MATHEMATICS Paper 3 (Core)

*058001*

0580/03 0581/03

May/June 2006 2 hours

w w w e tr .X m eP e ap .c rs om

Candidates answer on the Question Paper. Additional Materials: Electronic calculator Geometrical instruments Mathematical tables (optional) Tracing paper (optional)

Candidate Name

Centre Number

Candidate Number

READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE IN THE BARCODE. DO NOT WRITE IN THE GREY AREAS BETWEEN THE PAGES. Answer all questions. If working is needed for any question it must be shown below that question. The number of marks is given in brackets [ ] at the end of each question or part question. For Examiner's Use

The total number of marks for this paper is 104. Electronic calculators should be used. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Given answers in degrees to one decimal place. For π , use either your calculator value or 3.142. This document consists of 11 printed pages and 1 blank page. IB06 06_0580_03/4RP UCLES 2006

[Turn over

2 1

y

For Examiner's Use

6 B 4

2 T x 2 4 6 8 10

–6

–4

–2

0

–2 A –4

–6

The shapes T, A and B are drawn on the grid above. (a) In each case describe fully the single transformation which maps (i) T onto A,

Answer(a)(i) (ii) T onto B.

[3]

Answer(a)(ii) (b) Draw on the grid the rotation of T by 90° anticlockwise about (0,0). Label your answer R. (c) Draw on the grid the reflection of T in the line y = –2. Label your answer M.

[3]

[2]

[2]

© UCLES 2006

0580/03 0581/03 Jun 2006

3 2 A candle, made from wax, is in the shape of a cylinder. The radius is 1.5 centimetres and the height is 20 centimetres. (a) Calculate, correct to the nearest cubic centimetre, the volume of wax in the candle. [The volume of a cylinder, radius r, height h, is πr 2 h .] For Examiner's Use

20 cm

NOT TO SCALE

1.5 cm

Answer(a) (b) The candle burns 0.8 cm3 of wax every minute. How long, in hours and minutes, will it last? Write your answer correct to the nearest minute.

cm3 [2]

Answer(b) (c) The candles are stored in boxes which measure x cm by 24 cm by 20 cm. Each box contains 96 candles. Calculate the minimum value of x.

h

min [3]

20 cm NOT TO SCALE 24 cm x cm

Answer(c) x = (d) A shopkeeper pays $25 for one box of 96 candles. He sells all the candles for 35 cents each. (i) How much profit does he make?

[2]

Answer(d)(i) $ (ii) Calculate his profit as a percentage of the cost price.

[2]

Answer(d)(ii)

% [3]

© UCLES 2006

0580/03 0581/03 Jun 2006

[Turn over

4 3 (a) Simplify the expression 5p – 2q – (p + q).

For Examiner's Use

Answer(a) (b) Solve the equation 3(2x – 5) = 27.

[2]

Answer(b) x = (c) A kite has sides of length j cm and k cm. (i) Write down an expression in terms of j and k for the perimeter of the kite. j cm k cm

[3]

NOT TO SCALE

Answer(c)(i) (ii) The perimeter of the kite is 72 centimetres. Write down an equation in j and k. Answer(c)(ii) (iii) If k = 2j, find the value of k.

cm [1]

[1]

Answer(c)(iii) k =

5 s−t (d) (i) Use the formula w = r to find the value of w when s = , t = 6 2 3

[2] and r =

1 2

.

Show all your working clearly.

Answer(d)(i) (ii) Rearrange the formula in part (d)(i) to find s in terms of w, r and t.

[3]

Answer(d)(ii) s =

[2]

© UCLES 2006

0580/03 0581/03 Jun 2006

5 4

For Examiner's Use

Diagram 1

Diagram 2

Diagram 3

Diagram 4

The diagrams show a sequence of regular hexagons. Sticks of equal length are used to make the...