*P40669A02024* Diagram NOT accurately drawn A O C. In the diagram A LV WKH SRLQW í B is the point (0, 4) C LV WKH SRLQW í

Transcription

1 Algebra

2 16 y Diagram NOT accurately drawn B A O C x In the diagram A LV WKH SRLQW í B is the point (0, 4) C LV WKH SRLQW í Find an equation of the line that passes through C and is perpendicular to AB.... (Total for Question 16 is 4 marks) 20 *P40669A02024*

3 15 Express the recurring decimal as a fraction.... (Total for Question 15 is 3 marks) 16 (a) Write down an equation of a straight line that is parallel to the straight line y = 3x 5 A straight line, L, is perpendicular to the straight line y = 3x 5 and passes through the point (6, 5) (b) Find an equation of L.... (1)... (3) (Total for Question 16 is 4 marks) 14 *P43996A01416*

4 15 L is a straight line. The gradient of L is 4 L passes through the point (0, 2). (a) Write down an equation of the straight line L.... (2) L 1 is a straight line parallel to L. L 1 passes through the point with coordinates (2, 6) (b) Find an equation of L (3) (Total for Question 15 is 5 marks) TOTAL FOR PAPER IS 60 MARKS *P44019A01516* 15

5 10 Susie has to deliver some packages and some parcels. The total number of packages is 4 times the number of parcels. The total number of packages and parcels is 40 Each parcel has a weight of 1.5 kg. The total weight of the packages and parcels is 37.6 kg. Each of the packages has the same weight. Work out the weight of each package.... kg (Total for Question 10 is 4 marks) *P40643A01120* 11 Turn over

6 16 (a) Make t the subject of the formula 2(a + t) = 5t + 7 t =... (3) (b) Solve the simultaneous equations 3x 4y = 8 9x + 5y = 1.5 x =... y =... (3) (Total for Question 16 is 6 marks) 16 *P40643A01620*

7 20 C F Diagram NOT accurately drawn Area = 4 cm 2 Area = T cm 2 A 2(x 1) cm B D (x 2 1) cm E Triangles ABC and DEF are mathematically similar. The base, AB, of triangle ABC has length 2(x 1) cm The base, DE, of triangle DEF has length (x 2 1) cm The area of triangle ABC is 4 cm 2 The area of triangle DEF is T cm 2 Prove that T = x 2 + 2x + 1 (Total for Question 20 is 4 marks) *P40671A02124* 21 Turn over

8 21 Solve the simultaneous equations x 2 + y 2 = 25 y = 2x + 5 or x =... and y =... x =... and y =... (Total for Question 21 is 6 marks) TOTAL FOR PAPER IS 80 MARKS 22 *P40671A02224*

9 17 Make x the subject of 4x 3 = 2(x + y) x =... (Total for Question 17 is 3 marks) 16 *P42055RA01624*

10 18 Solve 5x 2 + 6x 2 = 0 Give your solutions correct to 2 decimal places.... (Total for Question 18 is 3 marks) *P43614A01720* 17 Turn over

11

12

13 Data

14 15 Jeremy has 10 socks. 6 of the socks are red 2 of the socks are blue 2 of the socks are green Jeremy takes at random two of the socks. Work out the probability that he takes two socks of the same colour.... (Total for Question 15 is 4 marks) TOTAL FOR PAPER IS 60 MARKS 18 *P43610A01820*

15 15 Ulrika recorded the times some people took to run a race. The histogram gives information about these times. Frequency density Time (t minutes) 25% of the people took a time less than T minutes. Work out an estimate for T.... minutes (Total for Question 15 is 3 marks) 16 *P44017A01620*

16 16 There are 11 girls and 8 boys in a tennis club. Jake is going to pick at random a team from the tennis club. The team will have two players. Work out the probability that Jake will pick two boys or two girls for the team.... (Total for Question 16 is 4 marks) *P44017A01720* 17 Turn over

17 17 Clive wants to estimate the number of bees in a beehive. Clive catches 50 bees from the beehive. He marks each bee with a dye. He then lets the bees go. The next day, Clive catches 40 bees from the beehive. 8 of these bees have been marked with the dye. (i) Work out an estimate for the number of bees in the beehive.... bees (ii) Write down any assumptions you have made (Total for Question 17 is 4 marks) TOTAL FOR PAPER IS 60 MARKS 18 *P44017A01820*

18 Geometry

19 *15 A M B Diagram NOT accurately drawn O y N M and N are two points on the circumference of a circle centre O. The straight line AMB is the tangent to the circle at M. Angle MON = y Prove that angle BMN = 1 2 y (Total for Question 15 is 5 marks) *P40669A01924* 19 Turn over

20 *14 Diagram NOT accurately drawn C D A 27 B E A, B and C are three points on a circle. DBE is a tangent to the circle. AB is parallel to CD. BC is a diameter. Angle ABC = 27. Find the size of angle CDB. Give reasons for your answer. (Total for Question 14 is 4 marks) 14 *P42053A01416*

21 10 E A F Diagram NOT accurately drawn H B D G C ABCDE and AFGCH are regular pentagons. The two pentagons are the same size. Work out the size of angle EAH. You must show how you got your answer.... (Total for Question 10 is 4 marks) 10 *P43996A01016*

22 *14 O B Diagram NOT accurately drawn A T A and B are points on the circumference of a circle, centre O. AT is a tangent to the circle. Angle TAB = 58. Angle BTA = 41. Calculate the size of angle OBT. You must give reasons at each stage of your working. (Total for Question 14 is 5 marks) 14 *P44019A01416*

23 22 F G Diagram NOT accurately drawn E D A C B In the diagram, ADE is a right-angled triangle, ABCD and AEFG are squares. Prove that triangle ABE is congruent to triangle ADG. (Total for Question 22 is 3 marks) 20 *P42055RA02024*

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26 Miscellaneous

27 14 Here are three graphs. y A O x y O x B y O x C Here are four equations of graphs. y = x 3 y = x y = 1 x y = 2 x Match each to the correct equation. A and y =... B and y =... C and y =... (Total for Question 14 is 3 marks) 14 *P42051RA01416*

28 12 An object is travelling at a speed of 2650 metres per second. How many seconds will the object take to travel a distance of metres? Give your answer in standard form, correct to 2 significant figures.... seconds (Total for Question 12 is 3 marks) 13 y is directly proportional to x. When x = 600, y = 10 (a) Find a formula for y in terms of x. (b) Calculate the value of y when x = 540 y =... (3) y =... (1) (Total for Question 13 is 4 marks) *P40643A01320* 13 Turn over

29 16 Work out Give your answer in standard form.... (Total for Question 16 is 2 marks) 17 T is inversely proportional to d 2 T = 160 when d = 8 Find the value of T when d = (Total for Question 17 is 3 marks) 16 *P43614A01620*

30 21 Sasha drops a ball from a height of d metres onto the ground. The time, t seconds, that the ball takes to reach the ground is given by t = 2d g where g m/s 2 is the acceleration due to gravity. d = 35.6 correct to 3 significant figures. g = 9.8 correct to 2 significant figures. (a) Write down the lower bound of d.... (1) (b) Calculate the lower bound of t. You must show all your working.... (3) (Total for Question 21 is 4 marks) TOTAL FOR PAPER IS 80 MARKS 20 *P43614A02020*

31 Solids

32 17 Ali has two solid cones made from the same type of metal. Diagram NOT accurately drawn 80 cm 160 cm The two solid cones are mathematically similar. The base of cone A is a circle with diameter 80 cm. The base of cone B is a circle with diameter 160 cm. Ali uses 80 mo of paint to paint cone A. Ali is going to paint cone B. (a) Work out how much paint, in mo, he will need. A B... mo (2) The volume of cone A is cm 3. (b) Work out the volume of cone B.... cm 3 (3) (Total for Question 17 is 5 marks) *P40643A01720* 17 Turn over

33 12 Ella is designing a glass in the shape of a cylinder. The glass must hold a minimum of 1 litre of liquid. 2 The glass must have a diameter of 8 cm. Calculate the minimum height of the glass. 8 cm Diagram NOT accurately drawn... cm (Total for Question 12 is 5 marks) *P40671A01324* 13 Turn over

34 16 Here is a vase in the shape of a cylinder. Diagram NOT accurately drawn Water 5 cm The vase has a radius of 5 cm. There are 1000 cm 3 of water in the vase. Work out the depth of the water in the vase. Give your answer correct to 1 decimal place.... cm (Total for Question 16 is 3 marks) *P42055RA01524* 15 Turn over

35

36 Surds and Indices

37 17 Rationalise the denominator of ( 6 5)( 6 + 5) 31 Give your answer in its simplest form.... (Total for Question 17 is 3 marks) TOTAL FOR PAPER IS 60 MARKS *P40669A02124* 21

38 Write your name here Surname Other names Edexcel GCSE Centre Number Mathematics B Unit 2: Number, Algebra, Geometry 1 (Non-Calculator) Monday 4 March 2013 Morning Time: 1 hour 15 minutes Candidate Number Higher Tier Paper Reference 5MB2H/01 You must have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser. Tracing paper may be used. Total Marks 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. Answer the questions in the spaces provided there may be more space than you need. Calculators must not be used. Information The total mark for this paper is 60 The marks for each question are shown in brackets use this as a guide as to how much time to spend on each question. Questions labelled with an asterisk (*) are ones where the quality of your written communication will be assessed. Advice Read each question carefully before you start to answer it. Keep an eye on the time. Try to answer every question. Check your answers if you have time at the end. Turn over P42053A 2013 Pearson Education Ltd. 6/6/8/5/3/ *P42053A0116*

39 GCSE Mathematics 2MB01 Formulae: Higher Tier You must not write on this formulae page. Anything you write on this formulae page will gain NO credit. Volume of prism = area of cross section length Area of trapezium = 1 2 (a + b)h cross section h a length b Volume of sphere = 4 3 ʌu 3 Surface area of sphere = 4ʌU 2 Volume of cone = 1 3 ʌu 2 h Curved surface area of cone = ʌuo r l h r In any triangle ABC A b c C a B The Quadratic Equation The solutions of ax 2 + bx + c = 0 where D 0, are given by b b ac x = ± ( 4 ) 2a 2 Sine Rule a b c = = sin A sin B sin C Cosine Rule a 2 = b 2 + c 2 2bc cos A Area of triangle = 1 2 ab sin C 2 *P42053A0216*

40 Answer ALL questions. Write your answers in the spaces provided. You must write down all stages in your working. You must NOT use a calculator. 1 (a) Complete the table of values for y = 2x + 2 x í í y í 6 (2) (b) On the grid, draw the graph of y = 2x + 2 y ± O x 2 4 (2) (Total for Question 1 is 4 marks) *P42053A0316* 3 Turn over

41 2 Grant drives a lorry to deliver some equipment from a factory to a hospital. The distance from the factory to the hospital is 200 miles. The lorry uses one litre of fuel to go 5 miles. $ OLWUH RI IXHO IRU WKH ORUU\ FRVWV Work out the total cost of the fuel the lorry used.... (Total for Question 2 is 3 marks) 3 Work out (Total for Question 3 is 2 marks) 4 *P42053A0416*

42 4 Here is a diagram of part of a wall in Sarah s house. Diagram NOT accurately drawn 3 m 2 m Sarah is going to cover this part of the wall with square tiles. The square tiles have sides of 20 cm. Work out the number of tiles Sarah needs.... tiles (Total for Question 4 is 3 marks) *P42053A0516* 5 Turn over

43 5 (a) Simplify 4x + 3y x 4y... (2) (b) Simplify 2 + 4x 7x... (1) (c) Simplify t 4 t 7... (1) (d) Simplify y 6 y 2... (1) (e) Simplify (c 3 ) 4... (1) (Total for Question 5 is 6 marks) 6 *P42053A0616*

44 6 Bill gives away to help animals. He gives 20% of the to a donkey sanctuary. He shares the rest of the between a dogs home and a cats home in the ratio 3 : 2 How much money does Bill give to the cats home?... (Total for Question 6 is 4 marks) *P42053A0716* 7 Turn over

45 7 The first five terms of an arithmetic sequence are (a) Write down an expression, in terms of n, for the nth term of this sequence. An expression for the nth term of a different sequence is 20 5n... (2) E :RUN RXW WKH WK WHUP RI WKLV VHTXHQFH... (2) (Total for Question 7 is 4 marks) 8 *P42053A0816*

46 8 D Diagram NOT accurately drawn E P C x A B ABCDE is a regular pentagon. ABP is an equilateral triangle. Work out the size of angle x.... (Total for Question 8 is 4 marks) *P42053A0916* 9 Turn over

47 9 (a) Factorise 3t... (1) (b) (i) Expand and simplify 7(2x x + 3)... (ii) Show that when x is a whole number is always a multiple of 5 7(2x x + 3) (3) (Total for Question 9 is 4 marks) 10 *P42053A01016*

48 10 Here is a solid prism. 2 cm 2 cm 4 cm Diagram NOT accurately drawn 2 cm 6 cm 3 cm On the grid, draw an accurate side elevation of the solid prism from the direction of the arrow. (Total for Question 10 is 2 marks) *P42053A01116* 11 Turn over

49 11 The diagram represents a shed. 4 m Diagram NOT accurately drawn 6 m 30 m 8 m P The shed is in the shape of a prism. The cross section of the prism is a hexagon. The hexagon has one line of symmetry. The walls of the shed are vertical. Calculate the volume of the shed.... m 3 (Total for Question 11 is 4 marks) 12 *P42053A01216*

50 12 Write these numbers in order of size. Start with the smallest number. î 5 î 4 î 6 ± î 4 î 6... (Total for Question 12 is 3 marks) 13 y Diagram NOT accurately drawn C O A (8, 4, 7) x B (8, 0, 0) z A, B and C are 3 corners of a cuboid. (a) Write down the coordinates of C. (...,...,...) (1) M is the midpoint of the line AB. (b) Find the coordinates of M. (...,...,...) (2) (Total for Question 13 is 3 marks) *P42053A01316* 13 Turn over

51 *14 Diagram NOT accurately drawn C D A 27 B E A, B and C are three points on a circle. DBE is a tangent to the circle. AB is parallel to CD. BC is a diameter. Angle ABC = 27. Find the size of angle CDB. Give reasons for your answer. (Total for Question 14 is 4 marks) 14 *P42053A01416*

52 15 The straight line L has equation y = 3x 4 (a) Write down an equation of the line parallel to L which passes through the origin.... (2) (b) Find an equation of the straight line that passes through (0, 5) and is perpendicular to L.... (2) (Total for Question 15 is 4 marks) Turn over for Questions 16 and 17 *P42053A01516* 15 Turn over

53 16 Work out the value of Give your answer in its simplest form.... (Total for Question 16 is 3 marks) 17 Simplify x 2 2 3x 2x 5x 3... (Total for Question 17 is 3 marks) TOTAL FOR PAPER IS 60 MARKS 16 *P42053A01616*

54 17 (a) Write down the value of (1) (b) Find the value of (2) (c) Write 75 in the form k 3, where k is an integer.... (2) (Total for Question 17 is 5 marks) 18 Simplify fully 2 2x + 6x 2 x 2x (Total for Question 18 is 3 marks) TOTAL FOR PAPER IS 60 MARKS *P43996A01516* 15

55 13 The perimeter of a square is 120 cm. Work out the area of the square. Give your answer in its simplest form....cm 2 (Total for Question 13 is 3 marks) *P44019A01316* 13 Turn over

56 Trigonometry

57 18 ABCD is a quadrilateral. A 8.2 cm B Diagram NOT accurately drawn cm D 80 C Work out the length of DC. Give your answer correct to 3 significant figures.... cm (Total for Question 18 is 6 marks) TOTAL FOR PAPER IS 80 MARKS 18 *P40643A01820*

58 14 A B Diagram NOT accurately drawn 36 D 5 cm C ABCD is a parallelogram. DC = 5 cm Angle ADB = 36 Calculate the length of AD. Give your answer correct to 3 significant figures.... cm (Total for Question 14 is 4 marks) *P40671A01524* 15 Turn over

59 19 A Diagram NOT accurately drawn 9.2 m C m B AC = 9.2 m BC = 14.6 m Angle ACB = 64 (a) Calculate the area of the triangle ABC. Give your answer correct to 3 significant figures.... m 2 (2) (b) Calculate the length of AB. Give your answer correct to 3 significant figures.... m (3) (Total for Question 19 is 5 marks) 20 *P40671A02024*

60 19 D Diagram NOT accurately drawn 2 cm C 3 cm In the diagram, ABC, ACD and APD are right-angled triangles. AB = 4 cm. BC = 3 cm. CD = 2 cm. Work out the length of DP. B P A 4 cm... cm (Total for Question 19 is 5 marks) 18 *P42055RA01824*

61 19 ABC is a triangle. A Diagram NOT accurately drawn 73 B 12.3 cm C BC = 12.3 cm Angle ABC = 73 The area of triangle ABC is 50 cm 2. Work out the length of AC. Give your answer correct to 3 significant figures.... cm (Total for Question 19 is 6 marks) 18 *P43614A01820*

62 Vectors

63 15 B A b O a Diagram NOT accurately drawn C D ABCD is a parallelogram. The diagonals of the parallelogram intersect at O. OA = a and OB = b (a) Write an expression, in terms of a and/or b, for (i) CA,... (ii) BA,... (iii) BC.... (3) X is the point such that OX = 2a b (b) (i) Find an expression, in terms of a and b, for AX.... (ii) B, A and X lie on the same straight line. Explain why (3) (Total for Question 15 is 6 marks) *P40643A01520* 15 Turn over

64 23 B Q a A Diagram NOT accurately drawn c P M b 2a C M is the midpoint of BC. Q is the midpoint of AM. AP = a PC = 2a CM = b PQ = c (a) Find AM in terms of a and b. AM =... (1) (b) Find QB in terms of c. QB =... (4) (Total for Question 23 is 5 marks) TOTAL FOR PAPER IS 80 MARKS *P42055RA02124* 21

65 20 OAB is a triangle. 2a A Diagram NOT accurately drawn N O 4b B N is the point on AB such that AN : NB = 3 : 1 OA = 2a OB = 4b (a) Find AB in terms of a and b.... (1) (b) Find ON in terms of a and b. Give your vector in its simplest form.... (3) (Total for Question 20 is 4 marks) Turn over for Question 21 *P43614A01920* 19

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67 beaster-session.notebook March 31, 2015 Welcome! Today is NOT: - comprehensive - we'll just look at a handful of topics - any substitute for your own revision and HARD WORK Today is: - a chance to WORK on some of the harder questions from the end of the GCSE paper - a preview of how the skills you've learnt can be applied in a-level maths Jan 15-10:11 AM 1

68 beaster-session.notebook March 31, 2015 What would you do if you had actual numbers? Does it factorise? Difference of two squares Flip-and-switch for perpendicular algebra 2

69 beaster-session.notebook March 31, 2015 What are the events/stages? Remember they're just rectangles: area frequency Set it out as an equivalent ra o or pair of frac ons data 3

70 beaster-session.notebook March 31, 2015 Try it with numbers first Give complete reasons Angles in a triangle Alternate angles Opposite angles in a cyclic quadrilateral Tangent and radius Draw an extra line, e.g. a radius geometry 4

71 beaster-session.notebook March 31, 2015 Remember the humble trapezium, parallelogram and triangle Use the LAV if you have SIMILAR solids 1 litre = 1000 ml = 1000 cm 3 Avoid schoolgirl errors like 3 m 3 = 300 cm 3 solids 5

72 beaster-session.notebook March 31, 2015 FOIL for fun Use the Evil Twin to Ra onalise that Demonimator surds 6

73 beaster-session.notebook March 31, 2015 Remember the humble angles in a triangle add to when looking at sine rule. You can't always use sine rule, cosine rule directly; that's ok. Sine rule in pairs - flip if necessary Cos - unknown opposite the angle trig 7

74 beaster-session.notebook March 31, 2015 To prove a straight line? vectors 8

75 algebra be a star - answers 1

76 algebra2 be a star - answers 2

77 data be a star - answers 3

78 geometry be a star - answers 4

79 geometry2 be a star - answers 5

80 solids be a star - answers 6

81 surds & indices be a star - answers 7

82 trig be a star - answers 8

83 trig2 be a star - answers 9

84 vectors be a star - answers 10

85 miscellaneous be a star - answers 11

86 2,3,5,6 1,3,5,9 c1 jan 2012 be a star - answers 12

87 c1 jan 2011 be a star - answers 13