MATHEMATICS 0580/3, 0581/3

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1 Centre Number Candidate Number Candidate Name International General Certificate of Secondary Education UNIVERSITY OF CAMBRIDGE LOCAL EXAMINATIONS SYNDICATE MATHEMATICS 0580/3, 0581/3 PAPER 3 Wednesday 8 NOVEMBER 2000 Morning 2 hours Candidates answer on the question paper. Additional materials: Electronic calculator Geometrical instruments Mathematical tables (optional) Tracing paper (optional) TIME 2 hours INSTRUCTIONS TO CANDIDATES Write your name, Centre number and candidate number in the spaces at the top of this page. Answer all questions. Write your answers in the spaces provided on the question paper. If working is needed for any question it must be shown below that question. INFORMATION FOR CANDIDATES The number of marks is given in brackets [ ] at the end of each question or part question. The total of the 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, the answer should be given to three significant figures. Answers in degrees should be given to one decimal place. π, use either your calculator value or FOR EXAMINER S USE This question paper consists of 11 printed pages and 1 blank page. SB (SLC/DJ) QK07554/3 UCLES 2000 [Turn over

2 1 2 The diagram shows the first three triangles in a sequence of equilateral triangles of increasing size. Each is made from triangular tiles of side 1 cm which are either black or white. (a) Draw the fourth equilateral triangle in the sequence on the diagram above, shading in the black tiles. [2] Complete the following table for the equilateral triangles. Length of base (cm) Number of white tiles 0 3 Number of black tiles 1 6 Total number of tiles 1 9 [6] (c) Write down the special name given to the numbers in the Total number of tiles row. Answer (c)... [1] (d) How many white tiles would there be in the equilateral triangle with base 10 cm? Answer (d)... [3]

3 2 (a) ABCDEFGH is a regular octagon. The interior angles of a regular octagon are each 135. ABP and DCP are straight lines and the B P NOT TO y SCALE x C 3 d i a g o n a l s AE and DH are drawn. Calculate w, A D Answer (a) w =... [1] z x, Answer (a) x =... [1] H E (iii) y, G w 135 F (iv) z. Answer (a)(iii) y =... [1] Answer (a)(iv) z =... [2] A decagon has ten sides. How many lines of symmetry does a regular decagon have? Answer... [1] Showing all your working, calculate the size of each interior angle of a regular decagon. Answer... [2] [Turn over

4 3 (a) A square has sides of length 9 cm. 4 Write down its area. Answer (a)...cm 2 [1] Write down its perimeter. Answer (a)...cm [1] (iii) Pythagoras Theorem to calculate the length of a diagonal of the square. Give your answer correct to two decimal places. Answer (a)(iii)...cm [3] 9cm B h C NOT TO SCALE A 55 9cm D The diagram shows a rhombus with sides of length 9 cm. Angle BAD = 55. Calculate h, the height of the rhombus, Answer h =...cm [2] the area of the rhombus. Answer...cm 2 [1]

5 4 BBC World Service Radio 36 million listeners. 5 Europe 4.5 million Central & SW Asia 2.5 million Americas 4.5 million Africa & Middle East 16 million SE Asia & the Pacific? million The diagram shows that 36 million people listen to the BBC s World Service Radio programmes. (a) The number of listeners for SE Asia and the Pacific is missing from the diagram. Work out the missing number. Answer (a)...million [2] Complete the table below. In the given circle, draw an accurate pie chart to show this information. Region Number of Pie listeners chart (million) angle Americas 4.5 Europe Central & SW Asia Africa & Middle East SE Asia & the Pacific TOTAL 36 [Turn over [5]

6 5 A bag contains 17 sweets, of which r are red, g are green and y are yellow. Written as an equation, this is r + g + y = (a) Write the following statements as equations or inequalities. There are more yellow sweets than green sweets. Answer (a)... [1] The number of red sweets is three times the number of green sweets. (iii) The number of green sweets is greater than 2 but less than 6. Answer (a)... [1] Answer (a)(iii)... [2] the information above to work out how many sweets of each colour are in the bag. Answer... red sweets,... yellow sweets,... green sweets. [3] 6 A circular pool of water has a radius of 6 metres. [ π, use either your calculator value or ] (a) Work out the circumference of the pool. Answer (a)...m [2] John walks round the circumference of the pool in 20 seconds. Work out his average speed in metres per second, correct to 1 decimal place. Answer (a)...m/s [2] Calculate the surface area of the water in the pool, giving your answer in square metres, Answer...m 2 [2] in square centimetres. Answer...cm 2 [1] (c) The water is 25 centimetres deep. Work out the volume of water in the pool, giving your answer in cubic centimetres, Answer (c)...cm 3 [2] in litres. [1 litre = 1000 cm 3.] Answer (c)...litres [1]

7 7 (a) B 7 What special name is given to quadrilateral ABCD? A C Answer (a)... [1] Describe fully the transformation which maps triangle ABC onto triangle CDA. D Answer (a) [2] E F What special name is given to quadrilateral EFGH? Answer... [1] H G Reflect quadrilateral EFGH in the line FG. [2] (c) P Q R L M N O 5 2 Translate triangle LMN using the vector. [2] Describe fully the transformation which maps triangle LMN onto triangle PQR. Answer (c)... [2] (iii) Enlarge triangle LMN with centre of enlargement O and scale factor 3. [3] [Turn over

8 8 (a) Complete the table of values for y = x 2 4x. 8 x y [3] On the grid below, plot these points and then draw the graph of y = x 2 4x for 2 x 6. y x -2-4 [4]

9 (c) your graph to find the two values of x when x 2 4x = 2. 9 (d) Complete the table of values for y = 3 x. Answer (c) x =... and... [2] x y [2] (e) On the same grid, draw the graph of y = 3 x for 2 x 6. [2] (f) Write down the coordinates of the two points where the graphs intersect. Answer (f) (...,...) and (...,...) [2] [Turn over

10 9 A person s body-mass index, I, is calculated by using the formula 10 I = M, where M is the mass in kilograms and h is the height in metres. h 2 (a) Anne s height is 1 m 62 cm. Write 1 m 62 cm in metres. Answer (a)...m [1] Anne s mass is 60 kilograms. Calculate her body-mass index. Answer (a)... [3] Body-mass index (I) I < I < I < I 30 I > 30 Body type Very thin Thin Normal Fat Very fat Make M the subject of the formula I = M. h 2 Answer M =... [2] John s height is 1.80 metres. Between what limits must his mass lie if his body type is Normal, using the table above? Answer...kg < John s mass...kg [4] (c) With h as the subject, the body-mass index formula is h = M I. Bill s mass is 86.7 kilograms. His body type is Very fat. After a suitable calculation, write an inequality for Bill s height. Answer (c)... [3]

11 11 10 Each digit on the display of a calculator uses up to seven bars. (a) Complete the table below, showing the number of bars used for each digit. Digit Number of bars [2] Work out the mean number of bars per digit. Answer... [2] (c) One of the ten digit keys 1, 2, 3, 0 on a calculator is pressed at random. What is the probability that the digit has six bars? Answer (c)... [1] (d) The numbers 17 and 71 use six bars each. Which other two digit numbers use exactly six bars? Answer (d)... [2] (e) List all the different numbers that you can make using exactly eight bars. Your numbers can have any number of digits. [4]

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Cambridge International Examinations Cambridge Ordinary Level

Cambridge International Examinations Cambridge Ordinary Level * 5 4 5 9 2 0 9 1 8 5 * MATHEMATICS (SYLLABUS D) 4024/22 Paper 2 May/June 2015 Candidates answer on the Question Paper. Additional Materials: