Grade 9 Applied Exam Review

 

Remember that there is Free Math Tutoring available 5:30-9:30 Sunday to Thursday at homeworkhelp.ilc.org

Part A

    

1. Find the length of the ramp.

 

 

Solution

 

2.  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

 

 

 

 

 

 

3. Calculate the volume of the pyramid shown below.

 

 

Solution

 

 

4. Calculate the volume of the pyramid shown below.

 

 

Solution

5. 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 rate of change (slope) of the line? How does this relate to his rate of pay?        

c) What is the initial value (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

6. 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 rate of change (slope) of the line? How does this relate to the rate of his descent?    

c)  What is the initial value (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

 

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

 

 

 

 

8.      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

 

 

 9.     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

 

 

 

 


10. Calculate the volume 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

 

 

 

 

 

 

11. Calculate the volume of the cone.

 

 

 

Solution

 

Grade 9 Applied Exam Review Part B

 

Remember that there is Free Math Tutoring available 5:30-9:30 Sunday to Thursday at homeworkhelp.ilc.org

 

 

1.  Solve algebraically. Show all steps!!!

 

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

 

 

 

 

 

 

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

 

 

 

 

 

e)                                                f)                         Solutions cdef

 

 

 

 

 

 

 

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

 

 

                                                                                                                        Solutions g-i

 

 

 

 

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

 

 

 

 

 

 

2. 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

 

i)

 

 Solution

j)

 

 Solution

 

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

 

a)     

        

 

 

 

 

 

 

 

 

      Solution

b)

        

 

 

 

 

 

 

Solution

4. 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 rate of change (slope) and the initial value (y-intercept) of the graph.

d) What does the initial value (y-intercept) represent?

 

e) What does the rate of change (slope) represent? What are the units for the rate of change (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

 

Grade 9 Applied Exam Review Part C

 

Remember that there is Free Math Tutoring available 5:30-9:30 Sunday to Thursday at homeworkhelp.ilc.org

 

1. Simplify                             Solutions #1 and 2abcd

 

a)                                          b)

 

2  Simplify

 

a)                                          b)

 

c)                             d)

 

 

 

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

 

 

 

3. 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

 

 

 

4.      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     

 

 

5.      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



 

6. 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



 

7. 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






 

8.      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












9. 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

 










10.    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

    









11.    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

 









12. Complete the following table.

 

Fraction

Decimal

Percent

 

 

 

0.32

 

 

 

7%

 

 

 

0.77

 

 

 

125%

 

Solution ab                           Solution cde

 

 

 

13. 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

 

14. 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

 

 

 

 

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

      

        

       Solution

 

 

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

 

 

Solution

 

 

17. 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

 

18.    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