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

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 12: Question 1: The cost of granola bars at two different stores is shown below. ⚪

The first sign says: ⚪ Food-O-Rama, ⚪ Box of 12 granola bars: 7 dollars and forty four cents. ⚪

The second sign says: ⚪ Groceryland, ⚪ each box has 5 granola bars, 2 boxes for 6 dollars: ⚪

What is the difference in the cost per granola bar at these two stores?

A: 2 cents, ⚪

B: 6 cents, ⚪

C: 58 cents, ⚪

D: 62 cents, ⚪

Question 2: Cornerstone High School has 1 thousand 8 hundred 60 students.

• 45% of the students bike or walk to school. ⚪

• 3 hundred 72 students drive to school. ⚪

• The remaining students travel to school by bus. ⚪

How many students travel to school by bus?

A: 6 hundred 51: ⚪

B: 8 hundred 37: ⚪

C: 1209: ⚪

D: 1 thousand 4 hundred 43: ⚪

Question 3: What value of x makes the following equation true?

Square root of x =16: ⚪

A: 4: ⚪

B: 8: ⚪

C: 32: ⚪

D: 2 hundred 56: ⚪

Question 4: A cake is made of two cylindrical layers of ice cream stacked on top of each other as pictured below.

The bottom layer is a cylinder with a height of 6 centimetres and a radius of 15 centimetres. The top layer is a cylinder with a height of 6 centimetres and a radius of 8 centimetres.

The formula for the volume of one layer of this cake, capital V, is: ⚪

Capital V = π, r to the power of

2, h,

where r is the radius of the layer and h is the height of the layer.

Which of the following is closest to the total volume of ice cream needed to make the two layers of this cake?

A: 4 hundred 34 centimetres cubed: ⚪

B: 8 hundred 67 centimetres cubed: ⚪

C: 5 thousand 4 hundred 48 centimetres cubed: ⚪

D: 17 thousand 1 hundred 14 centimetres cubed: ⚪

Question 5: Which of the following shows an appropriate line of best fit for the data?

A:

The horizontal axis, labelled n, starts at 0, and every other grid line is labelled in increments of 1, up to 5. The vertical axis, labelled capital A, starts at 0, and every other grid line is labelled in increments of 10, up to 50. The co-ordinates of the eight points are: ⚪ 1, ⚪ 50: ⚪ 1, ⚪ 40: ⚪

2, ⚪ 40: ⚪ 2, ⚪ 30: ⚪ 3, ⚪ 30: ⚪ 3, ⚪ 20: ⚪ 4, ⚪ 20: ⚪ 4, ⚪ 10: ⚪ A horizontal line through 0, 30, ⚪ and 4, 30: ⚪

B:

The horizontal axis, labelled n, starts at 0, and every other grid line is labelled in increments of 1, up to 5. The vertical axis, labelled capital A, starts at 0, and every other grid line is labelled in increments of 10, up to 50. The co-ordinates of the eight points are: ⚪

1, ⚪ 50: ⚪ 1, ⚪ 40: ⚪ 2, ⚪ 40: ⚪ 2, ⚪ 30: ⚪ 3, ⚪ 30: ⚪ 3, ⚪ 20: ⚪ 4, ⚪ 20: ⚪ 4, ⚪ 10: ⚪

A line starting at 0, 0, and going up to the right through the point 4, 50: ⚪

C:

The horizontal axis, labelled n, starts at 0, and every other grid line is labelled in increments of 1, up to 5. The vertical axis, labelled capital A, starts at 0, and every other grid line is labelled in increments of 10, up to 50. The co-ordinates of the eight points are: ⚪

1, ⚪ 50: ⚪ 1, ⚪ 40: ⚪ 2, ⚪ 40: ⚪ 2, ⚪ 30: ⚪ 3, ⚪ 30: ⚪ 3, ⚪ 20: ⚪

4, ⚪ 20: ⚪ 4, ⚪ 10: ⚪ A line through 0, 50, and 4, 10, where 4 of the points are on the line and 4 of the points are above the line: ⚪

D:

The horizontal axis, labelled n, starts at 0, and every other grid line is labelled in increments of 1, up to 5. The vertical axis, labelled capital A, starts at 0, and every other grid line is labelled in increments of 10, up to 50. The co-ordinates of the eight points are: ⚪ 1, ⚪ 50: ⚪ 1, ⚪ 40: ⚪ 2, ⚪ 40: ⚪ 2, ⚪ 30: ⚪ 3, ⚪ 30: ⚪ 3, ⚪ 20: ⚪

4, ⚪ 20: ⚪ 4, ⚪ 10: ⚪ A line through 0, 53, and 4, 15, where 4 of the points are above the line and 4 of the points are below the line: ⚪

Question 6: The temperatures at 2 a.m. and 4 a.m. on a winter day are recorded in the table.

Time and Temperature in degrees Celsius.

Time, 2 a.m., ⚪ Temperature in degrees Celsius, minus 8: ⚪ Time, 3 a.m., ⚪ Temperature in degrees Celsius, blank space: ⚪ Time, 4 a.m., ⚪ Temperature in degrees Celsius, minus 2: ⚪

Time, 5 a.m., ⚪ Temperature in degrees Celsius, blank space: ⚪

If the relationship between temperature and time is linear, what are the temperatures at 3 a.m. and 5 a.m.?

A: minus 4 °Celsius and 0 °Celsius. ⚪

B: minus 4 °Celsius and 2 °Celsius. ⚪

C: minus 5 °Celsius and 1 °Celsius. ⚪

D: minus 5 °Celsius and 5 °Celsius. ⚪

Question 7: Information about the amount of money A amari has left at the end of each month is shown by the graph.

The horizontal axis, labelled Number of months, n, starts at 0 and every other gridline is labelled in increments of 2, up to 10. The vertical axis, labelled Amount of money, in dollars, capital A: starts at 0 and every other grid line is labelled in increments of 100, up to 400. 7 points are plotted on the graph. The coordinates of these points are: ⚪

0, ⚪ 300: ⚪ 1, ⚪ 2 hundred 50: ⚪ 2, ⚪ 200: ⚪ 3, ⚪ 1 hundred 50: ⚪ 4, ⚪ 100: ⚪ 5, ⚪ 50: ⚪ 6, ⚪ 0: ⚪

A amari started with 300 dollars and spent the same amount each month. He reached 0 dollars afters 6 months.

If A amari had spent 100 dollars more per month, and had started with 300 dollars, when would he have reached 0 dollars?

A: 2 months: ⚪

B: 3 months: ⚪

C: 6 months: ⚪

D: 8 months: ⚪

Question 8: Information about four different linear relationships is given below. ⚪

The first linear relationship is represented by an, Equation: ⚪ capital K = 2n plus 7: ⚪

The second linear relationship is represented by a, Description: ⚪ the total cost to print T-shirts is made up of a set-up fee of 65 dollars and a cost of 7 dollars per T-shirt. ⚪ Information about the third linear relationship is given in a Table with two columns: ⚪ h and capital T: ⚪ h, ⚪ 0: ⚪ Capital T, ⚪ 10: ⚪ H, ⚪ 1: ⚪ Capital T, ⚪ 17: ⚪

H, ⚪ 2: ⚪ Capital T, ⚪ 24: ⚪ The fourth linear relationship is represented by a Graph with the horizontal axis, labelled t, starts at 0 and every other gridline is labelled in increments of 1, up to 4. The vertical axis, labelled capital D, starts at 0 and every other gridline is labelled in increments of 2, up to 8. A line is drawn on the graph. The coordinates of two points on the line are: ⚪ 0, ⚪ 7: ⚪ 1, ⚪ 6: ⚪

Which two of these linear relationships have a rate of change of 7?

A: “Table” and “Graph”, ⚪

B: “Table” and “Description”, ⚪

C: “Equation” and “Graph”, ⚪

D: “Equation” and “Description”, ⚪

Question 9: Joel has a summer job cutting lawns. The relationship between his profit, capital P, in dollars, and the number of lawns cut, n, is shown by the graph below.

The origin is labelled zero. A line starts at negative 100 on the capital P-axis and continues up to the right. It passes through the n-axis at 5 and continues to extend upwards to the edge of the graph. No other values are labelled. ⚪

What type of variation is the relationship, and what is its initial value?

A: a direct variation with an initial value of 5 dollars: ⚪

B: a direct variation with an initial value of negative 100 dollars: ⚪

C: a partial variation with an initial value of 5 dollars: ⚪

D: a partial variation with an initial value of negative 100 dollars: ⚪

Question 10: The graph below represents information about the linear relationship between the total cost of a day at the fair and the number of rides taken.

The horizontal axis, labelled Number of rides taken, r, starts at 0, and every fourth grid line is labelled in increments of 1, up to 4. The vertical axis, labelled Total cost in dollars, capital C, has a break in it. It starts on the second grid line at 25 and every fifth grid line is labelled in increments of 5, up to 40. Three points are drawn on the grid. Here are the coordinates of the points: ⚪ 2, ⚪ 32: ⚪ 3, ⚪ 35: ⚪ 4, ⚪ 38: ⚪

Which of the following equations represents the relationship between capital C and r?

A: capi tal C = 3r: ⚪

B: capital C = 9. Decimal 5r: ⚪

C: capital C = 0. Decimal 7 5r plus 26: ⚪

D: capital C = 3r plus 26: ⚪

Question 11: Enviro-Car rents vehicles. The company is advertising a change in its total costs as shown below.

Our Costs Are Changing, ⚪ Old total cost: 25 dollars fixed cost; 25 cents per kilometre. ⚪

New total cost: 32 dollars fixed cost; 15 cents per kilometre. ⚪

Enviro-Car plans to graph the relationship between the total cost, capital C, and number of kilometres, n, for both total costs.

How will the graph of the new total cost be different from the graph of the old total cost?

The graph of the new total cost will be: ⚪

A: steeper and start higher on the capital C-axis. ⚪

B: steeper and start lower on the capital C-axis. ⚪

C: less steep and start higher on the capital C-axis. ⚪

D: less steep and start lower on the capital C-axis. ⚪

Question 12: Ariel and Hayden each have money in a bank account that does not give any interest. Hayden’s weekly account balance is shown by the graph below.

The horizontal axis, labelled Week, w, starts at 0 and every other grid line is labelled in increments of 1, up to 8. The vertical axis, labelled Account balance in dollars, capital A: starts at 0 and every other grid line is labelled in increments of 20, up to 220. A line labelled Hayden is drawn on the grid. Here are the coordinates of 4 points along the line:

0, ⚪ 50: ⚪ 4, 90: ⚪ 5, ⚪100: ⚪ 6, ⚪ 110: ⚪

Ariel starts with 200 dollars in her account and spends 20 dollars each week, without making any deposits.

Which of the following is true?

A: Hayden will have less money in his account than Ariel in Week 5. ⚪

B: Hayden will always have more money in his account than Ariel. ⚪

C: Ariel starts with less money in her account than Hayden. ⚪

D: Ariel has more money in her account than Hayden in Week 4. ⚪

Open-Response, questions 13 to 18: Question 13: Hamburgers and Hot Dogs: ⚪

At a local event, the ratio of hamburgers to hot dogs sold is 5 to: 3. ⚪

The number of hamburgers sold is 2 hundred 75. ⚪

How many more hamburgers than hot dogs are sold?

Show your work. ⚪

There are [blank space] ⚪ more hamburgers than hot dogs sold. ⚪

Question 14: Great Lengths: ⚪

The rectangular yard pictured below has algebraic expressions for its side lengths, in metres.

There are expressions for each of the sides of the yard. The two lengths are each labelled 3x. The two widths are each labelled 2x minus 1. ⚪

The perimeter of the yard is 1 hundred 26 meters. ⚪

Complete the equation below so that it represents the perimeter of the yard.

1 hundred 26 = [Blank space] ⚪.

Determine the value of x using your equation. ⚪

Show your work. ⚪

The value of x is [blank space] ⚪.

Question 15: Signed, Sealed and Delivered: ⚪

Two companies deliver packages. Information about the total cost, capital C, in dollars, for each company is given below.

Capital C = 3d: d represents the distance the package is shipped, in kilometres. Company 2: Express Delivery: ⚪

A graph titled Total Cost versus Mass of the Package. The horizontal axis, labelled Mass of the package, in kilograms, m, starts at 0 and every other grid line is labelled in increments of 1, up to 8. The vertical axis, labelled Total cost in dollars, capital C, starts at 0 and every other grid line is labelled in increments of 5, up to 25. A line is drawn on the graph. Here are the coordinates for two points on the line: ⚪ 0, ⚪ 5, and 6, ⚪ 20: ⚪

Complete the chart below by determining the initial value and the rate of change for each company.

Describe the meaning of the rate of change in each situation.

Flash Delivery: ⚪ Initial Value, ⚪ blank space: ⚪ Rate of change, ⚪ blank space: ⚪ Meaning of the rate of change in this situation, ⚪ blank space: ⚪

Express Delivery: ⚪ Initial Value, ⚪ blank space: ⚪ Rate of change, ⚪ blank space: ⚪ Meaning of the rate of change in this situation, ⚪ blank space: ⚪

Question 16: Charity Walk: ⚪

Emily participates in a 10 kilometre charity walk, where the walkers follow a straight path from the start then return along the same path to the finish. This graph shows the relationship between Emily’s distance from the start and her time.

The horizontal axis, labelled Time in minutes, t, starts at 0 and every other gridline is labelled in increments of 10, up to 100. The vertical axis, labelled Distance from start in kilometers, capital D, starts at 0 and every gridline is labelled in increments of 1, up to 6. Three line segments labelled capital A: capital B, and capital C, are plotted on the graph. The line segments are connected. The coordinates of the end points of each line segments are given: ⚪

Line segment Capital A: 0, ⚪ 0, and, 40: ⚪ 5: ⚪ Line segment Capital B: 40: ⚪ 5, and, 50: ⚪ 5: ⚪ Line segment Capital C: 50: ⚪ 5, and, 100, ⚪ 0: ⚪

Describe each segment of her walk. Include information about distance travelled, time, speed in kilometres per minute and direction.

Segment, Distance travelled, Time, Speed in kilometers per minute and Direction.

Segment, ⚪ A: ⚪ Distance travelled: blank space: ⚪ Time, ⚪ blank space: ⚪ Speed, ⚪ blank space: ⚪ Direction, ⚪ blank space: ⚪ Segment, ⚪ B: ⚪ Distance travelled, ⚪ blank space: ⚪ Time, ⚪ blank space: ⚪ Speed, ⚪ blank space: ⚪ Direction, ⚪ blank space: ⚪ Segment, ⚪ C: ⚪ Distance travelled, ⚪ blank space: ⚪ Time, ⚪ blank space: ⚪ Speed, ⚪ blank space: ⚪ Direction, ⚪ blank space: ⚪

Question 17: Grid School: ⚪

The diagram on the grid below represents the shape of a school. ⚪

The school is made up of 4 shapes that are joined. The shapes are 2 rectangles, 1 semi-circle, and 1 right triangle. ⚪

Clockwise around the diagram, the smaller rectangle is on the top right, the triangle is on the bottom right and the larger rectangle on the bottom left. All three shapes are connected by one side to the next shape. They do not overlap. The triangle is positioned so that the right angle of the triangle is on the top left corner of the triangle. The base of the triangle is on the top and this side is also the length of the smaller rectangle. The height of the triangle is on the left and this side is also the width of the larger rectangle. The smaller rectangle has a length of 60 metres and a width of 50 metres. The larger rectangle has a length of 80 metres and a width of 50 metres. A semi-circle is attached to one side of the bottom left rectangle. It has a diameter of 40 meters: ⚪

Determine the total area of the shape of the school. ⚪

Show your work. ⚪

Question 18: Magnificent Map: ⚪

A map is pictured below. ⚪

Two additional roads, that are not parallel to each other, are also shown. These two non-parallel roads start at the same point above the two parallel roads and form an upside down V as one goes down to the left and the other goes down to the right. They each intersect both of the parallel lines and end below the bottom parallel line. The angle below the point where these two roads start and formed by these roads is labelled y. The angle formed above the top parallel road, and to the right of the non-parallel road on the right, is labelled 1 hundred 18 degrees. There are 4 angles where the bottom parallel line intersects the non-parallel line on the left. The two angles above this parallel line are labelled. The angle on the right is labelled 76 degrees and the angle on the left is labelled x. ⚪

Complete the table below with the values of x and y. Justify your answers 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, questions19 to 22: Question 19: The ramp pictured below is 12 meters long and has a base of 10 meters.

Its base is labelled 10 metres and its hypotenuse is labelled 12 metres. The third side is labelled h. ⚪

Which of the following is closest to the height, h, of the ramp?

A: 2 meters: ⚪

B: 7 meters: ⚪

C: 16 meters: ⚪

D: 22 meters: ⚪

Question 20: Orange Dream sells drinks in two sizes of cylindrical cans. The smaller can is pictured below.

The height of the can is labelled 10 centimetres and the radius of the can is labelled 4 centimetres. ⚪

The larger can has the same height and a radius that is triple the radius of the smaller can.

How many times larger is the volume of the larger can than that of the smaller can?

A: 3 times larger: ⚪

B: 9 times larger: ⚪

C: 12 times larger: ⚪

D: 27 times larger: ⚪

Question 21: What is the value of x in the diagram below?

Starting at the top left corner and moving clockwise, the interior angles are labelled 1 hundred 28 degrees, 96 degrees, 84 degrees, 1 hundred 20 degrees, and x. ⚪

A: 60°: ⚪

B: 68°: ⚪

C: 1 hundred 12°: ⚪

D: 1 hundred 28°: ⚪

Question 22: What are the values of x and y in the diagram below?

A third line is drawn that starts on the top left side of the diagram, crosses through the parallel lines and ends on the bottom right side of diagram. The angle above the top parallel line and on the left side of the third line is labelled 62 degrees, and the angle below this top parallel line and to the right of the third line is labelled x. The angle above the bottom parallel line and to the right of the third line, is labelled y: ⚪ Answer Choices: ⚪

A: x = 62°, ⚪ y = 62°: ⚪

B: x = 62°, ⚪ y = 1 hundred 18°: ⚪

C: x = 1 hundred 18°, ⚪ y = 1 hundred 18°: ⚪

D: x = 1 hundred 18°, ⚪ y = 62°: ⚪