Solutions No Workings-Maths 3h

Write your name hereSurname Other names Edexcel Certificate Edexcel International GCSE Centre Number Candidate Number Mathematics A Paper 3H Higher Tier Friday 11 May 2012 – Afternoon Time: 2 hours Paper Reference 4MA0/3H KMA0/3H You must have: Total Marks Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used. Instructions black ink or ball-point pen. t Use in the boxes at the top of this page with your name, t Fill centre number and candidate number. all questions. t Answer sufficient working, correct answers may be awarded no marks. t Without the questions in the spaces provided t Answer – there may be more space than you need. may be used. t Calculators must NOT write anything on the formulae page. t You Anything you write on the formulae page will gain NO credit. Information total mark for this paper is 100. t The marks for each question are shown in brackets t The – use this as a guide as to how much time to spend on each question. Advice Read each question carefully before you start to answer it. t Check t your answers if you have time at the end. P40660A ©2012 Pearson Education Ltd. 6/6/6/4/4/3 *P40660A0124* Turn over Answer ALL TWENTY ONE questions. Write your answers in the spaces provided. You must write down all the stages in your working. 1 (a) The length of an Airbus A300 aeroplane is 54 m. The ratio of the length of this aeroplane to its wingspan is 6 : 5 Work out the wingspan of the aeroplane. 45 .................................................. . . . . . . . . . . . . (2) m (b) A model is made of the Airbus A300 aeroplane. The length of the model is 36 cm. The length of the real aeroplane is 54 m. Find the ratio of the length of the model to the length of the real aeroplane. Give your ratio in the form 1 : n 150 .................. 1 : ............................................ (3) (Total for Question 1 is 5 marks) Do NOT write in this space. *P40660A0324* 3 Turn over .. 1..5 k = . ... .... . . .... .... ... ...... ... . ... .. . .... ..... . .. .. 4 *P40660A0424* ..... ........ ... .. ... . 6 A = ... . . ..... . . ... (2) (b) A = 38 x=4 Work out the value of k. ..2 A = 2x2 + kx (a) x!"!#$!! k=4 Work out the value of A...... ........ . (3) (Total for Question 2 is 5 marks) Do NOT write in this space. .. ........ .... .... . . ... . ........... .. 13 n = ...... ........ (1) (b) Write 9 3 as a single power of 3 34 3^5 ..... ..... (2) (Total for Question 3 is 4 marks) Do NOT write in this space. ... .. .. ....... ... .. .. ... . . .. ..... ....3 (a) Write 23 × 26 as a single power of 2 2^9 .. ... ... ...... .. . . ........... .... ....... .... . ............ ... ..... .. .......... .. . ..... *P40660A0524* 5 Turn over .... . (c) (1) n 5 = 53 6 5 ×5 4 Find the value of n.. ............... . ... 3 ..6 cm Work out the value of x. .......... .... . ....... 1 ....... (Total for Question 5 is 2 marks) 6 *P40660A0624* 8 .............. ........ .. ....... Give your answer correct to 3 significant figures.. .. .....71 ........... . 6...... ............ .7 cm Diagram NOT accurately drawn 5. ....... ....... x = .... ...4 x cm 3.. ... (Total for Question 4 is 3 marks) 5 Three positive whole numbers have a mean of 4 and a range of 7 Find the three positive whole numbers.. ........... .... .. .......... 2 O 2 4 6 8 x (Total for Question 6 is 3 marks) Do NOT write in this space.. y 6 .. *P40660A0724* 7 Turn over . .. 4 R . the region defined by all three of the inequalities x!5 y"3 y!x Label your region R.6 Show. by shading on the grid. . The area of rectangle ANCD is 36 cm2 Work out the area of shape ABCD........... 46 ... . ....... (Total for Question 7 is 4 marks) Do NOT write in this space.... .7 C D Diagram NOT accurately drawn A 9 cm 5 cm N B The shape ABCD is made from a rectangle ANCD and the right-angled triangle NBC. .......... .... ........ ANB is a straight line... .... 8 *P40660A0824* cm2 ....... AN = 9 cm..... NB = 5 cm........ .. . ... ... .....6% on the number of people who had swine flu on 8th May.... .. .8 On 9th May... ... . ... 2500 ......... (a) Express 1639 as a percentage of 3440 Give your answer correct to 1 decimal place.... . there were 3440 people in the world with swine flu.. .... .. (2) % The 3440 people who had swine flu on 9th May was an increase of 37. (b) Calculate the number of people who had swine flu on 8th May. ... 2009.... . . *P40660A0924* 9 Turn over . ... . Of these people.. ................ 1639 were in the USA...... . ...... . . ............ .. . ..6 ... .. 47. (3) (Total for Question 8 is 5 marks) Do NOT write in this space.... ...... . ......... .... . . .... x = .. ... ..... (3) 10 *P40660A01024* ..... -2 y = ....... . .... (3) 2y +1 y − 2 = 3 4 Show clear algebraic working.. ...... .... . (b) Solve 1...5 ..... 3... ..... ..... ....12 ........ ...... Number of peas 1 2 3 4 5 6 Number of pods 3 6 5 8 2 1 (a) Work out the mean number of peas in the 25 pods. ...... . ..9 (a) Solve 3(2x!#!%&!"!' Show clear algebraic working. . .. . ............ ....... ... .. . .. .. .. .... ....... . ....... ....... ....... (4) (Total for Question 9 is 7 marks) 10 The table shows information about the number of peas in each of 25 pods. ............... .. . (5) (Total for Question 10 is 10 marks) *P40660A01124* 11 Turn over .. ... 1/10 ...... .. . (ii) there is a total of 4 peas in the two pods she takes... .. .... . . ........ 1/30 ... .. . .... .. . . .. . ...... . .. ...... (2) (c) Laila puts the 25 pods in a bag. ... . ...... Find the probability that he takes a pod with 3 peas or a pod with 4 peas. .. She takes at random two pods without replacement.. ......... .. He takes at random one of the pods.............. .. ..... . ..... ..... . . . ..... ... .... .... . ... .(b) Tariq puts the 25 pods in a bag.... .. . .. .... . Calculate the probability that (i) there are 3 peas in each of the two pods she takes..... 13/25 .. ...... ..... . . . ..... ... ... ..... (2) (Total for Question 11 is 7 marks) 12 *P40660A01224* cm2 .. . cm The area of triangle ABC is 2 cm2 (c) Work out the area of triangle PQR... ..... . OA = 3 cm...... .................... OC = 3.......5 cm C R Triangle PQR is an enlargement...... ...........5 cm............ .... (a) Work out the length of CR. ... of triangle ABC....... .. AP = 12 cm..... (2) cm (b) Work out the length of AC.. . . 17. . centre O...... ..... PR = 19 cm....8 (3) ............... ...5 ...... OAP and OCR are straight lines..... ............. 3. ...... ..... .11 P Diagram NOT accurately drawn m 12 c A 3 cm O 19 cm Q B 3... . ......... .. 50 . ..... . .... .... ....... 9 .. ... ...... .. .. ................ ................... .. ...... (2) minutes (Total for Question 12 is 4 marks) Do NOT write in this space.... *P40660A01324* 13 Turn over . of 80 telephone calls...... ...... 80 60 Cumulative frequency 40 20 O 5 10 15 20 25 30 Length of call (minutes) (a) Find an estimate for the number of calls which were longer than 15 minutes. in minutes.. 5 .... ..... (2) (b) Find an estimate for the interquartile range of the lengths of the 80 calls....... . ...... ......12 The cumulative frequency graph gives information about the lengths.. ...... . . ..13 Diagram NOT accurately drawn P A The diagram shows two congruent regular pentagons and part of a regular n-sided polygon A.... Show your working clearly.... ... .. .... .. ..... ......... . 10 n = . .. . .... .. ... (Total for Question 13 is 5 marks) 14 *P40660A01424* .. Calculate the value of n.. Two sides of each of the regular pentagons and two sides of A meet at the point P.. .. . ... ..... . . . .. ... ..... ......14 (a) The equation of a line L is 2x!#!$y = 6 Find the gradient of L.. .... 2/3 . . .......... . . ...... ..... . .. . . . . 9). ... ..... *P40660A01524* 15 Turn over ..... (3) (b) Find the equation of the line which is parallel to L and passes through the point (6. . .... .... ...... . .... . . . ...... ............... .. .. . (2) (Total for Question 14 is 5 marks) Do NOT write in this space.... .. . y=2/3X+5 .. .... BOD is a diameter of the circle..........63 ... .. ...... 3..... . centre O.15 D Diagram NOT accurately drawn O 8 cm A C 63° 30° B B.... . .. .. .. Angle BAO = 30° Angle CBD = 63° Calculate the length of BC.. AB is the tangent to the circle at B.. ....... (Total for Question 15 is 4 marks) 16 *P40660A01624* cm ....... . C and D are points on a circle..... Give your answer correct to 3 significant figures. AO = 8 cm..... .......... Calculate the percentage by which the population of India increased between 1989 and 2009... .............. ... ....... 40....4 . .. % (Total for Question 16 is 3 marks) 17 (a) Simplify (3a 2 b) 4 81a^8b ^4 ...... ........ .16 The population of India increased by 20% between 1989 and 1999.. .. . .. ... . . ... .. ............... . . .... ..... ......... . ...... ... .. . .... .. ..... . .. .... ... .... (2) (Total for Question 17 is 4 marks) *P40660A01724* 17 Turn over . The population of India increased by a further 17% between 1999 and 2009. .. . .. ....... ... .. (b) Simplify (2) 1 8 2 (9c ) 3c^4 . . ... ... .... ..... .. .. ... (Total for Question 18 is 6 marks) 18 *P40660A01824* . ... .... . ... ..... CO = CE. .... B. .. Angle AOD = 69° Angle CEO = x° Calculate the value of x... AOBE and DCE are straight lines. ...... C and D are points on a circle. .. Show your working clearly.... ... .18 D Diagram NOT accurately drawn C A | x° | 69° O B E A.... centre O.. . . .. .... 23 x = .. . ....... . .... OA = OB = 5..... centre O. .... Give your answer correct to 3 significant figures....... ..4 cm 72° A B P The diagram shows a sector OAPB of a circle......19 O 5.................. 4...4 cm. ... AB is a chord of the circle.. Angle AOB = 72° Calculate the area of the shaded segment APB.4 cm Diagram NOT accurately drawn 5. ... . .....46 . .... cm2 (Total for Question 19 is 5 marks) *P40660A01924* 19 Turn over .. ......... (Total for Question 20 is 4 marks) Do NOT write in this space. 73. 20 *P40660A02024* cm2 ....5 . .......... the volume of a solid cube is 42...88 cm3 Calculate the lower bound for the surface area of the cube... ..... .......... ..... .... .... ....20 Correct to 2 decimal places.... ..........5 X=-4 and Y=32 . .......... . .5 and Y=12.. X=2. ... .. ...21 Solve the simultaneous equations y = 2x2 y = 20 #!$x Show clear algebraic working..... . ........ ....... .. (Total for Question 21 is 5 marks) (TOTAL FOR PAPER IS 100 MARKS) Do NOT write in this space... *P40660A02124* 21 .. ..... ... . ... ............. ...... . . ... .. ... . . .... .. . ...... ....5 X=-4 and Y=32 .... X=2.... ........21 Solve the simultaneous equations y = 2x2 y = 20 í x Show clear algebraic working.. .. .. ....... ......... .... *P40660A02124* 21 .. ...... (Total for Question 21 is 5 marks) (TOTAL FOR PAPER IS 100 MARKS) Do NOT write in this space.5 and Y=12.. ... ........ .... ......