1MA1 Practice papers Set 3: Paper 2H (Regular) mark scheme Version 1.0 Question Working Answer Mark Notes M1 use of cos

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1 1MA1 Practice papers Set : Paper H (Regular) mark scheme Version M1 use of cos = = = 05 M1 cos ("x") = (= 0.87 ) or ("x" =) cos 1 ( ) or M for sin and following correct Pythagoras or M for tan and following correct Pythagoras or correct Pythagoras and then correct use of sine or cosine rule with "1." A1 for ans rounding to 9.1 (9.110 ) 05 M (M n, n ) 5 M1 000 (oe) or 100 or 00 or 100 or 00 seen M1 (dep) ( ) 100 SC B for 15.5 seen ( yrs) 1MA1 Practice Papers: Set Regular (H) mark scheme Version 1.0 This publication may only be reproduced in accordance with Pearson Education Limited copyright policy. 016 Pearson Education Limited.

2 1MA1 Practice papers Set : Paper H (Regular) mark scheme Version 1.0. Angle ACB = 67º x = 180 ( ) 46 with reasons 4 B1 for angle ACB = 67º, could be marked on the diagram M1 for 180 ( ) A1 for x = 46 C1 for vertically opposite angles (or vertically opposite angles) and base angles of an isosceles triangle are equal B1 for angle ACB = 67º, could be marked on the diagram M1 for 180 ( ) A1 for x = 46 C1 for angles on a straight line add up to 180 o and base angles of an isosceles triangle are equal 1MA1 practice paper H (Set ) mark scheme: Version 1.0

3 1MA1 Practice papers Set : Paper H (Regular) mark scheme Version = M1 for oe M1 for 1 oe = A1 for or 0.97(...) oe M1 for or or oe M1 for ' ' + ' ' + ' ' oe A1 for or 0.97(...) oe ,1 1, 1, 1,4 1,5 1,6,1,,,4,5,6,1,,,4,5,6 4 4,1 4, 4, 4,4 4,5 4,6 5 5,1 5, 5, 5,4 5,5 5,6 6 6,1 6, 6, 6,4 6,5 6,6 M1 for probability space oe that can lead to the answer M1 for 1 ' number of 6,6' or ' number of non 6,6' 5 A1 for or 0.97(...) oe 1MA1 practice paper H (Set ) mark scheme: Version 1.0

4 1MA1 Practice papers Set : Paper H (Regular) mark scheme Version P = kr = k 0 P = 0.09 r P = 0.09 r M1 for P = kr (accept any k 0 or 1) M1 (dep) for = k 0 A1 for P = 0.09 r oe 0 r = M for p 0 r = oe, e.g. 0 : r = : P p P = r 0 A1 for P = r oe 0 1MA1 practice paper H (Set ) mark scheme: Version 1.0 4

5 1MA1 Practice papers Set : Paper H (Regular) mark scheme Version x + (x ± 9) < 00 x + x ± 18 < 00 4x ± 18 < 00 4x < 18 (or 18) x < 45.5 (x < 54.5, so width < 45.5) 00 4 = = = = = B1 for x ± 9 oe seen (it could just be on a diagram) or a rectangle with length 9 cm greater than the width M1 for x + (x ± 9) oe A1 for 45.5 B1 for answer of 45 M1 for 00 4 (= 50) M1 for (9 + 9) 4 (= 4.5) A1 for 45.5 B1 for answer of 45 M1 for (= 18) M1 for 18 4 A1 for 45.5 B1 for answer of 45 [SC: B for 45.5 seen from any method] 1MA1 practice paper H (Set ) mark scheme: Version 1.0 5

6 1MA1 Practice papers Set : Paper H (Regular) mark scheme Version = 45 No 4 M1 for or or = with working M1 for ' ' or '0 + 0 ' or ' ' = 100 = = 95 = = 5 = = = 5 M1 for ' ' (= 5 ) C1 for No AND < 60 oe M for (= = 5) M1 for ' 5' C1 for No AND < 60 oe ' 5' = B for correct locus within guidelines (overlay) (B1 for a line drawn parallel to either given line a line passing through the angle outside of the guidelines a line drawn within the guidelines but not passing through angle) 1MA1 practice paper H (Set ) mark scheme: Version 1.0 6

7 1MA1 Practice papers Set : Paper H (Regular) mark scheme Version M1 for 80% or 0.8 seen oe or 464 M1 for M1 for 80% or 0.8 seen oe M1 for or 464 (80 0) 464 (= 580) ( ) = 11.9(078 ) M1 for SA Jupiter SA Earth e.g. ( ) oe, e.g or digits 11. or digits 1 A1 for 11 1 A1 for M1 for (= 1695) or (= 960) M1 (dep) for ( ) 0 1. Rotation, 90 B1 for rotation clockwise centre B1 for 90 clockwise or 70 anticlockwise (1,4) B1 for (1,4) NB Award B0 if more than one transformation given 1MA1 practice paper H (Set ) mark scheme: Version 1.0 7

8 1MA1 Practice papers Set : Paper H (Regular) mark scheme Version (a) 5.5 M1 for (b) M1 for or 900 oe or 5 5 or 9 M1 for correct conversion of units (cm to m ) M1 for writing a correct expression for the perimeter of the square or the rectangle e.g. 4(x + 6) or 10x +0 or for the semiperimeter 15. (a) x + x 8x 15 (b) am 1 r = 5 a M1 for equating the two (semi) perimeters correctly M1 for resolving the fraction e.g. 0x + 10 = 0x + 60 or for rearranging the equation to the form. a = bx + c M1 for 10x + 60 = 10 or 4 = x + 1 or x = 6 M1 Correct expansion of any brackets (condone 1 error) M1 Correct expansion of previos product by remaining bracket (condone 1 error) A1 M1 for 5r ar = am 1 oe (terms in r isolated) M1 for r(5 a) = am 1 A1 1MA1 practice paper H (Set ) mark scheme: Version 1.0 8

9 1MA1 Practice papers Set : Paper H (Regular) mark scheme Version M1 for A1 for 49 C1 for alternate segment theorem and angles on a straight line add up to 180 o alternate segment theorem and angles in a triangle add up to 180 o Appropriate to methods shown M1 for a method to find an angle RAB = 70, ABR = 50, BRA = 60 or TAR = 0 M1 for substitution into sine formula AR sin"50" = 1 sin"60" 1 M1 for use of sine rule to find AR, AR = sin "50" sin"60" (= 10.61) M1 for substitution into cosine formula TR = cos0 (= 7.9) A1 for (a) (i)(ii) (, 0) and (6, 0) (0, 4) B1 for (, 0) and (6, 0) B1 for (0, 4) (b) Drawn curve M1 for a translation in the positive y-direction A1 for curve passing through (, 0), (0, ) and (4, ) 1MA1 practice paper H (Set ) mark scheme: Version 1.0 9

10 1MA1 Practice papers Set : Paper H (Regular) mark scheme Version (a) 11 M1 for tangent drawn at t = M1 (dep) for A1 for 9 14 ft from tangent (b) 66.5 M1 for splitting the area into 4 strips and a method of finding the area of one shape under the graph, e.g. ½ 1 (6 + 6) (= 44) M1 for complete process to find the area under the graph, e.g ½ 1 (8 + 6) (= 17) + ½ 1 ( ) (= 4.75) + + ½ 1 ( ) (= 0.75) [= 66.5] A1 NB Allow for ± 1 when reading the values of the diagram M1 for correct method to establish week 6 population as 100 x oe M1 for forming equation 100 x = 900 M1 for method to solve equation to establish x = M1 for correct method for week population e.g. 100 oe A1 for given as answer dependent on working seen 1MA1 practice paper H (Set ) mark scheme: Version

11 1MA1 Practice papers Set : Paper H (Regular) mark scheme Version 1.0 M1 for realising that population is 4 in weeks M1 for forming the equation 4 = x M1 for method to solve equation to establish x = M1 for correct method for week population e.g. 100 oe A1 for given as answer dependent on working seen M1 for establishing population is of form N = Ab t oe M1 for substituting t = 5, N = 100 gives 100 = Ax 5 M1 for substituting t = 7, N = 900 gives 900 = Ax 7 or 900 = 100x and x = 4 so x = M1 for correct method for week population e.g. 100 oe A1 for given as answer dependent on working seen 1MA1 practice paper H (Set ) mark scheme: Version

12 1MA1 Practice papers Set : Paper H (Regular) mark scheme Version (A =) 0.5 (4 + k ) = k + 4 = (k =) or (k =) ( 6) oe (k =) 10 4 M ( k 4) oe M1 correctly isolating k 5 but don't accept 10 4 followed by A1 Accept ( ) 5 1MA1 practice paper H (Set ) mark scheme: Version 1.0 1

13 National performance data from Results Plus Qu No Spec Paper Session Qu Topic Max score Mean % all ALL A* A B C D E 1 4MA0 1F 105 Q1 Trigonometry H 711 Q07 Compound interest AM1 1F 111 Q19 Angles AM H 111 Q1 Probability AM H 1111 Q17 Direct and indirect proportion MM H 1106 Q09 Bounds AM H 111 Q0 Pythagoras in D H 1006 Q16 Loci MA0 H 111 Q0 Reverse percentages H 1106 Q19 Standard form MA0 H 1406 Q0 Mean, median, mode MB0 H 1506 Q10 Properties of D shapes AM H 1411 Q17 Compound measures AM1 1F 1411 Q16 Solve linear equations NEW QUESTION Expand double /change subject of formula 6 No data available 16 MB0 H 1506 Q14 Circle Theory MB0 H 1506 Q Trigonometry MM H 1506 Q Transformation of functions a 5AM H 1111 Q Gradients as rate of change b NEW QUESTION Area under the graph No data available 0 5AM H 1506 Q Proportional change MA0 1H 1405 Q18 Surds MA1 practice paper H (Set ) mark scheme: Version 1.0 1