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4 ma0 3h_que_20150106

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IGCSE MATHS PAPERS

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  • Ex-Student reveals the number one secret to scoring an A* in GCSE/IGCSE Maths, click here to find out more ■■■ https://bit.ly/33W8jmf
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  • I am very grateful for Jeevan's program because it taught me many techniques on how to overcome common mistakes made in maths. Also, his revision strategy is unique because the same principles can be used in other subjects too and not only maths. Thank you Jeevan, your techniques are very useful!■■■ http://t.cn/AirraVnG
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  • Your GCSE maths program has had a big impact on my revision for the better. You have made everything really simple to understand while still keeping all the necessary information. This is vital to my revision as I can quickly understand the key concept of that type of question and then I can apply it to some practice questions, thus saving me time. Your other book �How To Maximise Your Result In Every GCSE Exam� has greatly helped me in all of my other subjects as I can revise effectively which frees up my time and in class tests I have noticed a significant improvement from getting B and C grades to now getting A and A* grades. Thank you very much for these guides, I wish I had found them sooner! ♣♣♣ http://ishbv.com/jeevan91/pdf
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  • I was always one of those students who were top of the class for maths during my KS3 years. However, we didn't have maths lessons for around 6 months in year 10, so I fell behind rapidly, and I was getting below average for my GCSE mocks. This package has really boosted my knowledge in a matter of only two weeks! I am vastly improving in maths and I am confident, given that I follow Jeevan's principles, I will achieve an A* in GCSE maths... In the end I achieved an 'A' grade in GCSE maths (summer 2014). I was a little disappointed in myself. However, considering the circumstances, I think I did pretty well. I am now taking A-Level maths at a grammar school and wanted to thank you for helping me along the way. You have inspired me to do well in this subject and I'm sure my 'A' grade will definitely help me to study Veterinary Medicine at a top University. Once again, thank you so much! ➤➤ https://bit.ly/33W8jmf
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  • I didn't think failing my maths back in high school would come back to haunt me but it did! After graduating from Edge Hill University, I was looking to undertake a PGCE in primary teaching. However, one of the requirements was a pass in GCSE maths so I had no choice but to re-take it. After failing it twice, my confidence was very low and I didn't think I could qualify for the PGCE. After running a Google search on passing GCSE maths, I came across Jeevan's revision system. The feedback it received looked very good so I decided to give it a try... And it was one of the best decisions I've ever made. After going through Jeevan's guide, I managed to grasp the entire subject and I passed my next GCSE maths exam, with ease. He (Jeevan) provided me with all the tools I needed to prepare for the exam. Together with his guidance, my pass was a foregone conclusion. Thank you so much Jeevan! You have potentially changed my life. I recommend anyone seeking a pass grade in GCSE maths to purchase this fantastic package!★★★ http://t.cn/AirraVnG
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4 ma0 3h_que_20150106

  1. 1. Centre Number Candidate Number Write your name here Surname Other names Total Marks Paper Reference Turn over P44613A ©2015 Pearson Education Ltd. 5/5/5/1/ *P44613A0124* Mathematics A Paper 3H Higher Tier Tuesday 6 January 2015 – Afternoon Time: 2 hours 4MA0/3H KMA0/3H You must have: Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used. Instructions Use black ink or ball-point pen. Fill in the boxes at the top of this page with your name, centre number and candidate number. Answer all questions. Without sufficient working, correct answers may be awarded no marks. Answer the questions in the spaces provided – there may be more space than you need. Calculators may be used. You must NOT write anything on the formulae page. Anything you write on the formulae page will gain NO credit. Information The total mark for this paper is 100. The marks for each question are shown in brackets – 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. Check your answers if you have time at the end. Pearson Edexcel Certificate Pearson Edexcel International GCSE
  2. 2. 2 *P44613A0224* International GCSE MATHEMATICS FORMULAE SHEET – HIGHER TIER r Pythagoras’ Volume of cone = Curved surface area of cone = Theorem a2 + b2 = c2 b a c adj = hyp cos opp = hyp sin opp = adj tan or opp tan adj adj cos hyp opp sin hyp a a Sine rule: Cosine rule: Area of triangle sin A b + sin B c sin C opp A B C b a c adj hyp Area of a trapezium = (a + b)h1 2 h1 2 2 b2 c 2bc ab sin C cos A2 3 b a h a h b Volume of prism = area of cross section length length section cross Volume of cylinder = r2 h Curved surface area The Quadratic Equation The solutions of ax where a x b b 4ac 2a 0, are given by bx c 0,+ + + of cylinder = 2 rh h r Circumference of circle = 2 Area of circle = r2 2 2 r r 4 3 3 1 2 r 2 r Volume of sphere = r r h l l Surface area of sphere = In any triangle ABC 4 r
  3. 3. 3 *P44613A0324* Turn over Answer ALL TWENTY TWO questions. Write your answers in the spaces provided. You must write down all the stages in your working. 1 1 euro = 120 yen £1 = 1.2 euros Change £50 to yen. .............................................. yen (Total for Question 1 is 2 marks) 2 (a) Work out the value of 451 4 14 1 10 3 . . .+ .............................................. (2) (b) Work out the value of 7 8 7 22 2 . .− .............................................. (2) (Total for Question 2 is 4 marks) Do NOT write in this space.
  4. 4. 4 *P44613A0424* 3 (a) Factorise 14x – 35 .............................................. (1) (b) Expand and simplify 3(2c – 5) – 2(c – 4) .............................................. (2) (c) Simplify (4e3 )2 .............................................. (2) (d) Expand and simplify (a + 5)(2a – 1) ............................................................ (2) (Total for Question 3 is 7 marks) Do NOT write in this space.
  5. 5. 5 *P44613A0524* Turn over 4 The diagram shows a shape with one line of symmetry. Work out the area of the shape. .............................................. cm2 (Total for Question 4 is 4 marks) Diagram NOT accurately drawn 12 cm 15 cm 4 cm 10 cm
  6. 6. 6 *P44613A0624* 5 A jar contains coloured beads. Ajit takes at random a bead from the jar. The probability that the bead is yellow is 0.08 The probability that the bead is pink is 0.1 The probability that the bead is blue is 0.25 (a) (i) Find the probability that the bead is yellow or blue. .............................................. (ii) Find the probability that the bead is neither yellow nor pink. .............................................. (4) Ajit replaces the first bead in the jar. He then takes at random a second bead from the jar. (b) Find the probability that the first bead is yellow and the second bead is blue. .............................................. (2)
  7. 7. 7 *P44613A0724* Turn over A second jar contains 100 coloured beads. 20 of these beads are brown. Ajit takes at random a bead from the jar. He records the colour of the bead and then returns the bead to the jar. He does this 60 times. (c) Work out an estimate for the number of times Ajit records a brown bead. .............................................. (2) (Total for Question 5 is 8 marks) 6 Solve 4(5y – 1) = 3(6y + 7) Show clear algebraic working. y = .............................................. (Total for Question 6 is 3 marks)
  8. 8. 8 *P44613A0824* 7 Eloy’s height was 125 cm when his age was 7 years. His height was 153 cm when his age was 12 years. (a) Work out the percentage increase in Eloy’s height between the ages of 7 and 12 years. ..............................................% (3) Eloy’s height at the age of 12 years was 85% of his height at the age of 20 years. (b) Work out Eloy’s height when his age was 20 years. .............................................. cm (3) (Total for Question 7 is 6 marks) Do NOT write in this space.
  9. 9. 9 *P44613A0924* Turn over 8 ABC is a triangle. The point D lies on AC. Angle BDC = 90 BD = 10 cm, AB = 15 cm and DC = 12.5 cm. (a) Calculate the length of AD. Give your answer correct to 3 significant figures. .............................................. cm (3) (b) Calculate the size of angle BCD. Give your answer correct to 1 decimal place. .............................................. (3) (Total for Question 8 is 6 marks) Diagram NOT accurately drawn A 15 cm 12.5 cm 10 cm B CD
  10. 10. 10 *P44613A01024* 9 (a) Find the sum of the interior angles of a polygon with 7 sides. .............................................. (2) The diagram shows a regular polygon with 7 sides. (b) Work out the value of x. Give your answer correct to 1 decimal place. .............................................. (2) (Total for Question 9 is 4 marks) Diagram NOT accurately drawn x
  11. 11. 11 *P44613A01124* Turn over 10 (a) Find the gradient of the line with equation 3y – 2x = 6 .............................................. (2) (b) Find an equation of the line with gradient –3 that passes through the point (2, 5). .............................................. (2) (Total for Question 10 is 4 marks)
  12. 12. 12 *P44613A01224* 11 3780 = 22 × 33 × 5 × 7 3240 = 23 × 34 × 5 (a) Find the highest common factor (HCF) of 3780 and 3240 Give your answer as a product of prime factors. .............................................. (2) (b) Find the lowest common multiple (LCM) of 3780 and 3240 Give your answer as a product of prime factors. .............................................. (2) (Total for Question 11 is 4 marks)
  13. 13. 13 *P44613A01324* Turn over 12 Solve the simultaneous equations 5y – 4x = 8 y + x = 7 Show clear algebraic working. x = .............................................. y = .............................................. (Total for Question 12 is 3 marks)
  14. 14. 14 *P44613A01424* 13 The cumulative frequency graph gives information about the intelligence quotients (IQ) of a random sample of 100 adults. (a) Use the cumulative frequency graph to find an estimate for the number of adults in the sample who have an IQ between 85 and 115 .............................................. (2) (b) Find an estimate for the upper quartile of the IQ of adults in the sample. .............................................. (2) (Total for Question 13 is 4 marks) Cumulative frequency 100 80 60 40 20 0 60 80 100 120 140 IQ
  15. 15. 15 *P44613A01524* Turn over 14 P, Q, R and S are points on a circle, centre O. QS is a diameter of the circle. QS and PR intersect at the point T. OS = 5 cm, QT = 3 cm and TR = 6 cm. Work out the length of PT. .............................................. cm (Total for Question 14 is 3 marks) Diagram NOT accurately drawn O T R P 3 cm 5 cm 6 cm Q S
  16. 16. 16 *P44613A01624* 15 Zane buys mineral water in large bottles and in small bottles. The large bottles are mathematically similar to the small bottles. Large bottles have a height of 32 cm and a volume of 2000 cm3 Small bottles have a volume of 500 cm3 Work out the height of a small bottle. Give your answer correct to 3 significant figures. .............................................. cm (Total for Question 15 is 3 marks) 2000 cm3 500 cm3 Diagram NOT accurately drawn 32 cm
  17. 17. 17 *P44613A01724* Turn over 16 Gemma has 9 counters. Each counter has a number on it. 1 2 3 4 5 6 7 8 9 Gemma puts the 9 counters into a bag. She takes at random a counter from the bag and does not replace the counter. She then takes at random a second counter from the bag. (a) Work out the probability that the number on each counter is an even number. .............................................. (2) (b) Work out the probability that the number on the first counter added to the number on the second counter gives an odd number. .............................................. (3) (Total for Question 16 is 5 marks)
  18. 18. 18 *P44613A01824* 17 P is directly proportional to q3 P = 270 when q = 7.5 (a) Find a formula for P in terms of q .............................................. (3) (b) Work out the positive value of q when P = q q = .............................................. (2) (Total for Question 17 is 5 marks)
  19. 19. 19 *P44613A01924* Turn over 18 y = x3 – 4x2 + 4x + 3 (a) Find d d y x .............................................. (2) The diagram shows a sketch of the curve with equation y = x3 – 4x2 + 4x + 3 The point P is a turning point on the curve. (b) Work out the coordinates of P. Show clear algebraic working. (................................ , ................................) (4) (c) Write down the range of values of x for which the curve has a negative gradient. .............................................. (2) (Total for Question 18 is 8 marks) y x P O
  20. 20. 20 *P44613A02024* 19 The Venn diagram shows all of the elements in sets A, B and E. (a) Write down the elements in A .............................................. (1) (b) Find n(A ∩ B) .............................................. (1) (c) Find the elements in (A B) ∪ (A ∪ B) .............................................. (1) A ∩ C = Ø B ∪ C = {5, 6, 7, 8, 9} n(C) = 3 (d) Write down the elements in C. .............................................. (1) (Total for Question 19 is 4 marks) Do NOT write in this space. E A 2 3 8 5 7 1 4 B 10 9 6
  21. 21. 21 *P44613A02124* Turn over 20 f:x 2x2 + 1 g:x 2 1 x x − where x 1 (a) Express the composite function gf in the form gf:x ... Give your answer as simply as possible. gf:x .............................................. (2) (b) Express the inverse function g–1 in the form g–1 :x ... g–1 :x .............................................. (3) (Total for Question 20 is 5 marks)
  22. 22. 22 *P44613A02224* 21 A solid cone has a height of 15 cm. The volume of the cone is 320 cm3 Work out the curved surface area of the cone. Give your answer correct to 3 significant figures. .............................................. cm2 (Total for Question 21 is 5 marks) Diagram NOT accurately drawn 15 cm
  23. 23. 23 *P44613A02324* 22 The diagram shows a triangle ABC. AB = (2x + 1) cm, AC = (2x – 1) cm and BC = 2 7 cm. Angle BAC = 60 Work out the value of x. Show clear algebraic working. x = ............................................. (Total for Question 22 is 3 marks) TOTAL FOR PAPER IS 100 MARKS Diagram NOT accurately drawn C A 60 (2x + 1) cm (2x – 1) cm 2 7 cm B
  24. 24. 24 *P44613A02424* BLANK PAGE Do NOT write in this space.

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