Thursday 28 February 2013 Afternoon Time: 1 hour 45 minutes

Transcription

1 Write your name here Surname Other names Edexcel GCSE Centre Number Mathematics A Paper 1 (Non-Calculator) Thursday 28 February 2013 Afternoon Time: 1 hour 45 minutes Candidate Number Higher Tier Paper Reference 1MA0/1H 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 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. 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 P42057A 2013 Pearson Education Ltd. 6/7/4/ *P42057A0128*

2 GCSE Mathematics 1MA0 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 = Surface area of sphere = 4 2 Volume of cone = h Curved surface area of cone = 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 0, are given by b b ac x = ± ( 4 ) 2a 2 Sine Rule a b c = = sin A sin B sinc Cosine Rule a 2 = b 2 + c 2 2bc cos A Area of triangle = 1 2 ab sin C 2 *P42057A0228*

3 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 Work out (Total for Question 1 is 3 marks) *P42057A0328* 3 Turn over

4 2 The scatter graph shows information about 10 apartments in a city. The graph shows the distance from the city centre and the monthly rent of each apartment Monthly rent ( ) Distance from the city centre (km) The table shows the distance from the city centre and the monthly rent for two other apartments. Distance from the city centre (km) Monthly rent ( ) (a) On the scatter graph, plot the information from the table. (1) (b) Describe the relationship between the distance from the city centre and the monthly rent (1) 4 *P42057A0428*

5 An apartment is 2.8 km from the city centre. (c) Find an estimate for the monthly rent for this apartment.... (2) (Total for Question 2 is 4 marks) 3 Paula wants to find out how much money people spend buying CDs. She uses this question on a questionnaire. How much money do you spend buying CDs? more than 70 (a) Write down two things wrong with this question (2) Paula asks 100 people in a CD store to do her questionnaire. (b) Her sample is biased. Explain why (1) (Total for Question 3 is 3 marks) *P42057A0528* 5 Turn over

6 4 (a) Complete the table of values for y = 2x + 5 x y 1 5 (2) (b) On the grid, draw the graph of y = 2x + 5 for values of x from x = 2 to x = 2 y O x (2) (Total for Question 4 is 4 marks) 6 *P42057A0628*

7 5 Here are the first 5 terms of an arithmetic sequence (a) Find an expression, in terms of n, for the nth term of this sequence.... (2) Ben says that 150 is in the sequence. (b) Is Ben right? You must explain your answer (1) (Total for Question 5 is 3 marks) *P42057A0728* 7 Turn over

8 6 You can use this conversion graph to change between pounds ( ) and dollars ($) Dollars ($) Pounds ( ) (a) Use the conversion graph to change 5 to dollars. Ella has $200 and 800 Her hotel bill is $600 Ella pays the bill with the $200 and some of the pounds. (b) Use the conversion graph to work out how many pounds she has left. $... (1) (Total for Question 6 is 5 marks)... (4) 8 *P42057A0828*

9 7 (a) Simplify 5x + 4y + x 7y... (2) (b) Solve 7(x + 2) = 7... (2) (Total for Question 7 is 4 marks) *P42057A0928* 9 Turn over

10 8 Trams leave Piccadilly to Eccles every 9 minutes to Didsbury every 12 minutes A tram to Eccles and a tram to Didsbury both leave Piccadilly at 9 am. At what time will a tram to Eccles and a tram to Didsbury next leave Piccadilly at the same time?... (Total for Question 8 is 3 marks) 9 (a) Simplify a 4 a 5 (b) Simplify 45e f 2 5ef (1)... (2) (c) Write down the value of (1) (Total for Question 9 is 4 marks) 10 *P42057A01028*

11 * 10 A 38 B Diagram NOT accurately drawn x C D E F CDEF is a straight line. AB is parallel to CF. DE = AE. Work out the size of the angle marked x. You must give reasons for your answer. (Total for Question 10 is 4 marks) *P42057A01128* 11 Turn over

12 11 Greg sells car insurance and home insurance. The table shows the cost of these insurances. Insurance car insurance home insurance Cost Each month Greg earns 530 basic pay 5% of the cost of all the car insurance he sells and 10% of the cost of all the home insurance he sells In May Greg sold 6 car insurances and 4 home insurances Work out the total amount of money Greg earned in May. 12 *P42057A01228*

13 ... (Total for Question 11 is 5 marks) *P42057A01328* 13 Turn over

14 12 5 schools sent some students to a conference. One of the schools sent both boys and girls. This school sent 16 boys. The ratio of the number of boys it sent to the number of girls it sent was 1 : 2 The other 4 schools sent only girls. Each of the 5 schools sent the same number of students. Work out the total number of students sent to the conference by these 5 schools.... (Total for Question 12 is 4 marks) 14 *P42057A01428*

15 13 Diagram NOT accurately drawn x The diagram shows a square and 4 regular pentagons. Work out the size of the angle marked x.... (Total for Question 13 is 3 marks) *P42057A01528* 15 Turn over

16 14 The grouped frequency table shows information about the weekly wages of 80 factory workers. Weekly wage ( x) Frequency 100 < x < x < x < x < x < x (a) Complete the cumulative frequency table. Weekly wage ( x) 100 < x < x < x < x < x < x 700 Cumulative Frequency (1) (b) On the grid opposite, draw a cumulative frequency graph for your table. (2) (c) Use your graph to find an estimate for the interquartile range. (d) Use your graph to find an estimate for the number of workers with a weekly wage of more than (2)... (2) 16 *P42057A01628*

17 Cumulative frequency Weekly wage ( ) (Total for Question 14 is 7 marks) *P42057A01728* 17 Turn over

18 15 Here is a scale drawing of a rectangular garden ABCD. A B D C Scale: 1cm represents 1 metre. Jane wants to plant a tree in the garden at least 5m from point C, nearer to AB than to AD and less than 3m from DC. On the diagram, shade the region where Jane can plant the tree. (Total for Question 15 is 4 marks) 18 *P42057A01828*

19 16 (a) Write as an ordinary number.... (1) (b) Write in standard form.... (1) (c) Work out the value of ( ) ( ) Give your answer in standard form.... (2) (Total for Question 16 is 4 marks) 17 Solve 4 x x = 3 x =... (Total for Question 17 is 3 marks) *P42057A01928* 19 Turn over

20 18 y P O x Shape P is reflected in the line x = 1 to give shape Q. Shape Q is reflected in the line y = 0 to give shape R. Describe fully the single transformation that maps shape P onto shape R (Total for Question 18 is 3 marks) 20 *P42057A02028*

21 19 D A Diagram NOT accurately drawn O 34 C B A, B and D are points on the circumference of a circle, centre O. BOD is a diameter of the circle. BC and AC are tangents to the circle. Angle OCB = 34. Work out the size of angle DOA.... (Total for Question 19 is 3 marks) *P42057A02128* 21 Turn over

22 20 (a) (i) Factorise x 2 12x (ii) Solve the equation x 2 12x + 27 = 0... (3) (b) Factorise y (1) (Total for Question 20 is 4 marks) * 21 Prove algebraically that the difference between the squares of any two consecutive integers is equal to the sum of these two integers. (Total for Question 21 is 4 marks) 22 *P42057A02228*

23 22 y O x Enlarge the shaded shape by scale factor 1 2 with centre ( 1, 2). (Total for Question 22 is 3 marks) *P42057A02328* 23 Turn over

24 23 The diagram shows a solid hemisphere of radius 5 cm. Diagram NOT accurately drawn 5 cm Find the total surface area of the solid hemisphere. Give your answer in terms of.... cm 2 (Total for Question 23 is 3 marks) 24 *P42057A02428*

25 24 There are three different types of sandwiches on a shelf. There are 4 egg sandwiches, 5 cheese sandwiches and 2 ham sandwiches. Erin takes at random 2 of these sandwiches. Work out the probability that she takes 2 different types of sandwiches.... (Total for Question 24 is 5 marks) *P42057A02528* 25 Turn over

26 25 y = f(x) The graph of y = f(x) is shown on the grid. y y = f(x) O x 2 4 (a) On the grid above, sketch the graph of y = f(x). (2) The graph of y = f(x) is shown on the grid. y y = f(x) 4 graph G O x The graph G is a translation of the graph of y = f(x). (b) Write down the equation of graph G.... (1) (Total for Question 25 is 3 marks) 26 *P42057A02628*

27 26 Y 5a b B Diagram NOT accurately drawn 6b X A 3a O OAYB is a quadrilateral. OA = 3a OB = 6b (a) Express AB in terms of a and b.... (1) X is the point on AB such that AX : XB = 1 : 2 and BY = 5a b *(b) Prove that OX = 2 5 OY (4) (Total for Question 26 is 5 marks) TOTAL FOR PAPER IS 100 MARKS *P42057A02728* 27

28 1MA0_1H Question Working Answer Mark Notes A1 for digits 8601 given as the answer 8601 or 8 or = 8601 or = = = = = M1 for a complete method to multiply 183 by 47 and attempt at addition (condone one multiplication error) B1 (dep on M1) for correctly writing their answer to 2 decimal places

29 1MA0_1H Question Working Answer Mark Notes 2 (a) Plot (2, 250) and (3.1, 190) Plot points 1 B1 for both points plotted accurately (b) Relationship 1 B1 for As the distance from the centre increases the monthly rent decreases or the nearer you are to the centre the more you have to pay oe (accept negative correlation) (c) 200 to M1 for attempting a correct method, eg a line of best fit or any other indication, on a line that could be used as a line of best fit eg line to graph at x = 2.8or a mark on the line at 2.8 A1 for value in the range 200 to (a) 2 reasons 2 B2 for 2 different reasons from given examples (B1 for 1 reason from given examples) eg No time frame eg No box for less than 10 accept no box for zero or none or 0 eg Overlapping intervals or boxes or 30 and/ or 50 in two boxes (b) 1 reason 1 C1 for reason why the sample is biased eg they are only in the CD store, the people in the store are more likely to buy CDs she needs to ask people outside the store oe

30 1MA0_1H Question Working Answer Mark Notes 4 (a) 3, 7, 9 2 B2 for all three values correct in the table x (B1 for 2 values correct) y (1) 3 (5) 7 9 (b) graph of y = 2x (From their table of values) M1 ft for plotting at least 2 of their points (any points from their table must be correctly plotted) A1 for correct line from x = 2 to x = +2 (Use of y = mx + c) M1 for line drawn with gradient of 2 or line drawn with a y intercept of 5 and a positive gradient) A1 for correct line from x = 2 to x = +2 2 O 2 x

31 1MA0_1H Question Working Answer Mark Notes 5 (a) 6n 3 2 M1 for attempt to establish linear expression in n with coefficient of 6 e.g. 6n + k where k is an integer (accept n = 6n 3 for one mark) A1 cao (b) No + Reason 1 C1 ft from their answer to part (a) for decision and explanation eg stating no and because all the terms in the sequence are odd and 150 is even or no and 6n 3 = 150, n = 153/6... so n is not an integer or Continuing the sequence to show terms 147 and 153 and state no as 150 is not in the sequence oe

32 1MA0_1H Question Working Answer Mark Notes 6 (a) 8 1 B1 for 8 (.00) (b) M1 for ( = 400) M1 for correct method to convert $400 to M1 (dep on the previous M1) for 800 $400 in s A1 for value in the range OR M1 for correct method to convert $600 and $200 to pounds M1 for M1 (dep on the previous M1) A1 for a value in the range OR M1 for correct method to convert 800 to dollars M1 for M1 (dep on the previous M1) for attempt to convert $880 back to A1 for value in the range (a) 6x 3y 2 M1 for an attempt to combine terms in x or terms in y correctly eg 5x + x(= 6x), 4y 7y(= 3y) A1 for 6x 3y oe (b) 7x + 14 = 7 or x + 2 = 1 7x = 7 x = 1 2 M1 for correctly expanding the bracket or an attempt to divide both sides by 7 e.g. 7x +14 or x + 2 = 7 7 oe A1 cao

33 1MA0_1H Question Working Answer Mark Notes M1 for listing 9, 18, 27, 36, 45,...(at least 3 correct multiples with at most one incorrect) M1 for listing 12, 24, 36, 48,... (at least 3 correct multiples with at most one incorrect) A1 for or 9 36 (am) 9 (a) a 9 1 B1 for a or a 9 OR M1 for listing (at least 3correct times with at most one incorrect) M1 for listing (at least 3 correct times with at most one incorrect) A1 for or 9 36 (am) OR M1 for 9 = 3 3 or 12 = (could be in factor tree) M1 for 9 = 3 3 and 12 = (could be in a factor tree) A1 for or 9 36 (am) SC B2 for 9 36 pm or (after) 36 (minutes) on the answer line (b) 9e 5 f 6 2 B2 cao (B1 for two of 9, e 6 1, f 8 2 as a product) (c) 3 1 B1 (accept ± 3 but not just 3)

34 1MA0_1H Question Working Answer Mark Notes *10 Angle AED = 38 alternate angles are equal Angle ADE = (180 38) 2 = 71 x = base angles of an isosceles triangle are equal angles in a triangle add up to 180 angles on a straight line sum to 180 OR angle AEF = 142 allied angles/co-interior angles add up to 180 ADE = = 71 base angles of an isosceles triangle are equal exterior angle of a triangle is equal to the sum of the interior opposite angles, x = angles in a straight line add to 180 OR Angle AED = 38 alternate angles are equal for angles BAE and AED and BAD and ADC (x) Angle DAE= (180 38) 2 = 71 base angles of an isosceles triangle are equal angles in a triangle add up to 180 Or Angle AED = 38 alternate angles are equal Angle ADE = (180 38) 2 = 71 base angles of an isosceles triangle are equal and angles in a triangle sum to 180 x = alternate angles BAD and ADC(x) are equal x = B1 for angle AED = 38 or AEF = 142 M1 for a complete method to find one of the base angles of the isosceles triangle C2 (dep M1) for x = 109 with complete reasons (C1 (dep M1) for one reason correctly used and stated)

35 1MA0_1H Question Working Answer Mark Notes M1 for 200 ( = 10) oe 100 M1 for ( = 35) oe M1 for 6 10 or 4 35 M1 (dep on M1 earned for a correct method for a percentage calculation) for A1 cao Or M1 for (= 1200) or (= 1400) 5 M1 for "1200"( 60) 100 = oe M1 for 10 "1400"( 140) 100 = oe M1(dep on M1 earned for a correct method for a percentage calculation) for A1 cao

36 1MA0_1H Question Working Answer Mark Notes M1 for 16 2 (= 32 girls) M1 for (= 48) M1 (dep on the previous M1) for ( ) 5 or ( ) (4 + 1) A1 cao OR M1 for 1 : 2 = 3 parts M1 for 5 schools 3 parts (= 15 parts) M1 (dep on the previous M1) for 15 parts 16 A1 cao SC B2 for 176 given on the answer line M1 for or 108 seen as the interior angle of a pentagon M1 (dep on previous M1) for A1 for 54 cao OR M1 for 180 (5 2) (= 540) 5 or 108 given as the interior angle of a pentagon M1 (dep on previous M1) for A1 for 54 cao

37 1MA0_1H Question Working Answer Mark Notes 14 (a) 8, 23, 53, 70, 77, 80 1 B1 cao (b) graph 2 M1 ft from their table for at least 5 points plotted correctly at the ends of the intervals provided table values are cumulative, condoning one arithmetic error A1 cao for correct graph with points joined by curve or straight line segments [SC B1 if the shape of the graph is correct and 5 points of their points are not at the ends but consistently within each interval and joined.] (c) Readings at 60 and to to M1 (dep on cf graph) for use of either cf = 20 or cf = 60 A1 ft from a cf graph (d) to M1 (dep on cf graph) for evidence of reading off the cf axis from 530 0n the wages axis (could be the answer) A1ft for 6-9

38 1MA0_1H Question Working Answer Mark Notes 15 Required region 4 M1 arc radius 5 cm centre C M1 bisector of angle BAD M1 line 3 cm from DC A1 for correct region identified (see overlay) 16 (a) B1 cao (b) B1 cao (c) M1 for oe or or A1 cao (accept M1 for multiplying throughout by 10 oe or writing LHS as a single 13 fraction e.g 2(4x 1) + 5(x + 4) = 3 10 or 2(4x 1) + 5( x+ 4) or + 10 M1 (dep) for a complete correct method to obtain linear equation of the form ax = b (condone one arithmetic error in multiplying out the bracket) A1 for 12 oe (decimal equivalent is ) 13

39 1MA0_1H Question Working Answer Mark Notes 18 Q at ( 3, 1), ( 6, 1) ( 5, 3) ( 3, 3) R at ( 3, 1), ( 6, 1), ( 5, 3) ( 3, 3) Rotation 180 about ( 1, 0) 3 M1 for showing R correctly on the grid without showing Q or for showing Q and R correctly on the grid A1 for rotation of 180 A1 for (centre) ( 1, 0) Or M1 for showing R correctly on the grid without showing Q or for showing Q and R correctly on the grid A1 for Enlargement Scale Factor 1 A1 for centre ( 1, 0) NB Award no marks for any correct answer from an incorrect diagram or any Accuracy marks if more than one transformation is given M1 for angle OBC = 90 or angle OAC = 90 (may be marked on the diagram or used in subsequent working) M1 for correct method to find angle BOC or AOC or AOB e.g. angle BOC = (= 56) or angle AOC = (=56) or angle AOB = (= 112) A1 cao NB (68 must be clearly stated as an answer and not just seen on diagram)

40 1MA0_1H Question Working Answer Mark Notes 20 (a)(i) (x 9)(x 3) 3 M1 for (x ± 9)(x ± 3) A1 for (x 9)(x 3) (ii) x = 9, x = 3 B1 cao (b) (y + 10)(y 10) 1 B1 for (y + 10)(y 10) *21 (n + 1) 2 n 2 = n 2 + 2n + 1 n 2 = 2n + 1 (n + 1) + n = 2n + 1 OR (n + 1) 2 n 2 = (n n)(n + 1 n) = (2n + 1)(1) = 2n + 1 (n + 1) + n = 2n + 1 OR proof 4 M1 for any two consecutive integers expressed algebraically eg n and n +1 M1(dep on M1) for the difference between the squares of two consecutive integers expressed algebraically eg (n + 1) 2 n 2 A1 for correct expansion and simplification of difference of squares, eg 2n + 1 C1 (dep on M2A1) for showing statement is correct, eg n + n + 1 = 2n + 1 and (n + 1) 2 n 2 = 2n + 1 from correct supporting algebra n 2 (n + 1) 2 = n 2 (n 2 + 2n + 1) = 2n 1 = (2n + 1) Difference is 2n + 1 (n + 1) + n = 2n Vertices at ( 2, 4), ( 4, 4), ( 4, 6), ( 2, 5) Correct diagram 3 M1 for a similar shape in the correct orientation in the third quadrant M1 for an image in the correct orientation of the correct size A1 cao

41 1MA0_1H Question Working Answer Mark Notes 23 75π 3 M1 for (4 π 5 2 ) 2 oe M1 for π 5 2 oe A1 for 75π accept Condone the use of π = EE + CC + HH Or EC+EH+CE+CH+HE+HC Or E,not E+ C,not C + H,not H 76 5 M1 for use of 10 as denominator for 2 nd probability 110 M1 for 4 3 or 5 4 or M1 for = M1 (dep on previous M1 for 1 A1 for 76 oe Or M1 for use of 10 as denominator for 2 nd probability M1 for 4 5 or 4 2 or 5 4 or 5 2 or 2 M2 for (M1 for at least 3 of these) A1 for 76 oe 110 Or M1 for use of 10 as denominator for 2 nd probability M1 for or or or M2 for (M1 for two of these added) A1 for 76 oe PTO for SC s

42 1MA0_1H Question Working Answer Mark Notes SC: B2 for SC: B1 for + + Or (= ) Or (a) sketch M1 for inverting the parabola, so maximum is at ( 2, 0 ) A1 for parabola passing through all three of the points ( 2, 0), (0, 4), ( 4, 4) (b) y = f (x 6) 1 B1 for y = f (x 6) or y = (x 4) 2 oe

43 1MA0_1H Question Working Answer Mark Notes 26 (a) 6b 3a 1 B1 for 6b 3a oe (b) 4 M1 for AX = 1 3 AB or 1 (6b 3a) or ft to 2b a 3 M1 for OY = OB + BY = 6b + 5a b (= 5b + 5a ) oe M1 for OX = 3a + 2b a = 2a + 2b oe Or OX = 6b (6b 3a) (= 2a + 2b) oe C1 for 5 2 OY = 5 2 5(a + b) = 2(a + b) = OX

44 4. y O 1 2 x 1

45 18. Q y P O x 1 R

46 Write your name here Surname Other names Edexcel GCSE Centre Number Mathematics A Paper 2 (Calculator) Monday 4 March 2013 Morning Time: 1 hour 45 minutes Candidate Number Higher Tier Paper Reference 1MA0/2H You must have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser, calculator. 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 may be used. If your calculator does not have a button, take the value of to be unless the question instructs otherwise. 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. Questions labelled with an asterisk (*) are ones where the quality of your written communication will be assessed. P42059A 2013 Pearson Education Ltd. 6/7/4/ 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. *P42059A0128* Turn over

47 GCSE Mathematics 1MA0 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 = Surface area of sphere = 4 2 Volume of cone = h Curved surface area of cone = 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 0, are given by b b ac x = ± ( 4 ) 2a 2 Sine Rule a b c = = sin A sin B sinc Cosine Rule a 2 = b 2 + c 2 2bc cos A Area of triangle = 1 2 ab sin C 2 *P42059A0228*

48 Answer ALL questions. Write your answers in the spaces provided. You must write down all stages in your working. 1 Here are the ages, in years, of 15 students Show this information in an ordered stem and leaf diagram. Key: (Total for Question 1 is 3 marks) *P42059A0328* 3 Turn over

49 * grams of flour are needed to make 9 cakes. Marian wants to make 20 of these cakes. She has 475 grams of flour. Does Marian have enough flour to make 20 cakes? You must show all your working. (Total for Question 2 is 3 marks) 4 *P42059A0428*

50 3 Simon went for a cycle ride. He left home at 2 pm. The travel graph represents part of Simon s cycle ride Distance from home (km) pm 3 pm 4 pm 5 pm 6 pm 7 pm Time 8 pm At 3 pm Simon stopped for a rest. (a) How many minutes did he rest?... minutes (1) (b) How far was Simon from home at 5 pm?... km (1) At 5 pm Simon stopped for 30 minutes. Then he cycled home at a steady speed. It took him 1 hour 30 minutes to get home. (c) Complete the travel graph. (2) (Total for Question 3 is 4 marks) *P42059A0528* 5 Turn over

51 4 Here is a four sided spinner. The spinner is biased The table shows the probabilities that the spinner will land on 1 or on 3 Number Probability The probability that the spinner will land on 2 is the same as the probability that the spinner will land on 4 (a) Work out the probability that the spinner will land on 4 Shunya is going to spin the spinner 200 times. (b) Work out an estimate for the number of times the spinner will land on 3... (3)... (2) (Total for Question 4 is 5 marks) 6 *P42059A0628*

52 5 5m Diagram NOT accurately drawn Jon has a flower garden in the shape of a circle. The diameter of the garden is 5 metres. Jon wants to put fencing around the edge of the garden. The fencing costs 1.80 per metre. Work out the total cost of the fencing.... (Total for Question 5 is 3 marks) *P42059A0728* 7 Turn over

53 6 Mr Watkins needs to buy some oil for his central heating. Mr Watkins can put up to 1500 litres of oil in his oil tank. There are already 850 litres of oil in the tank. Mr Watkins is going to fill the tank with oil. The price of oil is 67.2p per litre. Mr Watkins gets 5% off the price of the oil. How much does Mr Watkins pay for the oil he needs to buy?... (Total for Question 6 is 5 marks) 8 *P42059A0828*

54 7 Peter goes for a walk. He walks 15 miles in 6 hours. (a) Work out Peter s average speed. Give your answer in miles per hour.... mph (2) 5 miles = 8 km. Sunita says that Peter walked more than 20 km. *(b) Is Sunita right? You must show all your working. (2) (Total for Question 7 is 4 marks) *P42059A0928* 9 Turn over

55 8 The equation x x = 15 has a solution between 2 and 3 Use a trial and improvement method to find this solution. Give your answer correct to 1 decimal place. You must show all your working. x =... (Total for Question 8 is 4 marks) 10 *P42059A01028*

56 9 Here is a solid prism. Diagram NOT accurately drawn 5 cm 7 cm 4 cm 20 cm 11 cm Work out the volume of the prism.... cm 3 (Total for Question 9 is 3 marks) *P42059A01128* 11 Turn over

57 10 y P 1 Q O x Describe fully the single transformation that maps triangle P onto triangle Q (Total for Question 10 is 2 marks) 12 *P42059A01228*

58 11 (a) Expand and simplify 3(x + 4) + 2(5x... (2) (b) Expand and simplify (2x + 1)(x... (2) (c) Factorise completely 6y 2 xy... (2) (Total for Question 11 is 6 marks) *P42059A01328* 13 Turn over

59 12 n 1 n is an integer. (a) Write down all the possible values of n.... (2) (b) Solve the inequality 3p... (2) (Total for Question 12 is 4 marks) 14 *P42059A01428*

60 13 6 cm A 13 cm Diagram NOT accurately drawn C B ABC is a right-angled triangle. AC = 6 cm AB = 13 cm (a) Work out the length of BC. Give your answer correct to 3 significant figures. 17 cm P 25 cm Diagram NOT accurately drawn... cm (3) R Q PQR is a right-angled triangle. PR = 17 cm PQ = 25 cm (b) Work out the size of angle RPQ. Give your answer correct to 1 decimal place.... (3) (Total for Question 13 is 6 marks) *P42059A01528* 15 Turn over

61 14 A = 4bc A = 100 b = 2 (a) Work out the value of c.... (2) m = k (b) Make k the subject of the formula.... (3) (Total for Question 14 is 5 marks) 16 *P42059A01628*

62 15 R Q 12 cm Diagram NOT accurately drawn 4 cm P T 10 cm S PQR and PTS are straight lines. Angle PTQ = Angle PSR = 90 QT = 4 cm RS = 12 cm TS = 10 cm (a) Work out the area of the trapezium QRST.... cm 2 (2) (b) Work out the length of PT.... cm (3) (Total for Question 15 is 5 marks) *P42059A01728* 17 Turn over

63 16 Derek buys a house for He sells the house for (a) Work out Derek s percentage profit....% (3) Derek invests for 2 years at 4% per year compound interest. (b) Work out the value of the investment at the end of 2 years.... (3) (Total for Question 16 is 6 marks) 18 *P42059A01828*

64 17 Calculate the value of tan tan 60 1 Write down all the figures on your calculator display. You must give your answer as a decimal.... (Total for Question 17 is 2 marks) *P42059A01928* 19 Turn over

65 18 Here are the times, in seconds, that 15 people waited to be served at Rose s garden centre (a) On the grid, draw a box plot for this information Time (seconds) The box plot below shows the distribution of the times that people waited to be served at Green s garden centre. (3) Time (seconds) (b) Compare the distribution of the times that people waited at Rose s garden centre and the distribution of the times that people waited at Green s garden centre (2) (Total for Question 18 is 5 marks) 20 *P42059A02028*

66 19 A O 15 cm 30 B Diagram NOT accurately drawn OAB is a sector of a circle, centre O. The radius of the circle is 15 cm. The angle of the sector is 30. Calculate the area of sector OAB. Give your answer correct to 3 significant figures.... cm² (Total for Question 19 is 2 marks) *P42059A02128* 21 Turn over

67 20 Q cm Diagram NOT accurately drawn P R Calculate the length of PR. Give your answer correct to 3 significant figures.... cm (Total for Question 20 is 3 marks) 22 *P42059A02228*

68 21 The histogram shows some information about the weights of a sample of apples. Frequency density Weight (grams) Work out the proportion of apples in the sample with a weight between 140 grams and 200 grams.... (Total for Question 21 is 4 marks) *P42059A02328* 23 Turn over

69 22 20 cm 40 cm Diagram NOT accurately drawn 30 cm A frustrum is made by removing a small cone from a similar large cone. The height of the small cone is 20 cm. The height of the large cone is 40 cm. The diameter of the base of the large cone is 30 cm. Work out the volume of the frustrum. Give your answer correct to 3 significant figures.... cm 3 (Total for Question 22 is 4 marks) 24 *P42059A02428*

70 23 The table shows information about the ages, in years, of 300 students. Age (years) Number of students Ian takes a sample of 50 of these students, stratified by age. Calculate the number of 16 year old students he should have in his sample.... (Total for Question 23 is 2 marks) *P42059A02528* 25 Turn over

71 * 24 m = s t s = 3.47 correct to 2 decimal places t = correct to 3 decimal places By considering bounds, work out the value of m to a suitable degree of accuracy. You must show all your working and give a reason for your final answer. (Total for Question 24 is 5 marks) 26 *P42059A02628*

72 25 Here are two triangles T 1 and T 2. x x + 1 Diagram NOT accurately drawn T 1 T 2 30 x x The lengths of the sides are in centimetres. The area of triangle T 1 is equal to the area of triangle T 2. Work out the value of x, giving your answer in the form a + b where a and b are integers.... (Total for Question 25 is 5 marks) TOTAL FOR PAPER IS 100 MARKS *P42059A02728* 27

73 1MA0_2H Question Working Answer Mark Notes B2 for a fully correct ordered diagram (B1 for correct unordered diagram or ordered with at most two errors or omissions) B1 for a correct key 1 8 represents 18 *2 No + comparison 3 M1 for a correct start to the process Accept stem written as 10, 20 etc but key only acceptable if consistent with this eg. or or or M1 for completion of a fully correct method that will lead to an appropriate comparison C1 (dep on M2) for a correct statement with conclusion with 500 g or 25g more needed or 19 cakes or 25g and 23.75g SC :If no working then B1 for a correct statement with correct figures and units

74 1MA0_2H Question Working Answer Mark Notes 3 (a) 30 1 B1 for 30 minutes (b) 20 1 B1 cao (c) graph completed 2 B1 for horizontal line from (5, 20) to (5.30, 20) B1 for a single straight line with the correct gradient from (5.30, 20) to the time axis 4 (a) M1 for correctly using total probability is 1 or 100% if percentages used M1 (dep) for complete correct method to complete the solution A1 for 0.35 or 35% or (b) 20 2 M1 for oe A1 cao SC : If M0 then award B1 for an answer of 5 π M1 for use of π x (with x = 5 or x = 2.5) or 2 π x (with x = 5 or x = 2.5) M1 for π 5 1.8(0) or 2 π (0) A1 for or or or 28.3(0) or 28.8(0)

75 1MA0_2H Question Working Answer Mark Notes M1 for a correct method to work out the amount of oil required to fill the tank M1 for a correct method to find the cost of oil required before the discount M1 for a correct method of finding 5% of their calculated cost M1 (dep on previous M1) for a correct method to find the discounted cost A1 for correct answer of or 41496p OR M1 for a correct method of finding 5% of the cost of 1 litre of oil M1 (dep on previous M1) for a correct method to find the discounted cost of 1 litre of oil M1 for a correct method to work out the amount of oil required to fill the tank M1 for a correct method to find the discounted cost of the oil required A1 for correct answer of or 41496p OR M1 for a correct method to work out the amount of oil required to fill the tank M1 for a correct method of finding 5% of their calculated amount of oil M1 (dep on previous M1) for a correct method to find the reduced amount of oil M1 for a correct method to find the cost of the reduced amount of oil A1 for correct answer of or 41496p

76 1MA0_2H Question Working Answer Mark Notes 7* (a) M1 for 15 6 oe A1 for 2.5 or 2 *(b) Yes + evidence 2 M1 for a correct method to change 15 miles into kilometres C1(dep M1) for 24 km and statement with correct conclusion [SC: B1 for Yes oe and 24 km shown if M0 scored] or M1 for a correct method to change 20 kilometres into miles C1(dep M1) for 12.5 miles and statement with correct conclusion [SC: B1 for Yes oe and 12.5 miles shown if M0 scored]

77 1MA0_2H Question Working Answer Mark Notes 8 x x³ 3x B2 for a trial 2.8 x 2.9 evaluated correctly 2 2 (B1 for a trial evaluated correctly for 2 x 3 ) (961) 5.(267) (048) 6.(624) B1 for a different trial evaluated correctly for 2.85 x < 2.9 B1 (dep on at least one previous B1) for (125) NB (776) For trials where x has one decimal place: (583) x 2.6 trials must be evaluated to at least 1 sf truncated or rounded (552) 2.6 < x < 2.85 trials must be evaluated to at least 2 sf truncated or (89) rounded (99...) (13...) (29...) (47...) (67...) 2.85 x 2.9 trials must be evaluated to at least 3 sf truncated or rounded NB. Accept 15 or 15.0 for trial at x =2.87 No working scores 0 marks. If candidate is clearly working with x 3 3x 15 = 0 then use same scheme as above but subtract 15 from all evaluated values in the table

78 1MA0_2H Question Working Answer Mark Notes M1 for a correct method to find the area of the cross section M1 (dep) for a complete correct method for the volume of the prism A1 cao M1 for a correct method to find the volume of one cuboid M1 (dep) for a complete correct method for the volume of the prism A1 cao 10 Translation; 2 B1 for translation B1 for OR NB: B0 if more than one transformation given 11 (a) 3x x 2 13x M1 for correct method to expand one bracket eg 3 x or 3x + 12 or 2 5x 2 1 or 10x 2 A1 for 13x + 10 (b) 2x² 8x + x 4 2x² 7x 4 2 M1 for all 4 terms (and no additional terms) correct ignoring signs or 3 out of no more than four terms correct A1 for 2x² 7x 4 (c) 3y(2y 3x) 2 B2 for 3y(2y 3x) (B1 for 3(2y² 3xy) or y(6y 9x) or 3y(2y + 3x) or 3y(2y ax) where a is any positive integer except 3 or 3y(by 3x) where b is any positive integer except 2)

79 1MA0_2H Question Working Answer Mark Notes 12 (a) 2, 1, 0, 1, 2 B2 for all 4 correct values; ignore repeats, any order (B1 for 3 correct (and no incorrect values) eg. 2, 1, 0 or one additional value eg. 3, 2, 1, 0, 1) (b) p>6 2 M1 for clear intention to add 7 to both sides or 3p > or clear intention to divide all 3 terms by 3 as a first step or 3p > 18 or 3p = 18 or 3p < 18 or A1 for p > 6 as final answer NB: (p =) 6 on the answer line scores M1 A0 13 (a) M1 for 13² 6² or or 133 M1 (dep on M1) for "13 6 " or 133 A1 for answer in the range (b) M1 for cos (RPQ)= oe OR sin PQR = with PQR clearly identified M1 for (RPQ =+) cos -1 oe OR PQR = sin-1 with PQR clearly identified A1 for answer in the range SC : B2 for an answer of 0.823(033...) or 52.3(95...) or 52.4

80 1MA0_2H Question Working Answer Mark Notes 14 (a) 100 = 4 2 c M1 for correct substitution into formula A1 for 12.5 oe (b) k + 1 k = 4m² 1 or 2m = ( k + 1) 4 k + 1 k = 4m² 1 k = 4m² 1 3 M1 for correct method to clear fraction or remove square root sign M1 (dep) for a fully correct method to both clear fraction and remove square root sign A1 for k = 4m² 1 or k = (2m + 1)(2m 1) 15 (a) (4 + 12) M1 for a fully correct method for area of QRST A1 cao (b) For example 3 PT + 10 = 3PT 2PT = M1 for a correct scale factor or ratio using two corresponding sides from two similar triangles or two sides within the same triangle (may be seen within an equation) oe or 4 : 12 oe or or eg. or etc. M1 for a correct equation with PT or PS as the only variable or complete correct method using scale factor A1 cao

81 1MA0_2H Question Working Answer Mark Notes 16 (a) M1 for or M1 for A1 cao OR M1 for ( 100) 100 oe M1 for oe A1 cao (b) or ² M1 for or 6180 or or or or M1 (dep) for ( ) or (0) or A1 for (0) as final answer OR M2 for ² (M1 for ) A (0) as final answer

82 1MA0_2H Question Working Answer Mark Notes M1 for 2.73 or or 3.73 or or or 1.93 or (1 + 3) or ( 3 1) or (2 + 3) or or A1 for (5 ) SC: B1 for (17...) 18 (a) minimum = 5 lower quartile = 14 median = 25 upper quartile = 30 maximum = 44 box plot 3 B3 for fully correct box plot (B2 for at least 3 correct values plotted including box and tails or 5 correct values indicated) (B1 for at least 2 correct values plotted including box or tails or 3 or 4 correct values indicated) (b) comparisons 2 B1 for a correct comparison (ft) of medians B1 for a correct comparison (ft) of ranges or IQRs 19 π 15² M1 for a correct method to find the area of sector OAB A1 for answer in range

83 1MA0_2H Question Working Answer Mark Notes M1 for cos 140 M1 (dep) for correct order of evaluation or 226.(05...) A1 for answer in range OR M1 for M1 for PR = sin 140 A1 for answer in range OR M1 for 8 sin70 or 8 cos20 M1 for 2 8 sin70 or 2 8 cos 20 A1 for answer in range

84 1MA0_2H Question Working Answer Mark Notes 21 Total area = ( ) + ( ) + (0.7 20) + ( ) + ( ) = M1 for a method to find the frequency or the area of any one block Area (140 < w < 200) = ( ) + (0.7 20) + ( ) = M1 for a method (with correct values) to find total area of all blocks or 44.4 or 1110 or a correct method (with correct values) to find total area of middle 3 blocks or 32.4 or 810 M1 (dep on M2) for a correct method to find required proportion (could lead to a decimal or a percentage or a fraction) A1 for answer which rounds to 0.73 or 73% or or equivalent fraction

85 1MA0_2H Question Working Answer Mark Notes 22 π 15² B1 for 15cm as diameter or 7.5 cm as radius of smaller cone π 7.5² 20 (may be marked on diagram or used in a formula) M1 for a 50 oe A1 for 11 (accept 12) M1 for a numerical expression for the volume of one cone eg. π 15² 40 (= ) or π 7.5² 20 (= ) M1 for π 15² 40 oe π 7.5² 20 oe A1 for answer in the range OR B1 for 2³ M1 for a numerical expression for the volume of the large cone eg. π 15² 40 (= ) M1 volume of frustrum = π 15² 40 oe A1 for answer in the range

86 1MA0_2H Question Working Answer Mark Notes * because the LB and UB agree to that number of figures 5 B1 for or or B1 for or or M1 for.. as UB OR as LB.. C1 (dep on all previous marks) for and both values must clearly come from working with correct values C1 for from and and both LB and UB round to M1 for x x sin30 oe M1 for (x 2)( x + 1) oe or 2 1 sin90 M1 (dep on at least one previous M1) for formation of equation from equating areas with x as the only variable A1 for x² 2x 4 = 0 oe in the form ax 2 + bx + c = 0 or ax 2 + bx = c A1 cao

87 Write your name here Surname Other names Edexcel GCSE Centre Number Mathematics A Paper 1 (Non-Calculator) Tuesday 11 June 2013 Morning Time: 1 hour 45 minutes Candidate Number Higher Tier Paper Reference 1MA0/1H 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 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. 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 P43598A 2013 Pearson Education Ltd. 6/5/5/ *P43598A0128*

88 GCSE Mathematics 1MA0 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 = Surface area of sphere = 4 2 Volume of cone = h Curved surface area of cone = 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 0, are given by b b ac x = ± ( 4 ) 2a 2 Sine Rule a b c = = sin A sin B sinc Cosine Rule a 2 = b 2 + c 2 2bc cos A Area of triangle = 1 2 ab sin C 2 *P43598A0228*

89 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 Given that = write down the value of (a) (b) (Total for Question 1 is 2 marks) 2 Mr Mason asks 240 Year 11 students what they want to do next year. 15% of the students want to go to college. 3 of the students want to stay at school. 4 The rest of the students do not know. Work out the number of students who do not know.... (Total for Question 2 is 4 marks) *P43598A0328* 3 Turn over

90 3 Sixteen babies are born in a hospital. Here are the weights of the babies in kilograms Show this information in an ordered stem and leaf diagram. Key: (Total for Question 3 is 3 marks) 4 (a) Expand 3(2 + t) (b) Expand 3x(2x + 5)... (1) (c) Expand and simplify (m + 3)(m + 10)... (2)... (2) (Total for Question 4 is 5 marks) 4 *P43598A0428*

91 5 Write 525 as a product of its prime factors.... (Total for Question 5 is 3 marks) 6 Ed has 4 cards. There is a number on each card ? The mean of the 4 numbers on Ed s cards is 10 Work out the number on the 4th card.... (Total for Question 6 is 3 marks) *P43598A0528* 5 Turn over

92 7 y P O x (a) Translate shape P by the vector 5 2 (2) 6 *P43598A0628*

93 y B O A 2 x 3 4 (b) Describe fully the single transformation that maps shape A onto shape B (3) (Total for Question 7 is 5 marks) *P43598A0728* 7 Turn over

94 8 Margaret has some goats. The goats produce an average total of 21.7 litres of milk per day for 280 days. Margaret sells the milk in 1 litre bottles. 2 Work out an estimate for the total number of bottles that Margaret will be able to fill with the milk. You must show clearly how you got your estimate.... (Total for Question 8 is 3 marks) 9 Matt and Dan cycle around a cycle track. Each lap Matt cycles takes him 50 seconds. Each lap Dan cycles takes him 80 seconds. Dan and Matt start cycling at the same time at the start line. Work out how many laps they will each have cycled when they are next at the start line together. Matt... laps Dan... laps (Total for Question 9 is 3 marks) 8 *P43598A0828*

95 10 The diagram shows a garden in the shape of a rectangle x Diagram NOT accurately drawn x + 6 All measurements are in metres. The perimeter of the garden is 32 metres. Work out the value of x... (Total for Question 10 is 4 marks) *P43598A0928* 9 Turn over

96 *11 Debbie drove from Junction 12 to Junction 13 on a motorway. The travel graph shows Debbie s journey Distance from Junction 12 (kilometres) Time (minutes) Ian also drove from Junction 12 to Junction 13 on the same motorway. He drove at an average speed of 66 km/hour. Who had the faster average speed, Debbie or Ian? You must explain your answer. (Total for Question 11 is 4 marks) 10 *P43598A01028*

97 12 On the grid, draw the graph of y = 1 x + 5 for values of x from 2 to 4 2 y O x 1 (Total for Question 12 is 3 marks) *P43598A01128* 11 Turn over

98 *13 Here is a map. The position of a ship, S, is marked on the map. N C S Scale 1 cm represents 100 m Point C is on the coast. Ships must not sail closer than 500 m to point C. The ship sails on a bearing of 037 Will the ship sail closer than 500 m to point C? You must explain your answer. (Total for Question 13 is 3 marks) 12 *P43598A01228*

99 14 2 < n 3 (a) Represent this inequality on the number line n (2) (b) Solve the inequality 8x 3 6x (2) (Total for Question 14 is 4 marks) *15 One sheet of paper is cm thick. Mark wants to put 500 sheets of paper into the paper tray of his printer. The paper tray is 4 cm deep. Is the paper tray deep enough for 500 sheets of paper? You must explain your answer. (Total for Question 15 is 3 marks) *P43598A01328* 13 Turn over

100 16 The normal price of a television is reduced by 30% in a sale. The sale price of the television is 350 Work out the normal price of the television.... (Total for Question 16 is 3 marks) 14 *P43598A01428*

101 17 Sumeet has a pond in the shape of a prism. 1 m 2 m 0.5 m 1.3 m Diagram NOT accurately drawn The pond is completely full of water. Sumeet wants to empty the pond so he can clean it. Sumeet uses a pump to empty the pond. The volume of water in the pond decreases at a constant rate. The level of the water in the pond goes down by 20 cm in the first 30 minutes. Work out how much more time Sumeet has to wait for the pump to empty the pond completely.... (Total for Question 17 is 6 marks) *P43598A01528* 15 Turn over

102 18 Solve the simultaneous equations 4x + 7y = 1 3x + 10y = 15 x =... y =... (Total for Question 18 is 4 marks) 19 Write these numbers in order of size. Start with the smallest number (Total for Question 19 is 2 marks) 16 *P43598A01628*

103 20 A N x D Diagram NOT accurately drawn 4x M B C ABCD is a square with a side length of 4x M is the midpoint of DC. N is the point on AD where ND = x BMN is a right-angled triangle. Find an expression, in terms of x, for the area of triangle BMN. Give your expression in its simplest form.... (Total for Question 20 is 4 marks) *P43598A01728* 17 Turn over

104 21 The table below shows information about the heights of 60 students. Height (x cm) Number of students 140 < x < x < x < x < x < x (a) On the grid opposite, draw a cumulative frequency graph for the information in the table. (3) 18 *P43598A01828*

105 60 50 Cumulative frequency Height (cm) (b) Find an estimate (i) for the median, (ii) for the interquartile range.... cm... cm (3) (Total for Question 21 is 6 marks) *P43598A01928* 19 Turn over

106 22 P and Q are two triangular prisms that are mathematically similar. B E A 10 cm 2 6 cm C 15 cm D 12 cm F Diagram NOT accurately drawn Prism P Prism Q Prism P has triangle ABC as its cross section. Prism Q has triangle DEF as its cross section. AC = 6 cm DF = 12 cm The area of the cross section of prism P is 10 cm 2. The length of prism P is 15 cm. Work out the volume of prism Q.... (Total for Question 22 is 4 marks) 20 *P43598A02028*

107 23 Simplify 4( x + 5) 2 x + 2x (Total for Question 23 is 2 marks) *P43598A02128* 21 Turn over

108 24 Bill works for a computer service centre. The table shows some information about the length of time, t minutes, of the phone calls Bill had. Time (t minutes) 0 < t < t < t < t < t 45 Number of calls On the grid, draw a histogram to show this information. Frequency density Time (t minutes) (Total for Question 24 is 3 marks) 22 *P43598A02228*

109 25 The expression x 2 8x + 21 can be written in the form (x a) 2 + b for all values of x. (a) Find the value of a and the value of b. a =... The equation of a curve is y = f(x) where f(x) = x 2 8x + 21 The diagram shows part of a sketch of the graph of y = f(x). b =... (3) y y = f(x) M O x The minimum point of the curve is M. (b) Write down the coordinates of M. (...,...) (1) (Total for Question 25 is 4 marks) *P43598A02328* 23 Turn over