mathematics (project maths phase 2) - m. selkirk confey college -...

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Pre-Junior Certificate Examination, 2012

Triailscrúdú an Teastais Shóisearaigh, 2012

_______________

Mathematics

(Project Maths – Phase 2)

Paper 1

Higher Level

2½ hours

300 marks

For examiner

Question Mark

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Total

*PM60*

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Instructions

There are thirteen questions on this examination paper.

Answer all questions.

Questions do not necessarily carry equal marks. To help you manage your time during this

examination, a maximum time for each question is suggested. If you remain within these times, you

should have about 10 minutes left to review your work.

Write your answer in the spaces provided in this booklet. There is space for extra work at the back

of the booklet. You may also ask the superintendent for more paper. Label any extra work clearly

with the question number and part.

The superintendent will give you a copy of the booklet of Formulae Tables. You must return it at

the end of the examination. You are not allowed to bring your own copy into the examination.

Marks will be lost if all necessary work is not clearly shown.

Answers should include the appropriate units of measurement, where relevant.

Answers should be given in simplest form, where relevant.

Write the make and model of your calculator(s) here:

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Question 1 (Suggested maximum time: 5 minutes)

1,2,3,4,6,12A and multiples of 3 less than 20B .

(a) Find A B .

(b) Write down a proper subset of the set A.

(c) Write down all the subsets of A B .

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100 teenagers were asked if they had a Personal Computer, a games console or a laptop at home.

45 had a Personal Computer (PC), 62 had a Games Console (GC) while 66 had a Laptop (L). 32 had

a PC and a Games Console, 39 had a Games Console and a Laptop and 29 had a PC and a Laptop,

24 owned all three while 3 owned none of the three.

(a) Represent the above information on the following Venn diagram.

(b) Find the probability that a student chosen at random from the group will own exactly two of

the items.

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(a) Draw a Venn diagram to illustrate the relationship between the Natural Numbers (N), the

Integers (Z) and the Real Numbers (R).

(b) Using your Venn diagram or otherwise explain whether the following statement is true

or false:

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Aoife has an annual salary of 65,000. Income up to the standard rate cut off point of

28,000 is taxed at 23%. If the high rate of tax is 42% and Aoife has tax credits of 3,500

calculate her monthly take home pay correct to the nearest euro.

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12,000 is invested at 4% compound interest for 3 years. Tax of 5% is deducted from the interest in

each year except the final year of the investment.

(a) Calculate the value of the investment at the end of the first two years correct to

the nearest euro.

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(b) At the beginning of the third year a further 12,000 is invested at r%. If at the end of

the year the investment amounts to 26,175.45 calculate the value of r.

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Seán is considering purchasing a new television for Christmas. The present cost of the

television is 390 excluding VAT of 21%. Seán knows that his local shop will have a 15%

sale on the cost of the television exclusive of VAT in January, but also knows that the VAT

rate will increase by 2% after the budget in December.

By calculating the cost of the television now and in January, decide whether Seán should

purchase now or wait until after Christmas.

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(a) Find the value of x if 9 5x .

(b) The length of a rectangle of perimeter 24 cm is three times the width.

Calculate the area of the rectangle.

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(a) Solve the inequality 5 3 4 25,x x .

(b) Graph your solution on the number line below.

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Four CDs and three DVDs cost a total of 68. One CD and two DVDs cost 27.

(a) If both items are less than 12 each, choose suitable values to find the cost of both items.

(b) By letting x be the price of a CD and y be the price of a DVD write down two

equations in x and y to represent the above information.

Equation 1:

Equation 2:

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(c) Use the equations above to find the cost of a DVD and a CD.

(d) Verify your solution by plotting the lines below.

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A farmer is fencing a small plot of land to grow vegetables as shown below.

(a) If the farmer has 26 m of wire to enclose the plot, write an expression in x for the length of

the plot.

(b) Show that the area of the plot can be expressed in the form 213x x .

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(c) If the plot must have an area between 22 m2 and 42 m

2, find the possible range of values

for the length of the plot.

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A graph of the function 2y x bx c , where ,b c is shown below.

(a) Using the information on the graph find the value of a and the value of b.

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(b) Find the coordinates of the point R.

(c) Find the coordinates of the points S and T where the graph crosses the x-axis.

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(d) Hence, solve the equation 2

3 1 2 3 1 15 0t t for 0t .

¯

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A Gaelic football player takes a free kick off the ground. The ball’s height above the ground is

given by the formula 28y x x , where x is the time in seconds the ball is in flight and y is the

height of the ball in metres.

(a) How long will it take the ball to hit the ground after it has been kicked?

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(b) Choose a suitable range and draw a graph of the height of the ball as it travels.

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(c) Use your graph to estimate the maximum height of the ball.

(d) If the ball travelled at an average speed of 4 metres per second, calculate the distance

the ball travelled.

(e) How far from the player was the ball at its maximum height?

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(a) Write the following formula in terms of V.

21

2W CV

(b) A function is defined by 12 3f x x . If 3f t , find the value of t.

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(c) For each of the following mapping diagrams, circle the diagrams that represent a function.

(i) (ii)

(iii) (iv)

(d) Explain your answer fully.

mathematics (project maths phase 2) - m. selkirk confey college -...

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