[PDF] Cambridge Secondary Progression Test - Stage 7 Math MS.pdf | Plain Text

Mathematics Stage 7 V2

© UCLES 2011 P110/M/A/M/11 2 These tables give general guidelines on marking answers that involve number and place value, and units of length, mass, money or duration. If the mark scheme does not specify the correct answer, refer to these general guidelines. Number and Place value The table shows various general rules in terms of acceptable decimal answers. Accept Accept omission of leading zero if answer is clearly shown, e.g. .675 Accept tailing zeros, unless the question has asked for a specific number of decimal places, e.g. 0.7000 Always accept appropriate tailing zeros, e.g. 3.00 m; 5.000 kg Accept a comma as a decimal point if that is the convention that you have taught the children, e.g. 0,638 Units For questions involving quantities, e.g. length, mass, time or money, correct units must be given in the answer. The table shows acceptable and unacceptable versions of the answer 1.85 m. Correct answer Also accept Do not accept Units are not given on answer line and the question does not specify a unit for the answer 1.85 m Correct conversions provided the unit is stated, e.g. 1 m 85 cm 185 cm 1850 cm 1850 mm 0.00185 km 1.85 185 m If the unit is given on the answer line, e.g. ………………… m ……1.85…… m Correct conversions, provided the unit is stated unambiguously, e.g. ……185 cm…… m ……185…… m ……1850…… m etc. If the question states the unit that the answer should be given in, e.g. “Give your answer in metres” 1.85 m 1.85 1 m 85 cm 185; 1850 Any conversions to other units, e.g. 185 cm

© UCLES 2011 P110/M/A/M/11 3 Money For questions involving money, it is essential that appropriate units are given in the answer. The table shows acceptable and unacceptable versions. Accept Do not accept If the amount is in dollars and cents, the answer should be given to two decimal places. $0.30 $9 or $9.00 $09 or $09.00 If units are not given on answer line Any unambiguous indication of the correct amount, e.g. 30 cents; 30 c $0.30; $0.30 c; $0.30 cents $0-30; $0=30; $00:30 30 or 0.30 without a unit Incorrect or ambiguous answers, e.g. $0.3; $30; $30 cents; 0.30 cents If $ is shown on the answer line $......0.30…… $......0.30 cents…… Accept all unambiguous indications, as shown above $......30…… $......30 cents…… (this cannot be accepted because it is ambiguous, but if the dollar sign is deleted it becomes acceptable) If cents is shown on the answer line ……30……cents ……$0.30……cents ……0.30……cents ……$30……cents Duration Accept any unambiguous method of showing duration and all reasonable abbreviations of hours (h, hr, hrs), minutes (m, min, mins) and seconds (s, sec, secs). Accept Do not accept Any unambiguous indication using any reasonable abbreviations of hours (h, hr, hrs), minutes (m, min, mins) and seconds (s, sec, secs), e.g. 2 hours 30 minutes; 2 h 30 m; 02 h 30 m 5 min 24 sec; 00 h 05 m 24 s Incorrect or ambiguous formats, e.g. 2.30; 2.3; 2.30 hours; 2.30 min; 2 h 3; 2.3 h Any correct conversion with appropriate units, e.g. 2.5 hours; 150 mins 324 seconds 2.5; 150 304 Also accept unambiguous digital stopwatch format, e.g. 02:30:00 00:05:24; 05:24 s Do not accept ambiguous indications, e.g. 02:30 5.24

© UCLES 2011 P110/M/A/M/11 4 Time There are many ways to write times, in both numbers and words, and marks should be awarded for any unambiguous method. Accept time written in numbers or words unless there is a specific instruction in the question. Some examples are given in the table. Accept Do not accept Any unambiguous indication of correct answer in numbers, words or a combination of the two, e.g. 07:30; 19:00 0730; 07 30; 07.30; 07,30; 07-30; 7.30; 730 a.m.; 7.30am; 7.30 in the morning Half past seven (o’clock) in the morning Thirty minutes past seven am Also accept: O-seven-thirty 1900; 19 00; 19_00 etc. Nineteen hundred (hours) Seven o’clock in the afternoon/evening Accept correct conversion to 12-hour clock, e.g. 16:42 4.42 p.m. Sixteen forty two Four-forty-two in the afternoon/evening Four forty two p.m. Forty two (minutes) past four p.m. Eighteen (minutes) to five in the evening Also accept a combination of numbers and words, e.g. 18 minutes to 5 p.m. 42 minutes past 4 in the afternoon Incorrect or ambiguous formats, e.g. 07.3; 073; 07 3; 730; 73; 7.3; 7.3 am; 7.30 p.m 19; 190; 19 000; 19.00 am; 7.00 am 4.42 am; 0442; 4.42 Forty two (minutes) past sixteen Eighteen (minutes) to seventeen

© UCLES 2011 P110/M/A/M/11 5 Stage 7 Paper 1 Mark Scheme Question 1 Part Mark Answer Further Information 1 2 (°C) Total 1 Question 2 Part Mark Answer Further Information (a) 1 225 (b) 1 9 Total 2 Question 3 Part Mark Answer Further Information (a) 1 17 260 (b) 1 100 Total 2 Question 4 Part Mark Answer Further Information 1 50 15 or equivalent Total 1

© UCLES 2011 P110/M/A/M/11 6 Question 5 Part Mark Answer Further Information (a) 1 6 4 3 (b) 1 5 19 Total 2 Question 6 Part Mark Answer Further Information 1 ($) 12 Total 1 Question 7 Part Mark Answer Further Information 1 Correct reflection in y = x y x y = x Accept slight inaccuracy in drawing as long as the intention is clear. Ignore any shading. Total 1

© UCLES 2011 P110/M/A/M/11 7 Question 8 Part Mark Answer Further Information 1 57 Accept 57° Total 1 Question 9 Part Mark Answer Further Information 1 5.7 Total 1 Question 10 Part Mark Answer Further Information (a) 1 70 Accept 70° (b) 1 Yes and a correct reason e.g. the angles do not add up to 360 Do not accept yes with no reason. Do not accept an explanation of angles add up to 370 on its own. Total 2

© UCLES 2011 P110/M/A/M/11 8 Question 11 Part Mark Answer Further Information (a) 1 5(°C) Do not accept 6 – 11 or 11 – 6 (b) 1 21(°C) (c) 2 Any two valid distinct comments. e.g. The temperature everyday is higher in Sydney than in London. On average, Sydney is hotter. same range or equally spread 1 mark for each Do not accept the general statement 'Sydney is hotter than London' without reference to either an average or the time period. Total 4 Question 12 Part Mark Answer Further Information 1 ( 18 + 7 ) ÷ ( 3 + 2 ) = 5 Total 1 Question 13 Part Mark Answer Further Information (a) 1 y = 12 + x y = 12 ÷ x y = 12x y = 12 – x Accept any clear indication. (b) 1 240 (screws) Accept 32 if y = 12 + x is ringed in (a). Total 2

© UCLES 2011 P110/M/A/M/11 9 Question 14 Part Mark Answer Further Information 2 Type of triangle Triangle Scalene Right angled Isosceles A


B  
C 

D
  2 marks for all 3 rows. 1 mark for 1 or 2 rows. Award 1 mark if all ticks are correct but no crosses are used. Total 2 Question 15 Part Mark Answer Further Information 2 8 5 1 mark for sight of 8 3 in working. Total 2 Question 16 Part Mark Answer Further Information 2 Number of faces Number of vertices Number of edges Square based pyramid 5 5 8 Cube or cuboid 6 8 12 Triangular prism 5 6 9 1 mark for cube or cuboid. Accept any other shape with the correct properties. 1 mark for 8 and 6 in the correct positions. Total 2

© UCLES 2011 P110/M/A/M/11 10 Question 17 Part Mark Answer Further Information 2 1 mark for each correct connection. Do not accept any answer where two lines are joined to one box. Total 2 Question 18 Part Mark Answer Further Information 2 6 (cm) Accept 2 marks for 6 cm, with no working shown. 1 mark for perimeter = 24 (cm) or 1 mark for evidence of a correct method. Total 2 Question 19 Part Mark Answer Further Information 2 16 (rows) 1 mark for 15 or 15 r22 Total 2 Question 20 Part Mark Answer Further Information 1 7 : 4 correct answer only Total 1

© UCLES 2011 P110/M/A/M/11 11 Question 21 Part Mark Answer Further Information 1 30 16 20 12 25 14 3528 159 Accept any clear indication. Both correct answers must be indicated with no extras for the mark to be awarded. Total 1 Question 22 Part Mark Answer Further Information 2 ($)17.87 1 mark for sight of $32.13 in the working. 1 mark for a complete method with no more than one arithmetic error. Total 2 Question 23 Part Mark Answer Further Information (a) 1 Bar for car height 6 Bar can be any width but must not be a single line. Accept any clear intention. (b) 1 24 (students) Follow through from incorrect answer in part (a). Total 2

© UCLES 2011 P110/M/A/M/11 12 Question 24 Part Mark Answer Further Information (a) 1 27 (litres) (b) 1 8 (litres) Total 2 Question 25 Part Mark Answer Further Information 2 55 (°) 1 mark for angle CAD or angle CDA = 35° Total 2 Question 26 Part Mark Answer Further Information 1 any 5 squares in A shaded Accept any clear intention including half squares provided that they add up to 5 Total 1 Question 27 Part Mark Answer Further Information 1 Yes and correct explanation e.g. A and D both round to 5000 Do not award mark for Yes without valid explanation. Accept A and D both round to the same number. Total 1

© UCLES 2011 P110/M/A/M/11 13 Stage 7 Paper 2 Mark Scheme Question 1 Part Mark Answer Further Information 2 2 marks for all 4 correct. 1 mark for 3 correct. Total 2 Question 2 Part Mark Answer Further Information 1 6.6 Total 1 Question 3 Part Mark Answer Further Information 1 57.5 cm, 0.6 m, 180 cm, 2043 mm, 2.4 m Accept any clear intention including omission of units. Total 1 Question 4 Part Mark Answer Further Information 1 ($) 70(.00) Total 1

© UCLES 2011 P110/M/A/M/11 14 Question 5 Part Mark Answer Further Information 2 Number of lines of symmetry Order of rotational symmetry Square 4 4 Rectangle 2 2 Rhombus 2 2 Kite 1 1 Award 1 mark for two correct rows. or Award 1 mark for one column completed correctly. Total 2 Question 6 Part Mark Answer Further Information (a) 1 21 and 15, in the correct order Both numbers must be correct for the award of the mark. (b) 1 17 and 16, in the correct order Both numbers must be correct for the award of the mark. Total 2 Question 7 Part Mark Answer Further Information 2 Ages (years) Frequency 1-20 4 21-40 7 41-60 6 61-80 3 Award 1 mark for 2 or 3 correct frequencies. or Award 1 mark for frequency column completed with the correct number of tally marks only. Total 2

© UCLES 2011 P110/M/A/M/11 15 Question 8 Part Mark Answer Further Information 1 4 hundredths or 1004 Total 1 Question 9 Part Mark Answer Further Information (a) 1 x 0 1 2 4 y 1 3 5 9 Both numbers must be correct. (b) 2 12345678910 x 1 2 10 3 4 5 6 7 8 9 y 0 y = 2x + 1 Award 1 mark for points plotted correctly. Allow follow through from incorrect table. Award 1 mark for straight line correctly labelled. Total 3

© UCLES 2011 P110/M/A/M/11 16 Question 10 Part Mark Answer Further Information 1 Uses 6 dots to form the vertices of a hexagon that is symmetrical but not regular, e.g. Accept slight inaccuracy in drawing so long as intention is clear. Total 1 Question 11 Part Mark Answer Further Information 1

Accept any clear indication. Total 1 Question 12 Part Mark Answer Further Information (a) 1 D plotted at (–2,1) Accept correct point plotted without label. Accept slight inaccuracy in the position of the point (b) 1 (–2,1) Follow through from incorrect point D. Total 2

© UCLES 2011 P110/M/A/M/11 17 Question 13 Part Mark Answer Further Information 1 –20 Total 1 Question 14 Part Mark Answer Further Information 1 Any four odd numbers and any two even numbers. Accept repeated numbers. Total 1 Question 15 Part Mark Answer Further Information 1

Accept any clear indication. Both must be correct with no extras selected. Total 1 Question 16 Part Mark Answer Further Information 2 25 16 41 or 23 36 54 Award 1 mark for both a square number and a prime number using the given digits. Total 2

© UCLES 2011 P110/M/A/M/11 18 Question 17 Part Mark Answer Further Information (a) 1 Multiply by 2 or double. Accept any valid answer that generates these terms. (b) 1 21 Total 2 Question 18 Part Mark Answer Further Information 2 ($)4.76 Award 1 mark for the complete correct method. Do not award a mark for the price of one lemon only. Total 2 Question 19 Part Mark Answer Further Information 1 235 ÷ 25 = 9 52 correct answer only Do not accept 9.4 or any unsimplified fraction. Total 1 Question 20 Part Mark Answer Further Information (a) 2 188(cm²) Award 1 mark for any correct method. (b) 1 168(cm³) Total 3

© UCLES 2011 P110/M/A/M/11 19 Question 21 Part Mark Answer Further Information (a) 1 7 (b) 2 6.1 Award 1 mark for clear attempt to multiply scores by frequencies and adding them. Total 3 Question 22 Part Mark Answer Further Information 1

Accept any clear indication. Both must be ticked with no extras. Total 1 Question 23 Part Mark Answer Further Information 1 40° 55° 30° 35° 65° 70°

Accept any clear indication. Both must be ticked with no extras. Total 1

© UCLES 2011 P110/M/A/M/11 20 Question 24 Part Mark Answer Further Information (a) 1 4a + b Accept any equivalent expression. (b) 1 Any closed shape with the correct perimeter. e.g. Total 2 Question 25 Part Mark Answer Further Information (a) 1 (0).625 Do not accept rounded or truncated answers. (b) 1 5 3 8 5 20 13 107 4 3 Accept any equivalent decimals. Total 2 Question 26 Part Mark Answer Further Information (a) 1 12 and 8, in either order Both numbers must be correct. (b) 1 Any 6 squares shaded Accept any clear intention including half squares provided that they add up to 6 Total 2

© UCLES 2011 P110/M/A/M/11 21 Question 27 Part Mark Answer Further Information 2 regular pentagon correctly drawn Award 1 mark for all angles within 2° Award 1 mark for all sides within 2 mm. Total 2

© UCLES 2011 P110/M/A/M/11 22 Stage 7 Paper 3 Mark Scheme Question Mark Answer 1 ½ 62 2 ½ 7 3 ½ ($) 9 4 ½ 130 (mm) 5 ½ 133 (°) 6 ½ (7 + 3) x 4 7 ½ x + 4 (years) 8 ½ evens or 21, or equivalent (Do not accept equal or a ratio.) 9 ½ 30(°) ± 5° (Check the angle on your printed answer sheet.) 10 ½ 89 11 ½ 213 12 ½ 36 13 ½ 6.3 14 ½ 1 hour 30 mins or equivalent 15 ½ 56 16 ½ ($) 6 17 ½ 5 32 or exact equivalent (Do not accept a decimal.) 18 ½ 27 (cm³) 19 ½ X at 0 x 0 1 Any clear indication. 20 ½ 6 (people)