ࡱ>  K~@ ^NbjbjFF ^,,WE0000T|t&"JژFHHHHHH$Rll00,0lFF0,v P4wB2»$r0$Hv0000vll$t@|2@| Question Number Scheme Marks (a) (b) (b) 2 Penalise  EMBED Equation.3   EMBED Equation.3  EMBED Equation.3  or  EMBED Equation.3  or  EMBED Equation.3  Allow  EMBED Equation.3  =  EMBED Equation.3  or 0.25 B1 (1) M1 A1 (2) (3) M1 for understanding that - power means reciprocal  EMBED Equation.3  is M0A0 and -  EMBED Equation.3  is M1A0  (a) (b) (b) EMBED Equation.3   EMBED Equation.3  both ( EMBED Equation.DSMT4  is OK)  EMBED Equation.3   M1 A1 (2) M1 A1 A1 (3) (5) In (a) and (b) M1 is for a correct power of  EMBED Equation.3 in at least one term. This could be 6 in (a) or  EMBED Equation.3  in (b) 1st A1 for one correct term in EMBED Equation.3 :  EMBED Equation.3  or  EMBED Equation.3  (or better simplified versions) 2nd A1 for all 3 terms as printed or better in one line. N.B. M1A0A1 is not possible. SC. For integrating their answer to part (a) just allow the M1 if +c is present Question Number Scheme Marks (a) ALT EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  M1 A1 A1 (3) Compare coefficients  EMBED Equation.3  equation for  EMBED Equation.3   EMBED Equation.3  AND  EMBED Equation.3   EMBED Equation.3   M1 A1 A1 (3)  (b) (a) (b)  EMBED Equation.3  (follow through their a and b from (a))  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  ( EMBED Equation.3  OK)  M1 A1 A1 (3) (6) M1 for  EMBED Equation.3  or an equation for  EMBED Equation.3 (allow sign error  EMBED Equation.3 4 or  EMBED Equation.3 8 on ALT) 1stA1 for  EMBED Equation.3  can ignore -29 or for stating  EMBED Equation.3  and an equation for  EMBED Equation.3  2nd A1 for  EMBED Equation.3  Note M1A0 A1 is possible for  EMBED Equation.3  N.B. On EPEN these marks are called B1M1A1 but apply them as M1A1A1 M1 for a full method leading to  EMBED Equation.3  or  EMBED Equation.3  (condone x 4 =  EMBED Equation.3 ) N.B.  EMBED Equation.DSMT4  is M0A0A0 A1 for  EMBED Equation.3  and A1 for  EMBED Equation.3  N.B. M1 and A1 for c do not need  EMBED Equation.3  (so this is a special case for the formula method) but  EMBED Equation.3  must be present for the d mark) Note Use of formula that ends with  EMBED Equation.3  scores M1 A1 A0 (but must be EMBED Equation.3 ) i.e. only penalise non-integers by one mark.  Question Number Scheme Marks (a) (b) (a) (b) Shape Points   -2 and 4 maxB1 B1 (2) M1 A1 A1 (3) (5)Marks for shape: graphs must have curved sides and round top. Dont penalise twice. (If both graphs are really straight lines then penalise B0 in part (a) only) 1st B1 for  EMBED Equation.3  shape through (0, 0) and ( EMBED Equation.3  where  EMBED Equation.3 >0) 2nd B1 for max at (3, 15) and 6 labelled or (6, 0) seen Condone (15,3) if 3 and 15 are correct on axes. Similarly (5,1) in (b) M1 for  EMBED Equation.3  shape NOT through (0, 0) but must cut x-axis twice. 1st A1 for -2 and 4 labelled or (-2, 0) and (4, 0) seen 2nd A1 for max at (1, 5). Must be clearly in 1st quadrant  5.   EMBED Equation.3  and sub  EMBED Equation.3   EMBED Equation.3  i.e.  EMBED Equation.3  (  EMBED Equation.3  or  EMBED Equation.3  (o.e.) (both)  EMBED Equation.3  EMBED Equation.3  ;  EMBED Equation.3   EMBED Equation.3  (o.e)M1 A1 M1 A1 M1A1 f.t. (6) 1st M1 Attempt to sub leading to equation in 1 variable Condone sign error such as  EMBED Equation.3 , x = -(1+2y) penalise 1st A1 only 1st A1 Correct 3TQ (condone = 0 missing) 2nd M1 Attempt to solve 3TQ leading to 2 values for y. 2nd A1 Condone mislabelling x = for y = but then M0A0 in part (c). 3rd M1 Attempt to find at least one  EMBED Equation.3 value (must use a correct equation) 3rd A1 f.t. f.t. only in  EMBED Equation.3  (3sf if not exact) Both values. N.B False squaring. (e.g.  EMBED Equation.3 ) can only score the last 2 marks. EMBED Equation.3   Question Number Scheme Marks 6. (a) (b) ( c ) (a) (b) (c )  EMBED Equation.3  >  EMBED Equation.3   EMBED Equation.3  > 2  EMBED Equation.3  >  EMBED Equation.3  or 0.25 or  EMBED Equation.3   EMBED Equation.3  (> 0) Critical values  EMBED Equation.3 , 3 (both)  Choosing outside region x > 3 or  EMBED Equation.3  <  EMBED Equation.3   EMBED Equation.3 >3 or  EMBED Equation.3  <  EMBED Equation.3 <  EMBED Equation.3  [ EMBED Equation.DSMT4  is OK] ____________________________________________________________________ M1 Multiply out and collect terms (allow one slip and allow use of = here) 1st M1 Attempting to factorise 3TQ  EMBED Equation.3  2nd M1 Choosing the outside region 2nd A1 f.t. f.t. their critical values N.B.(x>3, x >  EMBED Equation.3  is M0A0) f.t. their answers to (a) and (b) 1st B1 a correct f.t. leading to an infinite region 2nd B1 a correct f.t. leading to a finite region Penalise  EMBED Equation.3  or  EMBED Equation.3  once only at first offence. For p < x < q where p > q penalise the final A1 in (b) . e.g. (a) (b) (c) Mark x > EMBED Equation.3   EMBED Equation.3  EMBED Equation.3  x >3, x >  EMBED Equation.3  x > 3 B1 B0M1 A1 (2) M1 A1 M1 A1 f.t. (4) B1f.t. B1f.t. (2) (8)  Question Number Scheme Marks 7. (a) (b) (a) (b)  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  use  EMBED Equation.3  and  EMBED Equation.3 :  EMBED Equation.3   EMBED Equation.3  c = - 12 So  EMBED Equation.3  EMBED Equation.3  -12 ____________________________________________________________________ M1 Attempt to multiply out  EMBED Equation.3 . Must have 3 or 4 terms, allow one sign error A1 cso Fully correct solution to printed answer. Penalise invisible brackets or wrong working 1st M1 Some correct integration:  EMBED Equation.3   EMBED Equation.3  A1 At least 2 correct unsimplified terms Ignore +  EMBED Equation.3  A2 All 3 terms correct (unsimplified) 2nd M1 Use of  EMBED Equation.3  and  EMBED Equation.3  to find  EMBED Equation.3 . No +  EMBED Equation.3  is M0. A1c.s.o. for -12. (o.e.) Award this mark if  EMBED Equation.3  " stated i.e. not as part of an expression for y A1f.t. for 3 simplified  EMBED Equation.3 terms with  EMBED Equation.3  and a numerical value for c. Follow through their value of c but it must be a number. M1 A1 c.s.o. (2) M1 A2/1/0 M1 A1 c.s..o. A1f.t. (6) (8)  Question Number Scheme Marks  (a) (b) (c ) ALT (a) (b) (c ) MR  EMBED Equation.3  or  EMBED Equation.DSMT4   EMBED Equation.3  (o.e.) (condone 3 terms with integer coefficients e.g. 3y+21=x) Equation of  EMBED Equation.3  is:  EMBED Equation.3  (o.e.) Solving  EMBED Equation.3  and  EMBED Equation.3  :  EMBED Equation.3   EMBED Equation.3  is point where  EMBED Equation.3 ,  EMBED Equation.3   EMBED Equation.3  or  EMBED Equation.3   EMBED Equation.3  or  EMBED Equation.3  ( EMBED Equation.3  is  EMBED Equation.3 ) C is (0, -7) or OC = 7 Area of  EMBED Equation.3 ,  EMBED Equation.3  or  EMBED Equation.DSMT4  By Integration: M1 for  EMBED Equation.DSMT4 , B1 ft for correct integration (follow through their  EMBED Equation.3 ) , then A1cao.  M1 A1 A1 (3) B1 M1 A1 A1f.t. ( EMBED Equation.3  (4) B1f.t. M1 A1c.a.o. (3) (10)  M1 for full method to find equation of  EMBED Equation.3  1stA1 any unsimplified form M1 Attempt to solve two linear equations leading to linear equation in one variable 2nd A1 f.t. only f.t. their  EMBED Equation.3  or  EMBED Equation.3  in  EMBED Equation.3  N.B. A fully correct solution by drawing, or correct answer with no working can score all the marks in part (b), but a partially correct solution by drawing only scores the first B1. B1f.t. Either a correct OC or f.t. from their  EMBED Equation.3  M1 for correct attempt in letters or symbols for  EMBED Equation.3  A1 c.a.o.  EMBED Equation.3  scores M1 A0 (x-axis for y-axis) Get C = (21, 0) Area of  EMBED Equation.3 = 63 (B0M1A0) Question Number Scheme Marks  9 (a) (b) (c ) (d) (e) (a) (b) (c) (d) (e)   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  EMBED Equation.3  either  EMBED Equation.3   EMBED Equation.3  ( EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  = 109  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  (*)  EMBED Equation.3   EMBED Equation.3  or 100  EMBED Equation.3  < 0  EMBED Equation.3  not sensible  B1 M1 dM1 A1 c.s.o (4) M1 A1 (2) M1 A1 A1 c.s.o (3) M1 A2/1/0 (3) B1 f.t. (1) (13) B1 requires at least 3 terms, must include first and last terms, an adjacent term and dots! There must be + signs for the B1 (or at least implied see snippet 9D) 1st M1 for reversing series. Must be arithmetic with a, n and d or l. (+ signs not essential here) 2nd dM1 for adding, must have 2S and be a genuine attempt. Either line is sufficient. Dependent on 1st M1 (NB Allow first 3 marks for use of l for last term but as given for final mark ) M1 for using a = 149 and d =  EMBED Equation.3  in  EMBED Equation.3 formula. M1 for using their  EMBED Equation.3 in  EMBED Equation.3  A1 any correct expression A1cso for putting  EMBED Equation.3 =5000 and simplifying to given expression. No wrong work NB EPEN has B1M1A1 here but apply marks as M1A1A1 as in scheme M1 Attempt to solve leading to  EMBED Equation.3  A2/1/0 Give A1A0 for 1 correct value and A1A1 for both correct B1 f.t. Must mention 100 and state  EMBED Equation.3  < 0 (or loan paid or equivalent) If giving f.t. then must have  EMBED Equation.3 . Question Number Scheme Marks  10 (a) (b) (c) (b) (c) MR  EMBED Equation.3   EMBED Equation.3  ( 9 36 + 27=0 is OK)  EMBED Equation.3  ( EMBED Equation.3  When x = 3,  EMBED Equation.3  Equation of tangent:  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  gives  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  or 5 5  EMBED Equation.3   EMBED Equation.3  or  EMBED Equation.3  ____________________________________________________________________ 1st M1 some correct differentiation ( EMBED Equation.3  for one term) 1st A1 correct unsimplified (all 3 terms) 2nd M1 substituting  EMBED Equation.3  in their  EMBED Equation.3  clear evidence 3rd M1 using their  EMBED Equation.3  to find tangent at  EMBED Equation.3 .The m must be from their  EMBED Equation.3 at EMBED Equation.3  Use of  EMBED Equation.3  here scores M0A0 but Could get all 3 Ms in Part (c). 1st M1 forming a correct equation their  EMBED Equation.3 = gradient of their tangent 2nd M1 for solving a quadratic based on their  EMBED Equation.3  leading to x = ... The quadratic could be simply  EMBED Equation.3 =0. 3rd M1 for using their x value (obtained from their quadratic) in y to obtain y coordinate. Must have one of the other two M marks to score this. For misreading (0, 3) for (3, 0) award B0 and then M1A1 as in scheme. Then allow all M marks but no A ft. 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