PiXL AQA Style Paper 2H (March 2017) Mark Scheme

Transcription

1 PiXL AQA Style Paper H (March 07) Mark Scheme 80n cm π 4 B Accept any clear indication (= 5.08) (= 5.8) (= 5.6) or = (= 5.8) (= 5.6) Largest number identified as representing the best value. Multibuy box ticked (= 0.97) 375 (6 330) (= 0.89) (= 0.94) or = (= 0.89) (= 0.94) Smallest number identified as representing the best value. Multibuy box ticked = = 64.0 Smallest number identified as representing the best value. Multibuy box ticked Multibuy box ticked with no working Alternative method (fruit juice per penny) A Alternative method (cost per ml) A Alternative method 3 (cost for 330ml) A Evidence of division to compare the amount of fruit juice for a common cost. All three amounts must be correct here. Evidence of division to compare the cost for a common amount of fruit juice. All three amounts must be correct here. Both amounts must be correct here. If the cost of one 330ml can is found as 6.5 pence in Multibuy option; this negates the need to compare the Standard option. Award up to full marks if pounds are used instead of pence or litres instead of millilitres; likewise, if 490ml is correctly used instead of 330ml in alternative method 3. M0 A0 B0

2 Rhydtalog Perpendicular bisector of line from Rhydtalog to Minera constructed. Construction arcs must be seen Circle (or arc) radius 6cm (allow ±mm tolerance) drawn with centre at Minera. 6 (a) Segment shaded in. Minera Schools are advised to check the relationship between Rhydtalog and the segment after printing papers. If the page is reproduced at full size, Rhydtalog and Minera are just over 0cm apart; if the A4 page is reduced to A5, they are just over 7cm apart. In either case, correctly drawn, the arc centred at Minera and the bisector will intersect to produce a segment that does not include Rhydtalog. An overlay is provided for use with questions 6 (a) and 6 (b) at the end of this mark scheme. Rhydtalog 7 Bearing of 7 constructed at Rhydtalog (allow ± tolerance). Llanfynydd 6 (b) Intersection with line constructed due North from Minera indicated (accept any clear indication) Minera North line from Minera is not sufficient for second mark; must have intersection with their 7 An overlay is provided for use with questions 6 (a) and 6 (b) at the end of this mark scheme. 6 (c) km = cm (may reach : ) : A Must be simplified

3 7 Alternative method (finds numbers of red and yellow) = 400 oe 0. their 400 (= 88) Divides their 400 "their in ratio : (5 to 68 and 84) 68 A Any reasonable method Alternative method (finds P(Green) first) = 400 oe ( ) (= 0.63) Divides their 0.63 in ratio : and then their A Any reasonable method (8 + 7) 4 (= 30) Correct method for area of trapezium their 30 (= 660) Correct method for volume of prism their (= ) Correct method for value of gold A A Must be correct and rounded to 3SF

4 y Either any enlargement scale factor or any enlargement centre ( 3, ). 0 (a) 4 3 R Q x Shape R; check all vertices correct y 7 0 (b) S R Any translation of R. Q x Shape S; check all vertices correct Enlargement 0 (c) Scale factor Check not negative. Centre of enlargement ( 7, ) ( x a) y = b x x + Multiplies to eliminate fraction ( y ) = b ay + Terms in x separated and factorised b ay x = A y +

5 60 (a) Fr eq ue nc 40 y de nsi ty 0 Width of bar correct (from 4.5kg to 5.3kg) Mass of a baby (kg) Height of bar correct (frequency density = 30) (b) 3.6 < median < 4.0; Total frequency for.0 < mass < 3.6 = 4 + = 35 Median = Alternative method (50 babies below median) ( ) 3.9 A 3.6 < median < 4.0; Total frequency for 4.0 < mass < 5.3 = + 4 = 45 May be implied Alternative method (50 babies above median) May be implied Median = ( ) 3.9 A 3 ( x x )( x + ) x 3 x Alternative method 5x A Three terms correct award A. ( x + 3 )( x 7x 4 ) x 3 x Alternative method 5x A Three terms correct award A. Can award up to full marks for any other valid method (comparing coefficients, etc) if seen.

6 4 (a) Both of The runner is slowing down after seconds The runner s maximum speed is 0.6 metres per second ticked and The runner is running backwards after seconds. The runner s average speed is more than 0 metres per second left blank Accept any clear indication (eg T or F for true and false, etc). 4 (b) Alternative method (division into triangle and three trapezia, width = ) Recognises that area under curve gives distance covered 7 + ( ) + ( ) + (0. + 0) 3.8 A May be implied could be a statement, or. any attempt to find an area. Should see division into triangle/trapezia and at least one correct area calculation. All velocities used should be correct Alternative method (division into triangle and trapezium, width = ) Recognises that area under curve gives distance covered May be implied could be a statement, or. any attempt to find an area. Should see division into triangle/trapezium ( ) and at least one correct area calculation. All velocities used should be correct 3. A Recognises that area under curve gives distance covered ( ) Alternative method 3 (trapezium rule, four strips) 3.8 A Can award up to full marks for any valid methods. May be implied could be a statement, or. any attempt to find an area. Allow for minor errors if intention is clear; must see at start and doubling of values used between t = 0 and t = 4 3., 3.8 or any other answer seen without working M0 M0 A0

7 5 (a) 5 (b) Each value ± 7 A On average, members of the cricket club are younger Wider range of ages at cricket club or more consistent ages at football club Allow follow through from ; value in range 5 (from 30 5) to 9 (from 3 3). Must see both medians stated (8± years for football club, 6±0 years for cricket club) Comparison must be made using interquartile range (follow-through from 5 (a) for football club, 40 = 9 for cricket club) B0 for any comparison that doesn t give evidence of use of data; values used to make comparison must be seen. B0 for comparison of spread using range (maximum minimum). States that last two digits are 5 and 0; 4 3 ( ) or 4! arrangements of remaining digits. 4 Accept any valid multiplicative method to find number of arrangements of digits,, 3 and 4 at start of number. 4 stated without justification M0 Strategy that relies on excessive listing (eg lengthy list of numbers without any multiplicative method) M0 7 Angle BDA is 90 Seen or implied Angle DAB is 80 5 (= 65 ) Seen or implied sin their 65 = BD AB or sin their 65 = BD 8 7.5cm A Can award up to full marks for use of cosabd = cos5, etc. Allow follow through from incorrect value for angle DAB.

8 8 7 5 oe 490 Allow other methods for finding HCF, including listing factors, multiplications, etc, if 490 is found. Any other common factor of and 8 80 ( ), award one mark (common factors are, 5, 7, 0, 4, 35, 49, 70, 98, 45) Award if 490 is stated without working B0 9 (a) : 9 9 (b) Scale factors APS to AQS and ABC (ie :.5 and : ) seen One area multiplier seen; Either APS to AQR; :.5 or :.5, or ratio 4 : 9 or APS to ABC; : 4 or : or any correct ratio for two shapes from APS, PQSR and QBCR; ratio of areas of APS : PQSR is :.5, or 4 : 5. ratio of areas of APS : QBCR is :.75 or 4 : 7. ratio of areas of PQRS : QBCR is.5 :.75 or 5 : 7 Ratio of areas of APS, PQRS and QBCS now given in any unsimplified form; :.5 :.75 4 : 5 : 7 A May be implied At least one correct ratio or multiplier must be given.

9 0 (a) 4 3 π 63 or 3 π 63 (= ) 4 or 3 π 53 or 3 π 53 (= 6.833) their their A oe. Correct method for volume of one hemisphere seen. Accept or 90.7 (π = 3.4) or or 90.6 (π button used) 0 (b) π 6 6 (= ) their their A Accept 8 or 8.09 b a (a) A is at ( 80, 0 ) B is at ( 70, ) y Any translation of original curve, in direction parallel to y axis. O x (b) Completely correct curve. Check locations of maximum and minimum points, and start and finish of curve. Co-ordinates or labels on axes do not need to be given but, if they are, they must be correct for award of second mark. Translation in positive direction parallel to y axis. Translation parallel to x axis. Any change in amplitude or orientation (eg reflection) of original curve. B0 B0 B0 B0 B0

10 Alternative method (finds fg(x) first) 3 (a) fg(x) = (x + 3) or fg(x) = x + 6x + 8 oe 63 A Alternative method (finds g(5) first) g(5) = (b) fg(x) = (x + 3) May be implied in 0 (a) Minimum value is, when x = 3 Accept ( 3, ) Alternative method (uses completed square form fg(x) = (x + 3) ) 3 (c) x + 3 = ± Must get past (x + 3) = and include ± x = or x = 4 A Both must appear Alternative method (factorises fg(x) = x + 6x + 8) (x + )(x + 4) = 0 Both factors correct x = or x = 4 A Both must appear Alternative method 3 (formula to solve fg(x) = x + 6x + 8 = 0) 6 ± x = x = or x = 4 A Both must appear Tolerate one sign error but only if x + 6x + 8 is seen correct elsewhere.

11 Overlay for questions 6 (a) and 6 (b). Use where the question paper has been reproduced at full size. Rhydtalog 7 Llanfynydd 5 9 North 6. cm 5.8 cm Minera Scale: cm represent km This overlay is provided for reproduction on acetate, or other semi-transparent media, for use when marking questions 6 (a) and 6 (b), and is designed to be used where the question paper is reproduced at full size. It is provided subject to the limitations of the printing processes available to schools and, before use, schools are advised to check all measurements after papers have been printed.

12 Overlay for questions 6 (a) and 6 (b). Use where the question paper has been reproduced at reduced size (scaled from A4 to A5). Rhydtalog 7 Llanfynydd 5 Minera 9 North Scale: cm represent km 6. cm 5.8 cm This overlay is provided for reproduction on acetate, or other semi-transparent media, for use when marking questions 6 (a) and 6 (b), and is designed to be used where the question paper and this overlay is reproduced at reduced size. It is provided subject to the limitations of the printing processes available to schools and, before use, schools are advised to check all measurements after papers have been printed.