Mathematics. Stage 8

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1 Mathematics Stage 8 V

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 Always accept appropriate tailing zeros, e.g m; 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.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.85 m Correct conversions provided the unit is stated, e.g. m 85 cm 85 cm 850 cm 850 mm km m If the unit is given on the answer line, e.g. m.85 m Correct conversions, provided the unit is stated unambiguously, e.g. 85 cm m 85 m 850 m etc. If the question states the unit that the answer should be given in, e.g. Give your answer in metres.85 m.85 m 85 cm 85; 850 Any conversions to other units, e.g. 85 cm

3 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 If $ is shown on the answer line If cents is shown on the 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 $ $ cents Accept all unambiguous indications, as shown above 30 cents $0.30 cents 30 or 0.30 without a unit Incorrect or ambiguous answers, e.g. $0.3; $30; $30 cents; 0.30 cents $...30 $...30 cents (this cannot be accepted because it is ambiguous, but if the dollar sign is deleted it becomes acceptable) 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 Any unambiguous indication using any reasonable abbreviations of hours (h, hr, hrs), minutes (m, min, mins) and seconds (s, sec, secs), e.g. hours 30 minutes; h 30 m; 0 h 30 m 5 min 4 sec; 00 h 05 m 4 s Any correct conversion with appropriate units, e.g..5 hours; 50 mins 34 seconds Also accept unambiguous digital stopwatch format, e.g. 0:30:00 00:05:4; 05:4 s Do not accept Incorrect or ambiguous formats, e.g..30;.3;.30 hours;.30 min; h 3;.3 h.5; Do not accept ambiguous indications, e.g. 0:30 5.4

4 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 Any unambiguous indication of correct answer in numbers, words or a combination of the two, e.g. 07:30; 9: ; 07 30; 07.30; 07,30; 07-30; 7.30; 730 a.m.; 7.30am; 7.30 in the morning Do not accept Incorrect or ambiguous formats, e.g. 07.3; 073; 07 3; 730; 73; 7.3; 7.3 am; 7.30 p.m Half past seven (o clock) in the morning Thirty minutes past seven am Also accept: O-seven-thirty 900; 9 00; 9_00 etc. 9; 90; 9 000; 9.00 am; 7.00 am Nineteen hundred (hours) Seven o clock in the afternoon/evening Accept correct conversion to -hour clock, e.g. 6:4 4.4 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 4.4 am; 044; 4.4 Forty two (minutes) past sixteen Eighteen (minutes) to seventeen Also accept a combination of numbers and words, e.g. 8 minutes to 5 p.m. 4 minutes past 4 in the afternoon

5 5 Stage 8 Paper Mark Scheme Question Question 4.96 Total Question 3 Both must be ticked with no extras. Accept any clear indication. Total Question 4 64

6 6 Question Accept equivalent answer, e.g Accept equivalent answer, e.g. 0 Question 6 5 (miles) Accept 4.8 to 5. inclusive. Total Question 7 Righthanded Lefthanded Total Boys Girls 3 5 Total 7 9 mark for either Boys or Girls row correct. Question Accept any clear indication. All three must be correct with no incorrect answers. Total

7 7 Question 9 3 cm 3 cm 4 cm 3 cm 3 cm cm Accept any clear indication. No extras ticked. 3 cm 3 cm 5cm 3cm 5 cm cm Total Question 0 x+3 (x 3) 3x x 3 3(x+) Accept any clear indication. No extras ticked. 3 (sweets) mark for x = x 3 or x = answer to. Total 3 Question 40 (cm 3 ) Total Question

8 8 Pattern number mark for each correct column. Number of white counters Total number of counters (n ) or equivalent, e.g. n (c) (n ) + = n or equivalent. Follow through for + if is algebraic. Total 4 Question 3 B and E, in either order B and D, in either order Question 4 75 (%) 7 mark for 00 or equivalent 36 method.

9 9 Question 5 (7,9) mark for each coordinate. or mark for clear method (algebraic or graphical) shown, e.g. evidence that coordinates of midpoint is average of two end points. Question 6 60% and 8 mark for each Question Accept equivalent answer, 3 e.g. 00

10 0 Question 8 Accept any clear indication. Both squares must be identified for the award of the mark. Accept any clear indication. Question 9 8 Do not accept 30. Do not accept answers on diagram, e.g. ringed. Question mark for common denominator of 5 (or multiple of 5)

11 Question Accurate construction with construction arcs, e.g. Accept ±. Correct construction arcs must be seen. mark for evidence of arcs in relevant position. Question Shape B and any valid reason, eg. A is 8 5 B is 3 = is more than Do not award any marks for B without a reason. mark for 8 5 and 3 Accept any valid method. Question 3 Diagonals are perpendicular Diagonals have equal length Square Rhombus Rectangle Trapezium marks for all correct. mark for correct rows or correct column. Do not accept blank cells.

12 Question 4 4 and 6, in either order Both must be correct. 6 and 7, in either order Both must be correct.

13 3 Stage 8 Paper Mark Scheme Question Total Question 3.75 Total Question 3 Yes, and a correct explanation, e.g. both are or LCM of 4 and 6 is and HCF of 4 and 36 is No mark for yes without an explanation. mark for as either LCM or HCF Question 4 0. Total

14 4 Question 5 corresponding Accept any discernable spelling. alternate Accept any discernable spelling. Question 6 David ($) 8.80 Jo ($) 3.0 Mary ($).(00) mark for attempt to divide 44 by 0 Award mark for all three correct answers but with currency information incorrect, e.g. 8.8 Question 7 (i) 36y (cents) or equivalent form Accept e.g. 36 y, y 36 (ii) (C=) 36y + z (cents) or equivalent form Follow through answer to (i) 340 (cents) Total 3

15 5 Question 8 (c) 8:35 (am) 3 (km) 8:6 (am) or 8:7 (am) Total 3 Question 9 x 0 3 y All three points must be correct. y y = x x Accept correct line without visible points. Accept line that stops at (, 5) and / or (3,3) Accept line without label. (c) No and or equivalent explanation. Do not award mark for NO without an explanation. Total 3

16 6 Question or equivalent mark for list of correct factors or a correct factor tree. mark for identification of 4 prime factors,, 3, 5, or for evidence of the correct method. Question (y =) 4x 3 or equivalent form Accept e.g. 4 x or x 4 for 4x 8 or equivalent

17 7 Question Method of travel Frequency Angle in pie chart 08 and 96 must be seen. Car 0 0 Accept omission of 360 Walk 9 08 Bus 8 96 Accept omission of Circle 3 36 Total Bus Cycle Car Award marks for correct chart correctly labelled; angle within ± Award mark for correct chart with no labels or at least one correct sector with label. Walk Total 3 Question 3 8 Do not accept 0.5 or Total

18 8 Question Both correct with no additional ticks. Accept any clear indication. Total Question 5 Accurate net with tolerance of ± mm per line and ± per angle, e.g. mark for inaccurately drawn net with 4 correctly positioned triangles. Question 6 ($) Accept any answer between ($) 943 and ($) 944 inclusive. mark for amount after year $ 480 or or equivalent seen

19 9 Question > or 0.75> or equivalent. Total Question 8 6 (girls) 8 < 0 or (or equivalent) The same number of boys and girls chose yellow but there are more boys than girls. 8 mark for partial answer, e.g. or 0 yellow more popular with girls No marks for sight of by itself. Total 3 Question 9 5. (00 ) Total

20 0 Question 0 5a 3a + b 4b = a b 3x 4y + 7x - 3y = 0x 7y Question All three must be correct with no incorrect answers. Accept any clear indication. Total Question 4(cm²) 4(cm) Allow follow through from part 6

21 Question 3 Can and a correct explanation Either Can ml for cents and Bottle ml for 0.7 cents or Can $ buys 600 ml and Bottle $ buys 588(...)ml Two comparative figures must be seen. Accept equivalent arguments, e.g. using cents or litres. mark for or 0.7 or mark for 600 or 588(...) No mark for Can with no explanation. Question 4 x + y + ABC = 80 x + y + ABC = z + ABC x + y = z Argument may be stated informally. Award mark for each element. Do not accept Exterior angle = sum of interior opposite angles on its own.

22 Stage 8 Paper 3 Mark Scheme Question Mark Answer ½ 400 ½ (0).4 3 ½ chord 4 ½ (0).48 5 ½ 7000(ml) 6 ½ 7 or equivalent 0 7 ½ a³ 8 ½ 4 (counters) 9 ½ ½ 70( ) ½ 70(cents) or equivalent ½ 7( C) ± 0.5 C 3 ½ 5 4 ½ (5,) 5 ½ 0 6 ½ 33 (cm²) 7 ½ or equivalent 7 8 ½ 5 (cm) 9 ½ 4 (accept TT, HH, TH, HT) or equivalent 0 ½ 4

Cambridge Secondary 1 Progression Test. Mark scheme. Mathematics. Stage 8

Cambridge Secondary 1 Progression Test Mark scheme Mathematics Stage 8 DC (CW/SW) 90762/9RP These tables give general guidelines on marking answers that involve number and place value, and units of length,