wrp examination general mathematics 2012

8/13/2019 WRP Examination General Mathematics 2012

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General Mathematics

General Instructions

o Reading Time- 5 minutes

o Working Time 1 hours

o Write using a blue or black pen

o Board approved calculators may be used

o A Formulae Sheet is provided at theback of this paper which may be

detached and used throughout the paper.

Total Marks 70

20 marks

o Attempt Questions 1-20

o Answer on the Multiple Choiceanswer sheet provided.

o Allow about 30 minutes for thissection.

50 marks

o Attempt questions 21 25

o Answer on the blank paper provided,

unless otherwise instructed. Start anew sheet for each question.

o Allow about 1 hours for thissection

Section II

Section I


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2012 Preliminary Final Examination General Mathematics

2

x-10 -5 5 10

y

-10

-5

5

10

x-10 -5 5 10

y

-10

-5

5

10

x-10 -5 5 10

y

-10

-5

5

10

x-10 -5 5 10

y

-10

-5

5

10

Section I

20 marks

Attempt Questions 1-20

Allow about 30 minutes for this section

Use the multiple choice answer sheet for questions 1 20.

1. Using the formula = b2 4ac , find when a = 2, b = 3 and c = -5.

(A) -31

(B) 2

(C) 5

(D) 49

2. Which graph below shows a line which has a gradient of 13

?

(A) (B)

(C) (D)


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3. Expand and simplify 2 (x + 3) + (3 2x) .

(A) 3x

(B) 9x

(C) 13x

(D) 4x2

+ 3x

4. The cost of a phone call consists of an initial fee of $0.50 plus $0.25 per minute ( m). Aformula for the price of the phone call could be:

(A) C= 2m + 5

(B) C= 0.5m + 0.25 (C) C= 0.25m + 0.5

(D) C= 4m + 12

5. If $5000 is invested for 4 years at 8% p.a. compounded quarterly. The final balance ofthe account after this time is:

(A) $1802.44

(B) $1863.93

(C) $6802.44

(D) $6863.93

6. A salesperson earns a retainer of $500 plus 5% commission on all the stock that theysell each month. If $32 000 was sold, how much would they have earned that month?

(A) $505

(B) $2100

(C) $2500(D) $32 025

7. Cameron is preparing a BAS statement for his business. He needs to determine howmuch GST to pass on to the tax office. If sales were $35 200 (including GST), whatamount of GST was collected by his business?

(A) $3200

(B) $3520

(C) $3911.11(D) $4400


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8. Vanessa has taken 4 weeks leave to go overseas. She will receive her normal pay plus

a leave loading of 17 12

%. If she normally earns $3600 per fortnight, how much will

she receive during her four weeks away?

(A) $630(B) $1260

(C) $4230

(D) $8460

9. If a six-sided die is thrown, what chance is there of the result being greater than 4?

(A) 16

(B) 13

(C) 12

(D) 23

10. If there are 12 red balls, 5 blue balls and 7 green balls in a bag, what is the likelihood

that a blue ball is not drawn out?

(A) 524

(B) 519

(C) 1924

(D) 195

11. When two six-sided dice are thrown, what chance is there of rolling a total of 9 ormore?

(A) 14

(B) 518

(C) 1

3

(D) 34


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12. For a good mortar mix when laying bricks, a ratio of 6 parts sand to 2 parts lime to

1 part cement is needed. If Ali has 6kg of lime, how many kilograms of sand andcement will he need?

(A) 18 kg sand & 3 kg cement

(B) 9 kg sand & 1.5 kg cement

(C) 6 kg sand & 1 kg cement

(D) 3 kg sand & 18 kg cement

13. What is the volume of the triangular prism in this diagram?

(A) 132 m3

(B) 180m

3

(C) 234 m

3

(D) 360 m3

12m6m

5m

14. These two triangles are similar. Find the value ofx.

8m 52.5m12m x m

21m

(A) 6.6 m

(B) 25 m

(C) 30 m

(D) 91.9 m


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15. How far is the 8 metre long ladder away from the wall at the base?

8 m

(A) 2.74 m

(B) 7.52 m

(C) 21.98 m 70

(D) 23.39 m

16. A flask has markings every 25mL up its side. What is the percentage error if 375mL ismeasured in this flask?

(A) 0.07%

(B) 1.5%

(C) 313%

(D) 623

%

17. An example of categorical data is:

(A) The number of cars passing through an intersection.

(B) The length of each car in a car park.

(C) The number of kilometres shown on the odometer of each car.

(D) The colour of each car in a car park.

18. For any given set of data, the interquartile range will be smaller than the range:

(A) Never.

(B) Mostly.

(C) Always.

(D) The two cannot be compared.


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19. A batter in a cricket team scores the following in one season:

{0, 0, 5, 21, 23, 24, 34, 36, 47, 49, 49}

The standard deviation of these scores is: (correct to one decimal place)

(A) 17.8

(B) 17.9

(C) 18.6

(D) 18.7

20. The mean, median and mode of a set of data, respectively, are:

(A) The average, middle number, most common number.

(B) Most common number, average, middle number.

(C) Lowest number, middle number, highest number.

(D) The average, most common number, middle number.

End Section 1


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Section II

Total Marks (50)

Attempt Questions 21 - 25

Allow about 1 hours for this section.

Answer all questions, starting each question on a new sheet of paper with yourname and question number at the top of the page. Do not write on the back ofsheets.All necessary working should be shown in every question.

Question 21 (10 marks) Start a new sheet of writing paper. Marks

(a) What is the equation of the line shown in the graph below?

x-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10

y

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

8

9

1011

2

(b) Solve the equation below, showing your working fully.

2x 15 =

3x

4

2

(c) If a = 3, b = -2 and c = 12, find the value of:

(i) cab

1

(ii) a(b + c) 1

(iii) a2

b

2

c 1


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Question 21 continues Marks

(d) The graph below gives the cost of parking in a secure parking area.

x5 10 15 20 25

y

5

10

15

20

25

30

35

(i) How much does it cost to park for 13 hours? 1

(ii) If I only have $25 and have parked my car at 3:00 am, when must I leave by? 1

(iii) I need to park for 5 12

hours. If I go out and repark the car just under 3 hours

after it is first parked, how much will I save?1

End of Question 21

Cost ($)

Time Parking (hours)


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(a) This is a table showing the income tax payable for Australians.

Taxable income Tax on this income

0 - $18,200 Nil

$18,201 - $37,000 19c for each $1 over $18,200

$37,001 - $80,000 $3,572 plus 32.5c for each $1 over $37,000

$80,001 - $180,000 $17,547 plus 37c for each $1 over $80,000

$180,001 and over $54,547 plus 45c for each $1 over $180,000

(i) James earns $74 983 this financial year in his primary occupation. He alsoearns another $2012 from share dividends. He has $13 075 worth ofdeductions. What is his taxable income?

1

(ii) Using the table above, calculate the amount of tax that James is due to pay. 1

(iii) James also has to pay the medicare levy which is 1.5% of his taxable income.How much is his medicare levy?

1

(iv) James has $550 deducted each fortnight from his pay for tax. CalculateJames bill or refund for the tax year.

1

(b) Jannesse receives $5000 as a gift from her grandmother.

(i) Find the value of an account where she invests the $5000 for 5 years,compounded annually at 5.5% p.a.

1

(ii) On the way to the bank, Jannesse sees that another bank is offering 5.4% p.a.for a 5 year deposit, but this account compounds quarterly. Which account is

better and by how much?

2

(c) Kanishka works as an electrician. He earns $45.60 per hour for a 35 hour week. He

will also receive time-and-a-half for the next 5 hours he works and double timebeyond that.

(i) If Kanishka worked 43 hours, what would his gross pay for the week be? 2

(ii) If 24% of Kanishkas earnings are put aside each week in PAYG tax, what ishis net pay?

1

End of Question 22


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(a) A is an acute angle, find its size to the nearest degree if:

cosA = 6.511.3

1

(b) Find the length ofxin the rectangle below correct to 1 d.p. All measurements are incentimetres:

2

(c) From the top of a building, 79 metres high, the angle of depression of a car on theground is 56o.

(i) Draw a diagram to represent this information. 1

(ii) Find the distance, correct to 1 dp. of the car from the base of the building. 2

(d) George and Barbara decide they would like to have children, and hope to havethree.

(i) Assuming it is equally likely to have a girl or a boy, list the sample space of allthe possible outcomes of their family of three children.

2

(e) Noel has discovered that when he drops his spanner while working on his car, that itlands underneath the car quite often. After making a tally, Noel determined thatthere is an 85% chance that the spanner will fall under the car.

(i) Given this experimental probability, what is the chance that the spanner willland away from the car where he can reach it easily?

1

(ii) If Noel was to drop his spanner 60 times, how many times would he expect thespanner to be under the car?

1

End of Question 23

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x

11


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(a) A length of string is measured to be 134.5cm correct to the nearest half centimetre.

(i) What is its length, correct to 2 significant figures? 1

(ii) What are the upper and lower limits of the true measurement? 1

(iii) What percentage error is there in this measurement (correct to 3 sig. fig.)? 1

(b) The fuel consumption of a car is measured at 11L/100km.

(i) Express the fuel consumption in km/L. 1

(ii) How far could a car travel with a full tank of 65L (to the nearest km)? 1

(c) A water tank which is made of sheet metal has a diameter of 4 metres and a heightof 2.5 metres and is cylindrical in shape.

(i) Find the volume of the tank in cubic metres, to the nearest cubic metre. 1

(ii) The tank is filled at a rate of 300L/h. How many hours would it take to fill thetank? (remember that 1 cubic metre equals 1000 litres)

1

(iii) The surface area of the tank in square metres can be found by substituting

r = 2 and h = 2.5 into the formula SA = 2r(r+ h) .Find the surface area of the cylinder; correct to the nearest square metre.

2

(iv) If the cost of the sheet metal used to build the tank is $240/ m2, what would

this tank cost to build?

1

End of Question 24


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(a) A national park ranger decides to find how many bilbies there are in her park. Sheinitially captures 15, tagging them and releasing them back into the park. A monthlater she captures 20, noting that 6 of them have been tagged.

Estimate how many bilbies there are in that area.

2

(b) Charles is measuring the length of a certain species of beetle. He has recorded thelength of 20 beetles, the results (in mm) are as follows:

53 47 37 38 57

61 46 52 63 43

48 53 55 49 39

52 65 50 42 52

(i) Draw an ordered stem and leaf plot of the data. 1

(ii) Find the range and interquartile range. 2

(iii) Describe the data in a five number summary, and use this to draw a box and

whisker plot.

2

(iv) Find the mean and standard deviation (sample) of the data (to 1 d.p.). 2

(c) A real estate agent is asked what the mean and median price of a house is in hissales area.Which is a better indication of a typical house price in the area and why?

1

End of Examination


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Section I

20 marks

Attempt Questions 1-20

Allow about 30 minutes for this section

Use this multiple choice answer sheet for questions 1 20.

Select the alternative A, B, C or D that best answers the question. Fill in the response oval completely.

Sample

2 + 4 = ? (A) 2 (B) 6 (C) 8 (D) 9

A B C D

If you think you have made a mistake, put a cross through the incorrect answer and fill in the new answer.

A B C D

If you change your mind and have crossed out what you consider to be the correct answer, then indicate this

by writing the word correctand drawing an arrow as follows:

correct

A B C D

wrp examination general mathematics 2012

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