AQA Qualifications GCSE MATHEMATICS Topic tests Higher tier - Mark schemes Version.
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Contents Algebra 4 Number 7 Probability and statistics Problem solving 4 Real life 9 Shape Glossary for mark schemes 7 Version. 3
Algebra Q Answer Mark Comments (a) 5x 0 (= 35) x = 7 5x = 45 x = 7 + 9 A ft ft for M0 or M0 (b) 9y = 3y or 6y 9y (= 3y) 3 (= ) or 3 (= ) 4 A ft ft for M0 or M0 with only one rearrangement error (a) < x 6 B (b),, 3, 4, 5, 6 B B For 5 correct and missing B For 6 correct and incorrect B For x < 7 B0 For or more errors,, 3, 4, 5 B,, 3, 4, 5, 6, 7 B, 3, 4, 5, 6, 7 B0 3 y = 3x + 6 B3 oe B y = 3x ± c or 3x + 6 B Indication that gradient is 6 or 3 or y = mx + 6 4 Version.
AQA GCSE MATHEMATICS TOPIC TESTS HIGHER TIER MARK SCHEMES Q Answer Mark Comments 4 (x + )(x + 7) B Either order B For (x + a)(x + b) where a + b = 9 or ab = ± 4 5 8x + 4y (= + 7y) x + y = + 7y 4 8x = + 7y 4y 8x = + 3y x = + 7y 4 y x = + 3y A ft ft M0 or M0 and only one error 8 in expansion or rearrangement SC + 3y 8 6 6x + y = 3 and 6x 0y = 4 or 0x + 0y = 5 and x 0y = 8 Either x =.5 or y = 0.5 Substituting their x or y into any of the linear equations and solving for the other variable, or balances again to eliminate and solve the other variable A dep Condone poor arithmetic if one coefficient is balanced 33, Condone poor arithmetic and rearrangement errors if the intention to solve is clear Either y = 0.5 or x =.5 A oe SC If T&I used and both answers correct Version. 5
Q Answer Mark Comments 7 Alternative method abx + a x + b x + ab or ab = 0 Identifies and 0 or and 5 9 or 0 A 9 and 0 A Correct answer gets all 4 marks Alternative method (x + 0)(0x + ) (x + 5)(5x + ) 0x + 00x + x + 0 0x + 4x + 5x + 0 9 or 0 A 9 and 0 A Correct answer gets all 4 marks 6 Version.
AQA GCSE MATHEMATICS TOPIC TESTS HIGHER TIER MARK SCHEMES Number Q Answer Mark Comments (a) 5 9 45 A oe fraction 4 Bft Correctly changes their improper fraction to a mixed number (b) Yes with correct comparison 00 99 and 0 0 B oe 45 0. or 0.454 ( ) or 0.455 and 0.45 45.4 % or 45.5% and 45% 00 99 > 0 0 9 5 or < 0 oe implies Yes. or 0% B 57. 57 0 00 470 A Version. 7
Q Answer Mark Comments 3 Alternative method 3 5 6 (= ) oe or seen 4 8 8 8 45 (litres) = their 8 5 45 their 5 (= 9) Their 5 cannot be or 7 A SC 60 Alternative method 6 oe Diagram with and indicated 8 8 45 identified between 8 and 8 6 Each section = 9 7 A SC 60 Alternative method 3 x 3x + 45 = oe 8 8 x = 360 = 6x oe 360 = 5x 7 A SC 60 4(a) (0).0046 B 4(b) 0. 0 3 80 000 ( ) 900 or 00 or 8 0 4 9 0 or 3. 8 0 9 or other correct equivalent expression (.0) 0 A 8 Version.
AQA GCSE MATHEMATICS TOPIC TESTS HIGHER TIER MARK SCHEMES Q Answer Mark Comments 5(a) 3 or 64 or ( ) 4 or 6 or ( ) 6 8 A 5(b) 7 7 7 or 7 7 or 7 49 3 7 A 5(c) Alternative method ( 6 ) + 6 + 6 + ( ) oe Any expansion with 4 correct terms implied 6 + 7 + 7 + A oe eg 36 + 7 + 44 8 + A ft ft 8 + their (a) for term Alternative method ( 6 ) ( + ) 6( + + ) A 8 + A ft Version. 9
Q Answer Mark Comments 6 9 = 3 or ( 7) = B 8 3 3 8 or 3 8 = = 83 or or 3 8 or 3 8 or = or oe implies 3 8 = A All three numbers correct evaluated and in correct order ( 7) A 3 8 9 0 Version.
AQA GCSE MATHEMATICS TOPIC TESTS HIGHER TIER MARK SCHEMES Probability and statistics Q Answer Mark Comments (a) 4 + 3 + 5 + or 0 5 oe 4 A (b) 4 + 5 or 9 4 00 or 0 0 5 or 00 or 5 0 4 + 5 0 00 dep oe their 0 + their 5 45 A (c) 3 out of or out of 8 or 3 or 8 oe 3 : or : 8 3 out of and out of 8 3 or and 8 or 4 or 5% or 0.5 A oe 3 : and : 8 All answers must be correct States the same Q ft Strand (iii) Must see a correct comparison from their relative frequencies dependent on SC For 0 3 and 0 and states boys larger oe Version.
Q Answer Mark Comments (a) No response section or No mention of websites or No mention of buying music B oe (b) Suitable question B eg Where do you buy music? Suitable response section B eg bookshops, websites, don t buy music Must include both shops and websites (c) Reason involving time or location B eg only Monday, only one morning, only customers asked, only in the shop (d) Complete description including correction of time and location B B Description correcting one problem Accept increased sample size as one of time / location 3 Fully correct labelled pie chart Spain 80 Portugal 90 Turkey 30 Other 60 Tolerance ± B4 B3 Two or three correct sectors and four sectors labelled correctly B3 Fully correct but incomplete or no labels B All angles calculated B Two or three sectors correct but incomplete or no labels B At least one angle calculated in table B One sector drawn an labelled correctly Version.
AQA GCSE MATHEMATICS TOPIC TESTS HIGHER TIER MARK SCHEMES Q Answer Mark Comments 4 B oe 5 B At least one correct pair of probabilities 5 or all top probabilities = 5 4 5 5 or all bottom probabilities = 5 4 4 5 4 4 oe or 5 5 5 May be at the end of tree diagram 8 5 or 0.3 A ft oe ft their tree diagram 5 5 58 (= 90) + 64 (= 354) (64 58) 6 (= ) Their 354 6 dep 58 + their NB 58 5 6 64 + is M 6 59 A Version. 3
Problem solving Q Answer Mark Comments Alternative method 3 5 (= 7) Check diagram y coordinate = 9 A 36 7 0 (= 9) oe eg 6 7 x coordinate = 3 A (9, 3) is A max Alternative method Graph drawn with A at (5, 0) and B at (3, 36) Any rectangles drawn from A and B matching the diagram. x coordinate = 3 y coordinate = 9 A A 4 Version.
AQA GCSE MATHEMATICS TOPIC TESTS HIGHER TIER MARK SCHEMES Q Answer Mark Comments Alternative method Any side chosen for square and squared, eg 0 = 00 Works out 75% of their square and a correct calculation of the circle area, or works out what percentage the circle area is of the square area A method mark gained and correct conclusion based on 75% of their square with their circle Alternative method r length of side of square giving 4r as area r as radius of circle giving πr as area of circle 75% of their square (= 3r ) and correct expression for area of circle with their chosen radius A method mark gained and correct conclusion based on 75% of their square with circle eg π > 3 M A Q A Q M Is for both squares and circle areas attempted with correct numerical values (eg if 0 chosen for side of square, then 5 must be used as radius of circle, or if 4 chosen as radius then 8 is used as side of square) If both square and circle area attempted with one incorrect numerical value (eg if 0 chosen as side of square, then 0 used as radius of circle, or if 4 chosen as radius then 4 used as side of square) This can be awarded even if only awarded Allow π used if a clear comparison, eg π 5 > 3 5 Strand (ii) Do not award if their circle area > square area eg 78.5 > 5 Strand (ii) Do not award if their circle area > square area eg πr > r Version. 5
Q Answer Mark Comments 3 Alternative method 3x (x 5) Condone omission of brackets x + 5 = 7 6 A SC Alternative method 3 x = 7 x 5 3x = + x 6 A SC Alternative method 3 Substitutes a value for x and evaluates correctly as a power of Substitutes a different value for x and evaluates correctly as a power of which is closer to 7 6 A SC 4 π 7 or [43.9, 44] oe 4π π 7 4 or [0.9, ] or π 7 3 or [3.9, 33] π 7 4 3 or [3.9, 3] dep dep oe 7π oe 4π oe π [46.9, 47] A 0.5π + 4 oe SC For [3.4, 3.5] or [30.4, 30.5] SC For [6.4, 6.5] 6 Version.
AQA GCSE MATHEMATICS TOPIC TESTS HIGHER TIER MARK SCHEMES Q Answer Mark Comments 5 4 and 40000 and 00 B B For any correct value of n 0^n, where n > 00, 3000, 40 000, 500 000, 6 000 000 etc 6 Alternative method n( n ) + n( n + ) B This mark is for combining fractions or if fractions dealt with separately, for combining n terms correctly n n n + n + is B0 as incorrect 4 combining of fractions n n n + n + = n B This is for eliminating n and n either by showing by crossing or writing on same line and writing next line without them n n n + n n + = n + n = n B This mark is for cancelling top and bottom n n + = n Alternative method n B This mark is for factorising out a ((n ) + (n + )) common factor n (n + n + ) is B0 4 n B This mark is for combining terms (n) inside bracket correctly n B n is OK Version. 7
Q Answer Mark Comments 7.5 or 3 seen oe : 8 or seen as a scale factor 8 : 8 tan C = or 36 8 EC = or = or EC 8 8.5 or or 8.5 dep oe CE = tan(their 36) 6.5 or 5.5 99 A 6.5 ( ) or 5.5 ( ) (8 + ) their 5.5 or their 99 8 their 6.5 8 their ED 8 + their ED 4 (8 + ) their ED 8 Version.
AQA GCSE MATHEMATICS TOPIC TESTS HIGHER TIER MARK SCHEMES Real life Q Answer Mark Comments (a) 5 B (b) Any correct conversion between miles and km seen eg 5 miles = 8 km 75 8 5 or mile =.6 km or km = 8 5 mile Slower as limit is 8 km A Slower as 46.875 < 50 Alternative method 57 B Driving school A total 0.5 3 ( 47) or 3.45 or 6.5 (3 their 3.45) 47 or 3 47 their 6.5 98.(85) or 99 or 0.(36 ) A Total for B or Price per lesson for A (Driving school) B Q ft Strand (iii) Alternative method ft conclusion based on two values if awarded 57 B Driving school A total 47 3 or 08 Their 08 0.85 98.(85) or 99 A Driving school B total (Driving school) B Q ft Strand (iii) ft conclusion based on two values if awarded Version. 9
Q Answer Mark Comments 3(a) Alternative method Midpoints seen or implied B 5, 5, 5, 35, 45 Their fx 5 5 + 5 + 5 8 + 35 + 45 4 or 5 + 330 + 700 + 735 + 80 or 970 This mark is for the sum of their midpoints frequencies but condone one error 5 5 = 5 5 = 330 5 8 = 700 35 = 735 45 4 = 80 Their fx 80 dep Their 970 80 4.6 ( ) A Accept 5 with working shown 3(b) Alternative method 5 + + 8 or 55 + 4 or 5 5 + + 8 80 00 + 4 80 00 68 ( )(%) or 69 and No A 3. ( )(%) and No Alternative method 5 + + 8 or 55 + 4 or 5 70 00 or 56 80 30 80 or 4 00 55 and 56 and No or 56 is in the 30-40 group so No A 4 and 5 and No 0 Version.
AQA GCSE MATHEMATICS TOPIC TESTS HIGHER TIER MARK SCHEMES Q Answer Mark Comments 4 80 64 (= 304) or AB + 64 = 80 64 cos (C) = 80 their 304 (= 48) cos - 64 (= [36.8, 36 9]) 80 64 their 48 (= 536) 64 80 sin their [36.8, 36 9] (= 536) Their 536 4047 6400 oe [46, 433.5] A Allow 430 with correct working seen 400 B ft ft value seen > 3sf rounded correctly to sf A Is implied by 400 if no incorrect working seen 5 3.5 36000 (= 6000) Answer of 38600 implies this (6000 + 0%) Their 6000 = 90% Implied by division by 90 Their 6000 90 ( 00) or 400 40 000 A Version.
Shape Q Answer Mark Comments (a) 5 and 43 or 65 and 849 or 474 5 + 43 or 65 + 849 or 474 49.7 A Accept 50 with correct working (b) tan chosen 5 tan y = 33 oe tan y = 0.4545 4.4 A Accept 4 with correct working π or [75.3, 75.4] oe 4π 35 π (+ 4) 360 or [8., 8.3] dep oe 9π (+ 4) [5., 5.3] A Do not award if π = 3 used Version.
AQA GCSE MATHEMATICS TOPIC TESTS HIGHER TIER MARK SCHEMES Q Answer Mark Comments 3 Alternative method (x =) 6 + 8 6 8 cos 75 oe [75., 75.] A [8.66, 8.7] A Alternative method XB = 7.77 and XC = 3.99 A X B C ( 7.77 + 3.99 [8.66, 8.7] A Alternative method 3 CY = 5.795 or 5.796 or 5.8 and BY = 6.447 A Y B C ( 5.796 + 6.447 [8.66, 8.7] A Version. 3
Q Answer Mark Comments 4(a) 50 B 4(b) 360 50 or 0 or 360 their 50 360 8 75 0 or 360 8 75 their 0 dep oe OCA = 8 seen or implied or 80 8 75 or 87 oe OCB = 75 8 or 57 seen or implied 80 93 30 or 87 30 57 A 5 5.7 4 or 6.8 Their 6.8 = π diameter dep oe Their 6.8 = π radius their 6.8 π dep Their 6.8 π radius = [9.95, 0] [9.9, 0] A SC For [4.9, 5] 6 w + 40 = 7 May be on diagram (w = ) 3 seen A w = 64 or w = their 3 or third angle = 7 or w + t + 7 = 80 oe 80 7 64 or 80 7 their 3 oe 08 64 44 A 4 Version.
AQA GCSE MATHEMATICS TOPIC TESTS HIGHER TIER MARK SCHEMES Glossary for mark schemes GCSE examinations are marked in such a way as to award positive achievement wherever possible. Thus, for GCSE Mathematics papers, marks are awarded under various categories. M A B ft SC M dep B dep oe Method marks are awarded for a correct method which could lead to a correct answer. Accuracy marks are awarded when following on from a correct method. It is not necessary to always see the method. This can be implied. Marks awarded independent of method. Follow through marks. Marks awarded for correct working following a mistake in an earlier step. Special case. Marks awarded within the scheme for a common misinterpretation which has some mathematical worth. A method mark dependent on a previous method mark being awarded. A mark that can only be awarded if a previous independent mark has been awarded. Or equivalent. Accept answers that are equivalent. eg, accept 0.5 as well as [a, b] Accept values between a and b inclusive. 3.4 Allow answers which begin 3.4 eg 3.4, 3.4, 3.49. Use of brackets It is not necessary to see the bracketed work to award the marks. Version. 5
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