the small rectangle which is removed, it is labelled x. Continuing on, the next side is the left side of the small rectangle that is removed, it is labelled 2x. The final bottom side of the floor plan is labelled 3x minus 3. ⚪

Determine an unsimplified expression for the total area of the floor, capital A, in metres squared.

Capital A: = [blank space] ⚪.

Simplify your expression fully. Show your work. ⚪

Question 10: Folding Time: ⚪

A piece of paper is folded in half, which results in two layers of paper. Then the paper is folded in half again to make four layers, and so on.

In the first stage the paper has not been folded. It has 0 folds and 1 layer. In the second stage the paper has been folded in half once. It has 1 fold and 2 layers are shown. In the third stage the paper has been folded in half again. It has 2 folds and 4 layers are shown: ⚪

The number of layers and the number of folds are recorded in the chart. ⚪

Number of folds and Number of layers: ⚪

Number of folds, ⚪ 0: ⚪ Number of layers, ⚪ 1: ⚪ Number of folds, ⚪ 1: ⚪ Number of layers, ⚪ 2: ⚪ Number of folds, ⚪ 2: ⚪ Number of layers, ⚪ 4: ⚪ Number of folds, ⚪ 3: ⚪ Number of layers, ⚪ blank space: ⚪

Number of folds, ⚪ 4: ⚪ Number of layers, ⚪ blank space: ⚪

Determine whether this relationship is linear or non-linear. ⚪

Circle one: ⚪ Linear: ⚪ Non-linear: ⚪

Justify your answer. ⚪

You have the option of using the grid if you wish. ⚪

The horizontal axis, labelled Number of folds, f, starts at 0 and every other gridline is labelled in increments of 1, up to 5. The vertical axis, labelled Number of Layers, capital L, starts at 0 and every other gridline is labelled in increments of 4, up to 32: ⚪

Question 11: Theatre Programs: ⚪

A company charges schools to print programs for school plays. Information about the linear relationship between the total cost and number of programs printed is shown below.

Number of programs, n, and Total cost, capital C, in dollars.

Number of programs, 3 hundred 50: ⚪ Total cost, 2 hundred 20 dollars: ⚪ Number of programs, 500: ⚪ Total cost, 2 hundred 50 dollars: ⚪ Number of programs, 7 hundred 50: ⚪ Total cost, 300 dollars: ⚪

Determine an equation to represent this relationship. ⚪

[Blank space] ⚪.

Show your work. ⚪

You have the option of using the grid if you wish.

Question 12: Standard Lines: ⚪

Two lines are represented by the equations below.

Line 1: x minus 2y plus 6 = 0: ⚪ Line 2: 3x plus 6y minus 18 = 0: ⚪

Determine which line could be represented by y = negative 1 over 2, ⚪ 𝟏𝟏𝟐𝟐 x plus 3. ⚪

Circle one: Line 1: ⚪ Line 2: ⚪ Both: ⚪

Justify your answer. Include information for both Line 1 and Line 2. ⚪

Question 13: Terrific Tees: ⚪

A school orders T-shirts from Terrific Tees. The total cost is made up of a set-up fee of 1 hundred 15 dollars and a cost of 3 dollars per T-shirt.

Terrific Tees requires a minimum order of 25 T-shirts. The school can spend a maximum of 800 dollars.

Determine all the possible values of the total cost, capital C, and the number of T-shirts, n, for this situation.

Show your work. ⚪

The possible values of n in this situation are [blank space] ⚪.

The possible values of capital C in this situation are [blank space] ⚪.

Question 14: Six and Five Sides: ⚪

A regular hexagon and a regular pentagon are joined as shown below. ⚪

They are connected by a shared side. An interior angle of the regular hexagone is labelled x. At one end of the shared side, where the side of the hexagone and pentagone meet, the exterior angle is labelled y. This angle is not in either shape: ⚪

Complete the table below with the values of x and y. Justify your answer using geometric properties. ⚪

Value, and Justification using geometric properties: Value, ⚪ x = blank space: ⚪

Justification using geometric properties, ⚪ blank space: ⚪ Value, ⚪ y = blank space: ⚪ Justification using geometric properties, ⚪ blank space: ⚪

Multiple-Choice, questions 15 to 22:

Question 15: Information about four different linear relationships between capital C and n is shown below. ⚪

Information about 2 of the relationships is shown in tables and there are graphs of the other 2 relationships. Relationship 1: There is a table with two columns; n and Capital C: ⚪ n, ⚪ 0: ⚪ Capital C, ⚪ 50: ⚪

n, ⚪ 8: ⚪ Capital C, ⚪ 90: ⚪ n, ⚪ 16: ⚪ Capital C, ⚪ 1 hundred 30: ⚪ Relationship 2: There is a table with two columns; n and capital C: ⚪

n, ⚪ 10: ⚪ Capital C, ⚪ 30: ⚪ n, ⚪ 12: ⚪ Capital C: 35: ⚪ n, ⚪ 14: ⚪ Capital C, ⚪ 40: ⚪

Relationship 3: An untitled graph is shown. The horizontal axis, labelled n, starts at 0 and every other gridline is labelled in increments of 2, up to 6. The vertical axis, labelled capital C, starts at 0 and every other gridline is labelled in increments of 10, up to 30. A line is drawn on the graph. The coordinates of two points on the line are: ⚪ 0, ⚪ 5, and, 2, ⚪ 10: ⚪ Relationship 4: An untitled graph is shown. The horizontal axis, labelled n, starts at 0 and every other gridline is labelled in increments of 2, up to 6. The vertical axis, labelled capital C, starts at 0 and every other gridline is labelled in increments of 2, up to 6. A line is drawn on the graph: The coordinates of two points on the line are: ⚪ 0, ⚪ 5, and, 2, ⚪ 5: ⚪

How many of the linear relationships have a rate of change of 5? Answer Choices: ⚪

A: 4: ⚪

B: 3: ⚪

C: 2: ⚪

D: 1: ⚪

Question 16: Which graph shows a line that is perpendicular to the line y = 𝟒𝟒𝟑𝟑

4 over 3, x minus 4?

A:

The horizontal axis, labelled x starts at negative 4 and every other grid line is labelled in increments of 2, up to 4. The vertical axis, labelled y, starts at negative 4 and every other grid line is labelled in increments of 2, up to 4. A line is graphed on the grid. The coordinates of two points on the line are: ⚪ 0, ⚪ negative 4, and, 3, ⚪ 0: ⚪

B:

The horizontal axis, labelled x starts at negative 4 and every other grid line is labelled in increments of 2, up to 4. The vertical axis, labelled y, starts at negative 4 and every other grid line is labelled in increments of 2, up to 4. A line is graphed on the grid. The coordinates of two points on the line are: ⚪ Negative 4, ⚪ 0, and, 0, ⚪ negative 3: ⚪

C:

The horizontal axis, labelled x starts at negative 4 and every other grid line is labelled in increments of 2, up to 4. The vertical axis, labelled y, starts at negative 4 and every other grid line is labelled in increments of 2, up to 4. A line is graphed on the grid. The coordinates of two points on the line are: ⚪

0, ⚪ 4, and, 3, ⚪ 0: ⚪

D:

The horizontal axis, labelled x starts at negative 4 and every other grid line is labelled in increments of 2, up to 4. The vertical axis, labelled y, starts at negative 4 and every other grid line is labelled in increments of 2, up to 4. A line is graphed on the grid. The coordinates of two points on the line are: ⚪ Negative 3, ⚪ 0, and, 0, ⚪ 4: ⚪

Question 17: What is an equation of the line: ⚪

• perpendicular to the line represented by y = negative 3 over 2,

𝟑𝟑𝟐𝟐x plus 1, and,

• with the same y-intercept as the line represented by y = 7 plus 5x?

A: y = 2 over 3, 𝟐𝟐𝟑𝟑 x plus 7: ⚪

B: y = 2 over 3, 𝟐𝟐𝟑𝟑x plus 5: ⚪

C: y = negative 2 over 3, 𝟐𝟐𝟑𝟑x plus 7: ⚪

D: y = negative 2 over 3, 𝟐𝟐𝟑𝟑x plus 5: ⚪

Question 18: The total cost to repair a fridge, capital C, in dollars, can be represented by the equation capital C = 60t plus 30, where t is the repair time in hours.

Which of the following statements is true about this relationship?

A: The hourly rate is 90 dollars. ⚪

B: The fixed fee is 90 dollars. ⚪

C: The hourly rate is 60 dollars, and the fixed fee is 30 dollars. ⚪

D: The hourly rate is 30 dollars, and the fixed fee is 60 dollars. ⚪

Question 19: What is the area of the shape represented below?

A large triangle with its base at the top and vertex at the bottom, has a smaller triangle with its base at the top and vertex at the bottom, removed from it. The small and large triangle share the same base. The length of the base is labelled 14 centimetres. The height of the small triangle that is removed is labelled 8 centimetres. The remaining height of the large triangle, without the height of the small triangle is labelled 12 centimetres. ⚪

A: 28 centimetres squared: ⚪

B: 56 centimetres squared: ⚪

C: 84 centimetres squared: ⚪

D: 1 hundred 68 centimetres squared: ⚪

Question 20: This diagram shows a greenhouse that is built in the shape of a half-cylinder. ⚪

The curved side of the half-cylinder forms the roof of the greenhouse. The rectangular face of the half-cylinder is flat on the ground. The length of this rectangular face is 80 metres. The width of this rectangular face is 20 metres. The width is also the diameter of the half-cylinder. The two semi- circular faces that are the ends of the greenhouse are shaded: ⚪

Material to cover the roof costs 3 dollars per metre squared. The shaded ends will not be covered. Which is closest to the cost of covering the roof?

A: 7 thousand 5 hundred 40 dollars: ⚪

B: 12 thousand 5 hundred 70 dollars: ⚪

C: 15 080 dollars: ⚪

D: 37 thousand 700 dollars: ⚪

Question 21: A cone is pictured below.

The height of the cone is 12 centimetres and the diameter of the circular base is 10 centimetres. There is a right angle between the height and diameter. ⚪

Hint: ⚪ Use Pythagorean theorem as part of your process. ⚪

Which of the following is closest to the surface area of the cone?

A: 2 hundred 67 centimetres squared:

B: 2 hundred 83 centimetres squared:

C: 6 hundred 91 centimetres squared:

D: 7 hundred 23 centimetres squared:

Question 22: Which of the following composite shapes has 900° as the sum of its interior angles?

A:

One side of the square is the same as one side of the polygon. A 6 sided figure is shown. It is formed by combining the square with a 4 sided shape. ⚪

B:

One side of the square is the same as one side of the polygon. A 7 sided figure is shown. It is formed by combining the square with a 5 sided shape: ⚪

C:

One side of the square is the same as one side of the polygone. A 9 sided figure is shown. It is formed by combining the square with a 7 sided shape: ⚪

D:

One side of the square is the same as one side of the polygone. A 10 sided figure is shown. It is formed by combining the square with an 8 sided shape: ⚪