Grade 9 Academic Exam Review

 

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Part A Cartesian coordinate graphing and equation of a line.

 

1.         What are the co-ordinates of each point?

 

 

Solution

 

2.         What is the slope of each line segment?

a)

 

 

b)

 

c)

 

d)

 

e)

 

f)

 

 

g)

 

h)

 

Solution

 

3.         Identify the y-intercept and the slope.

 

i)                ii)                         iii)       iv)

 

Solution

 

4. Match each graph to its equation.

(a) y = 3x + 1               (b) y = 3x - 1                (c) y=x+3                     (d) y=-x+3

 

          ­­

 

         

 

Solution

 

5.         Write the equation of each line in slope y-intercept form.

a)

         

 

 

 

 

Solution

 

 

b) Graph the following lines using the slope and y-intercept. Do not use a table of values.

 

i)     ii)               iii)             iv)

 

Solution

 

 

4.         Graph each of the following using a table of values.

 

a)                      Solution          

 

b)              Solution                      

 

c)                    Solution          

 

d)             Solution

5.         Using the proper formula, find the slope of the line between pair of points

 

a)     (5, -7) and (-3, -9)                                     Solution

b)    (4, -3) and (2, -1)                          Solution

c)     (3, 6) and (-3, 6)                                        Solution

d)    (-4, 12) and (-4, 5)                                    Solution

 

 

7. For each line in the graph below, identify the slope, the y-intercept and the equation of the line.

 

 

Solution a-d

 

 

Solution ef                   Solution gh­

8. Determine the equation of the line that passes through the point K(–4, –5) and has slope of .

Solution

 

 

9.         Find the slope and the y-intercept of the line.

            a) 2x + y = 4.                                      Solution

 

            b) 3x – y – 6  = 0.                                Solution                                              

 

            c) 4x – 5y +10  = 0.                             Solution

 

            d) 4x + 6y – 24 = 0.                             Solution

 

 

 

 

 

PART B

           

1.              Express each fraction as a decimal. Round to 1 decimal place.

                                                         

 

2.              Change to improper fractions.




3.              Change to mixed numbers.

 

           

 

4.         Add or subtract.

 

Solutions to #1-4

 

5.         Evaluate. Express your answer in lowest terms.

 

Solution

 

6.         Find the length of the ramp.

 

 

Solution

 

7.                     A 7 m ladder is leaning against a wall. The foot of the ladder is 2.6 m from the base of the wall. How high up the wall does the ladder reach?

 

 

Solution

 

 

 

 

 

 

8.         Calculate the volume of the pyramid shown below.

 

 

Solution

 

 

9.         Calculate the volume of the pyramid shown below.

 

 

Solution

10.       Adam has a summer job selling magazines subscriptions. The graph below shows his weekly earnings for the number of subscriptions he sells for a     given week.    

 

 

a) How much does Adam earn for selling 20 subscriptions? 45 subscriptions?       

b) What is the slope of the line? How does this relate to his rate of pay?    

c) What is the y-intercept of the line? How does this relate to his pay?

d) What is the equation of the line? Let E, represent pay and let n represent number of subscriptions.

 

Solution

11.       Luke is snow boarding at Whistler. The graph below illustrates his altitude             above the base of the hill as he descends.                              

a)     How far has he descended from the top of the hill after 2.5 min? 5 min?

b)    What is the slope of the line? How does this relate to the rate of his descent?

c)     What is the y-intercept? How does this relate to his snowboard run?

d)    What is the equation of the line? Let a, represent altitude and let t represent number of minutes

 

Solution

 

12.       Find the circumference and area of a circle with radius of 6 m. Round to the nearest hundredth.     Solution

 

13        a) Find the diameter of a circle with circumference of 56.55 m circle to the nearest m.
            b) Find the area of the circle to the nearest square metre.

 

            Solution

 14.      For the formula A = ½bh,
            a) find A if b = 18 cm and h = 4 cm
            b) find b if h = 12 m and A = 60 m2

            Solution


15.       Calculate the volume and surface area of a can of that has a height of 11.0 cm and a radius of 3.7 cm Round to 1 decimal point.

 

            Solution

 

16.       Calculate the height of a cylinder with a volume of 600 cm3 and a radius of 5 cm.

 

            Solution

 

17. Calculate the volume of the cone.

 

Solution

 

 

 

Part C: Final Exam Review

 

1.         Solve algebraically. Show all steps!!!

 

a)         2x – 12 = –2                                        b)         5 + 3x = 11

 

 

c)         –2x = –16                                            d)         9x = –27

 

e)                                                 f)        

 

Solutions ab

 

 

Solutions cdef

 

 

g) 5(2x + 3) = –15                                            h) 2x + 3 x = 8x – 3

 

 

 

 

i) 3r – 5r – 3 = 7                                              j) ) 4(x – 3) + 3x + 6  = 8

 

 

Solutions g-i

 

 

 

2. On the grid, draw lines with the following slopes.

 

i) slope =  3                        ii)  slope =              iii) slope =  0.75

 

Solution

 

 

3.   a) Plot each pair of points on the grid.

 

i)    (1, –5) and (3, –3)                         ii)   (2, –4) and (–6, 2)

 

 

b) Determine the equation of the line in slope y-intercept form that passes through each pair of points.

 

Solution

 

4.   Draw the line that passes through the point M(3, 4) and has slope  

Solution

 

 

 

 

Part D: Final Exam Review

 

                                                                                               

 

 

1. Write an equation and solve for the unknown. Sub your answer into each expression to determine the measure of the angle. Give reasons for your answers. Note: These diagrams are not drawn to scale.



 

 

 

 

 

 

 

 

 Solution

b)

Solution

 

 Solution

d)

Solution

 

 

e)

 

 

Solution

 

 

 Solution

 

 

 Solution

 

 

h)

 

 Solution

 

h)

 

 Solution

a)

 

 Solution

 

2.

 

3.   What is the slope and y-intercept of the line   

slope =                         y-intercept =

 

 

 

Solution

 

 

 

4.   Solve for x.  Give each answer correct to 1 decimal place.

 

a)                                                           

                                                        

 

 

 

 

 

 

 

 

                                                                                 Solution

b)

                                                        

 

 

 

 

 

 

 

 

 

                                                                        Solution

 

 

 

5.   Calculate the perimeter and area of the figure below.Text Box:

                       

                                                                               15x

 

 

                                                                                                              7x

 

 

 

                                    Solution

 

6.   Calculate the area and perimeter of the figure below.

 

 

                                        3x +2

 

 

 


               2x

                                           3x + 12

 

 

Solution

 

7.   A plumber charges a flat rate of $25.00 for a house call and $50.00 an hour for labour.

a)     Complete the following table of values.

Number of hours labour

Cost ($)

1

 

2

 

4

 

7

 

 

b)    Write an equation for the relation between total cost, C and the number of hours labour,h.

 

 

Solutions ab

 

c) Graph the relation and determine the slope and the y-intercept of the graph.

d) What does the y-intercept represent?

 

e) What does the slope represent? What are the units for the slope?

 

Solution cde

f) Use the equation from part b) to determine the cost of hiring the plumber for 11.5 hour job.



g) If the bill is $337.50, how long was the plumber on the job? 

 

Solution fg

Part E Exam Review

 

1          a) What is the y-intercept for the equation 3x + 4y = –12 ?

            b) What is the x-intercept for the equation 3x + 4y = –12 ?

            c) Graph the line 3x + 4y = –12 using the x and y intercepts.

 

Solution a

 

Solution b

 

Solution c

 

2.         Graph the line 6x - 3y = 24 using the intercept method.

 

Solution

 

3.         Find the equation of the line that has a slope  and y-intercept (0, 4).

 

Solution

 

4.         Find the equation of the line which has a slope 3 and passes through the point F(-2, -5). Express your answer in the slope y-intercept form.

 

Solution

 

5.         Find the equation of the line which has a slope    and passes through the point G(-9, -11). Express your answer in the slope y-intercept form.

 

Solution

 

6.         a) Verify algebraically, that the point (-8, -19) is a point on the line

 

Solution

 

            b) Verify algebraically, that the point (11, -323) is a point on the line                      

 

Solution

           

            c) Verify algebraically, that the point (-4, -1) is a point on the line

 

 

 

Solution

 

7.         Determine whether each point is on the line

            a) (2,6)                                                            b) (-3,-5)

 

Solution a                                                        Solution b

 

8.         Determine whether each point is on the line

 

            a) (-3,-5)                      b) (6,2)                       

 

Solution a                                Solution b

 

9.         a)  Find the slope of the line between the two points.

            b)  Find the y-intercept of the line.

            c)  Determine the equation of the line passing through each pair of points.

 

a)     (-3, -7) and (4, 7)                                                                          b)  (-1, -5) and (2, 7)

 

Solution a                                                                                            Solution b

 

 

11.       Find the slope of the line that passes through the point (3, 5) and is parallel to the line 2x + 5y = 4.

 

 

 

 

Solution

 

 

12.       Write the equation of the line parallel to 3x + y – 4  = 0 that passes through            the point A(2,-5).

 

 

 

Solution

 

13.       Show that the following points are the vertices of a parallelogram A(2, 1), B(14, 11), C(6, 5), and D(-6, -5).

 

 

 

Solution

 

14.       A line segment has slope    and one endpoint A(-4, -3).  Find y if the other         endpoint is B(12, y).

 

 

 

 

Solution

 

 

15.       Find the slope of the line that is perpendicular to the line -3x + 6y = -8.

 

 

Solution

 

16.       Write the equation of the line perpendicular to the line having the equation 5x - y = 4 and passes through the point (10, 8).

 

 

 

Solution

 

 

17.       Use calculations to show that the points, A (6, 5), B(1, -1), and C(-5,4), are the vertices of a right triangle.

 

 

Solution

 

18.       A line segment is perpendicular to a line with slope      . The line segment            has one endpoint (-4, -6).  Find y if the other endpoint is(-8, y).

 

Solution

 

Part F Exam Review

 

 

1.         Simplify

 

                   

 

2          Simplify

 

a)                                          b)

 

c)                              d)

 

Solutions #1 and 2abcd

 

e)         (6x + 8) + (9x + 2)                  f)          (4x2 + 6x - 5) + (– x2 – 7x – 10)

 

Solutions ef

 

g)         (–5x + 7) – (–3x – 6)               h)         (4x + 1) – (5x – 8)

 

Solutions gh

 

i)

 

Solution

 

 

3.         Express as a single power with a single exponent.

 

            a) (5-3)(57)                               b)

 

            c) (10-2)-3                                                 d) (7-9)(7-3)                 

 

 

Solution

 

 

 

4.         Solve.

 

            a)  5(2a – 3) = 15                                b) 7(2f + 6) = –12

 

 

            c) 3(4x – 4) – 6x = 10              d) 3(a – 9) = 2a

 

           

Solution abcd

 

 

            e) 5(r + 4) = –6(2r – 5)                       f)

 

Solution ef

 

 

 

 

            g)                                       h)

 

 

Solutions gh

 

 

 

 

 

5.         Simplify.

 

            a) 4a2(3a + 6)                          b) 4a2(3a + 6) – 9(3a2 – 3a)

 

 

 

Solution

 

 

Part G Exam Review

 

1.         Solve for x.

 

            a)                    b)                      c)                   

 

d)                               e) x:2 = 10:5              f) 6:x = 10:25            

 

g) 8:x = 66:33                       h) x:2.6 = 10:6.5

 

 

Solution a                  Solution b                  Solution c                  Solution d                 

Solution e                  Solution f                   Solution g                  Solution h     

 

 

2.         You are building a ramp that must rise to a ratio of 8cm rise for every        100cm of horizontal length. Your ramp must rise to a total height of            234cm. What is horizontal length will you need for the ramp?

 

Solution

 

3.         In a photograph of a mother and her son standing together, the son          measures 27 mm and the mother 63 mm. If the mother is actually 180 cm          tall, how tall is her son?

 

Solution

 

4.         The ratio of a person's height to his or her arm span is 32:24. How tall is a          person whose arm span is 144 cm?

Solution

 

5.         What is the unit rate for the following items?

 

a)    12 mp3 downloads for $9.99

b)    $2.75 for 6 oranges

c)    20 push-ups in 52 seconds

d)    $3.86 for 1 kg

e)    $34.40 for 8 h

f)      490 km in 7 h

 

Solution abc                         Solution def

 

6.         Maureen's car uses 213.6 L of gasoline in traveling 2400 km. 


            a) What is the car's fuel consumption in L/100km? 


            b) How many litres of gasoline would Maureen need for a 4000 km trip?

 

Solution a                                          Solution b

 

7.         In one season, Casey batted at a rate of 2 hits for every 5 official times at             bat.  At this rate:

            a) How many hits should he get in 400 official times at bat?

            b) How many times should Casey have at bat to get 180 hits?

 

Solution a                              Solution b

           

8.         What is a better deal?

 

            a) 100 cell phone minutes for $4.32 or 80 cell phone minutes for $3.04?

            a) A case of 50 chocolate bars for $17.00 or 3 chocolate bars for $0.99?

 

Solution a                              Solution b

 

9. Complete the following table.

 

Fraction

Decimal

Percent

 

 

 

0.32

 

 

 

7%

 

 

 

0.77

 

 

 

125%

 

Solution ab                              Solution cde

 

10. Calculate.

 

a) 5% of 365 is ________                               b) 8.5% of 4560 is _________


Solution a                                                        Solution b

 

c) 10% of $456.78 is ________                      d) 5.6% of $1276.99 is __________


Solution c                                                        Solution d

 

11. Complete the following table.

 

 

Scale

Diagram Measurement

Actual Measurement

a)

1:250

3 cm

 

b)

9500:1

 

0.0225 mm

c)

 

7.2 cm

0.6 cm

 

Solution a                    Solution b                    Solution c

 

 

12. This diagram was drawn using a scale of 1:7. What is the actual height of this penguin?

                 

                   

                                    Solution

 

 

13. The actual length of this cell is 0.032 cm across. What scale was used to draw this diagram?

 

 

Solution

 

 

14. HaroldŐs Futon Store is offering 25% off all regular priced futon frames. You have decided to purchase a futon mattress and frame from the store. The sales person, Harold Jr., shows you different models and you decide on a futon frame that costs $129.99 regular price, and a futon mattress that has a price of $79.99.

What will your total cost for the frame and mattress be after the discount and taxes?

Here is a sales receipt to assist in organizing your calculations.

 

HaroldŐs Futon Store

Item Description

Quantity

Ticketed Price

Amount of Discount

Final Price

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Subtotal

 

 

 

 

GST 5%

 

 

 

 

PST 8%

 

 

 

 

 

 

 

 

 

TOTAL

 

 

Solution

 

15.       A jacket is regularly priced at $89.49. It goes on sale at 25% off the regular             price.

What will your total cost for the jacket be after the discount and taxes?

Here is a sales receipt to assist in organizing your calculations.

 

Item Description

Quantity

Ticketed Price

Amount of Discount

Final Price

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Subtotal

 

 

 

 

GST 5%

 

 

 

 

PST 8%

 

 

 

 

 

 

 

 

 

TOTAL

 

           

 

Solution