PiXL AQA Style Paper 1H (March 2017) Mark Scheme

Transcription

1 PiXL AQA Style Paper 1H (March 017) Mark Scheme Q Answer Mark Comments 1 y kilometres (a) Must be simplified and expressed as a mixed number for. (b) Reaches Must be simplified for. 6 (a) n seen n + May have any constant to follow, or just n on its own. 6 (b) Either n + = 100 gives non integer value of n (no need to state 48.) or all values in the sequence (, 7, 9, 11, etc) are odd. Janet is incorrect box ticked Janet is incorrect box ticked with no justification M0 B0

2 7 (a) Interior angle in pentagon is their (= 4 ) (180 their 4 ) 6 Working not required. Angle must be correct for award of. 7 (b) their their States that TSP and PSR should add to Angela is incorrect box ticked 180. Notation not required for ; look for working out on diagram. Angela is incorrect box ticked with no justification If their their 6 = 180, followed by Angela is correct M0 B0 B0 8 Discounts all even numbers as divisible by, and discounts 01 as divisible by. Discounts 01 and 019 with reason (sum of digits is a multiple of, or division of either by ) 011 and 017 Both required for final. May use sum of digits to show that 01 and 019 are divisible by, or sight of any integer multiplications (not including 1 N) that give 01 and 019, for second mark. 671 = = = = = 019 (note: 67 is prime) If all other integers are correctly eliminated, no further justification is required in stating that 011 and 017, as the only two integers that remain, must both be prime. 9 (a) Tolerate rounding to 1.01 or 1.01; not (b) 17.8 No rounding here 9 (c) 10 0 Looking for , but allow long multiplication, or other methods.

3 10 (a) 10 (b) Valid attempt to divide 0 in ratio : Must see at least 0 their their their 48 or their Accept 100 but not 90 1 Valid attempt at finding FH Must reach at least + 4 = FG FH = cm Valid attempt at finding EF Must reach at least 1 their = EF their 1cm + cm + 4cm + 1 cm cm If cm and 1cm appear without working, can still award first two method marks (treat as B marks for recall/use of appropriate Pythagorean triples) 1 Money Maker % of 800 = (half of 80) = 40 % of 840 = (half of 84) = 4 % of 88 = (half of 88.0) = = Must be correct Cash Saver (% + % + % + 10%) = 16% 16% of 800 = (= 18) Cash saver box ticked Money Maker box ticked with no justification Allow slip-ups in individual values for if method is correct. If candidate successfully calculates 1.0 = (or (1 1 0 ) = ) and observes that this is less than 1.16 (= marks without explicit reference to 800 ), can award up to full M0 A0 M0 B0 14 and 1 1 Both must be indicated. 1 < x <

4 16 (a) m 8 4 m or m m or m m m 6 Can allow sight of correct cancelling on fraction for. 16 (b) 6x 10x + 9x 1 6x x 1 Terms in any order. Do not accept 1x 17 (a) 9π cm 17 (b) Circumference of complete circle is 6π May be implied in next. Sight of either 6 + 6π or 6 + their 6π 6 + π or ( + π) Do not accept attempt to change 6 + π to a decimal. Even if 6 + π or ( + π) is correct, penalise subsequent working to 1.4, etc. Must attempt to add length of straight line to arc length A0

5 Either (a) or + 7 or OA + OB or AO + OB Must be given as a column vector Either OB + AB or OA + OB Notation not crucial if intention is clear. May be implied by next mark. Look for indications of intent or method on diagram. 18 (b) Either + their 7 or + their 7 9 Must be given as a column vector or = 1.8 seen seen with statement that this is not in standard form Statement that this is not in standard form may be implied by final. Allow rounding to n = 1. or 90n =1 or 99n =1.1 n = or n = 990

6 1 (a) ( 1, 0 ) Check for minus sign Alternative method 1 (substitutes y = x 4 into x + y = 1) x + (x 4) = 1 Reaches x 16x + = 0 Solves to obtain x = or x = 1 1 (b) Substitutes their or their 1 into y = x 4 Q (, ) R ( 1, ) Accept 18 for y co-ordinate; accept decimal equivalents for either. y + 4 Alternative method (substitutes x = + y = 1 y + 4 into x + y = 1) Reaches y + 8y 6 = 0 Allow 4 y + y 9 = 0 Solves to obtain y = or y = Substitutes their or their y + 4 into x = Q (, ) R ( 1, ) Accept 18 for y co-ordinate; accept decimal equivalents for either.

7 First attempt Second attempt Third attempt Shape of tree diagram; should be no branches after a pass, two after every fail. 0.6 pass 0.6 pass Branches should go to three attempts after first two fails; B0 here if only two or greater than three attempts appear. (a) 0.4 fail 0.4 fail pass fail Headings Second attempt and Third attempt not required for this. All pass and fail branches labelled with correct probabilities. Branches with 1 for pass and 0 for fail could potentially appear following a pass branch for first mark ignore unless they clearly contradict a correct answer. Allow equivalent fractions throughout B0 or (b) 0.4 for three fails 1 their 0.4 for a pass Alternative method (including ) At least two alternatives from 0.6 (passes first time) (passes second time) (or ) (passes third time). All three alternatives calculated and added together Alternative method 0.96 (including ) May be one or more incorrect values at this stage; if so, only award this if the previous was also awarded.

8 (a) Chooses 60 and 4 and states that tan4 = 1 tan 60 + tan 4 tan( ) = tan 60 tan 4 or tan 4 + tan 60 tan( ) = tan 4 tan 60 May be implied + 1 tan10 = 1+ or tan10 = (b) tan10 = or tan10 = 1+ ( 1+ ) or tan10 = ( )( 1+ ) 4 + tan10 = Uses conjugate to complete the square on denominator and hence rationalise.. All previous values (including tan4 and tan60 ) must now be correct. tan10 = Allow follow through from incorrect tan60 up to maximum of marks Sight of tan10 on left hand side not required after initial substitution A0 A0