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1 Question Answer Marks Guidance Question (i) B for or B for 9 40 or SC for 49 and B for 6 5 [] (ii) [] if 0, allow for three terms correct in for soi or for 7 6 soi or for 6 oe (i) 6 8 B for 6 or B for 49 + found in expansion (may be in a grid) and B for 8 if B0, allow for at least three terms correct in [] the correct answer obtained then spoilt earns SC only (ii) 4 for 50 5 or 00 0 or [] or 48 seen

2 V r ( a b) oe www as final answer for dealing correctly with [] and for dealing correctly with π(a + b), ft and for correctly finding square root, ft their r = ; square root symbol must extend below the fraction line M0 if triple-decker fraction, at the stage where it happens, then ft; condone missing bracket at rh end M0 if ±... or r >... for M, final answer must be correct 4 (i) 5 5 oe or k = 7/ oe [] for 5 = 5 or 5 5 soi M0 for just answer of 5 with no reference to 5 4 (ii) attempting to multiply numerator and denominator of fraction by 5 some cands are incorporating the into the fraction. The s are available even if this is done wrongly or if is also multiplied by 5 denominator = 9 soi must be obtained correctly, but independent of first eg for denominator of 9 with a minus sign in front of whole expression or with attempt to change signs in numerator 8 5 A []

3 5 (i) 9 www oe as final answer for or soi [] 5 (ii) www as final answer for attempt to multiply numerator and denominator by 7 5 condone for marks [] B for each of numerator and denominator correct (must be simplified) eg M0B if denominator correctly rationalised to 44 but numerator not multiplied 6 [ b ] a c oe www M for [ b ] a c soi eg M for [ b ] a c [] or for other [ b ] ka c or [ b ] a kc oe and for correctly taking the square root of their b, including the ± sign; allow for a triple-decker or quadruple-decker fraction or decimals.5a eg, if no recovery later c square root must extend below the fraction line

4 Question er Marks Guidance 7 (i) as final answer B for and B for or mark one scheme or other, but not a or mixture, to advantage of candidate M for or more terms correct of or for terms correct eg M for [] 7 (ii) 5 6 isw condone 0 6 for marks eg isw for [] for 54 6 or V r l r for correctly getting non- l r terms on other side[m0 for triple decker fraction] may be done in several steps, if so, condone omission of brackets in eg 9V = π r 4 l r if they recover if not, do not give st [but can earn the nd ] V r l r V l r r oe or ft; for squaring correctly oe or ft; for getting l term as subject for combined steps, allow credit for correct process where possible; eg π r 4 l as the term on one side [ l ] V r r oe. or ft; mark final answer; for finding square root ( and dealing correctly with coefficient of l term if needed at this stage); condone ± etc For M4, the final expression must be totally correct, [condoning omission of l and insertion of ±] 6 9V r eg M4 for r

5 9 (i) 7 for 48 = 4 or 7 = 9 (ii) www isw B for 7 [B0 for 7 wrongly obtained] and B for 0 +5 or B for one term of numerator correct; if B0, then for attempt to multiply num and denom by + 0 (i) www (ii) 4 0 answer www as final for 4/6 or for 48 = or 4 or 7 = or 08 = or for M for terms correct of soi, for terms correct 5 (i) 9 for 5 or 4 seen (ii) 6 www for attempt to multiply num. and denom. by + and for denom. 7 or 9 soi from denom. mult by + 5

6 (i) 5 or 5 + ( ) or 5 or a = 5, b =, c = ; for attempt to multiply numerator and denominator by 5 (ii) 7 isw www for 7 and for 7 or for correct terms from or or o.e. eg using 6 or M for or or or o.e.; for but not other equivs 5 [ ] [ v = ] ± E m www M for v = E m or for E [ v = ][ ± ] or m for a correct constructive first step and for v= [ ±] k ft their v = k; if M0 then SC for E/ ½ m or E/m etc 4 t = [ ± ] s a o. s B for t omitted or t = o. a for correct constructive first step in rearrangement and (indep) for finding sq rt of their t

7 5 (i) or 8 for 7 or 5 seen (ii) 5 for attempt to multiply num. and denom. by 5 and (dep) for denom or 4 5 soi or for numerator V [] r = [ ± ] o.e. double-decke π h V V for r = or r = o.e. or π h π h for correct constructive first step or for r = k ft their r = k 7 (i) (ii) + or + 6 mixture of these or for 8= or 50 = 5 soi B for 6 50 or other correct a b for mult num and denom by 6+ and for denom = or 5