list of at least 3 multiples of any two of 20, 30, A1 for 180 or oe 7n 5 oe 2 A1 20, 40, 60, , 60, , 90,

Transcription

1 International GCSE in Mathematics A - Paper 4H mark scheme Question Working Answer Mark AO Notes 5 or 5 or 5 or two of 0, 40, 60 0, 60, 90 45, 90, 05 5 and 5 and 5 or all of 0, 40, 60, , 60, , 90, AO M for one of 0, 0, 45 written as product of prime factors or list of at least multiples of any two of 0, 0, 45 M 80 A for 80 or 5 oe AO M for 7n + k (k may be zero) 7n 5 oe A (0 4) 9 oe (= 08) AO M for area of cross section 08 6 (=648) M (dep on previous M) for volume of prism M (independent) A accept 454 Pearson Edexcel International GCSE in Mathematics (Specification A) Sample Assessment Materials

2 4 a p 9 AO B b m AO B c AO B d e 5x + 5 = x 0 or AO B AO M for removing bracket or dividing all terms by 5 x 0 x eg. 5x x = 0 5 or M for isolating x terms in a correct equation 0 x 7 x A dep on M (=56000) AO M NB. multiplication by 4 may occur before or after percentage decrease (=400) or (=050) or M A M (dep) 4 Pearson Edexcel International GCSE in Mathematics (Specification A) Sample Assessment Materials

3 6 a triangle with vertices (, -) (, -4) (5, -4) AO B b Rotation AO B centre (-, 0) B 90 o anticlockwise B accept +90 0, 70 o clockwise, 70 o NB. If more than one transformation then no marks can be awarded 7 a a b c d 4 5 (=60) or 5 or b d a = 0 or a = or a = 0 or b + c = 9 = 8 4 AO M A AO M ft from (a) (can be implied by, b c, OR a, b, c, d with b + c = 8) 4 A cao (=800) or (=40800) or 400 "40800" 0.0(=86) and "466" 0.0(=8.) OR 448. AO M M (dep) method to find interest for year and year A Pearson Edexcel International GCSE in Mathematics (Specification A) Sample Assessment Materials 5

4 9 x + y = or 6x + y = 6 x 6y = 7 + x y = 9 AO M multiplication of one equation with correct operation selected or rearrangement of one equation with substitution into second eg. x = or 5 + y = M (dep) correct method to find second variable 5, A for both solutions dependent on correct working AO M 4 9 or 6 96 or M answer given A correct answer from correct working (6 ) 80 (=70) AO M complete method to find sum of interior angles 70 ( ) (=66) or (=66) M dep on st method mark 66 M dep on st method mark 4 A 6 Pearson Edexcel International GCSE in Mathematics (Specification A) Sample Assessment Materials

5 a 8, 5, 50, 90,, 0 b Plotting points from table at ends of interval Points joined with curve or line segments c 60 (or 60.5) indicated on cf graph or stated AO B cao AO M + ½ sq ft from sensible table ie clear attempt to add frequencies A ft from points if 4 or 5 correct or if all points are plotted consistently within each interval at the correct heights Accept cf graph which is not joined to the origin NB A bar chart, unless it has a curve going consistently through a point in each bar, scores no points. AO M for 60 (or 60.5) indicated on cf axis or stated approx A If M scored, ft from cf graph If no indication of method, ft only from correct curve & if answer is correct (+ ½ sq tolerance) award M A P c ab AO M Isolate term in b ( P c ) a b M Isolate b ( P c ) b a A oe with b as the subject Pearson Edexcel International GCSE in Mathematics (Specification A) Sample Assessment Materials 7

6 4 a correct points plotted AO M eg (0, 4) and (, 0) 4x + y = drawn A b correct region AO B Correct region y x B for x = 4 and y = drawn and consistent shading correct for at least two inequalities B for x = 4 and y = drawn 5 a AO B Correct diagram A 4 M B for over-lapping circles with 7 in intersection and at least 8 other correct numbers 7 B for over-lapping circles with 7 in intersection D 0 b 4 00 AO B ft from diagram oe c AO B ft from diagram oe 46 8 Pearson Edexcel International GCSE in Mathematics (Specification A) Sample Assessment Materials

7 6 a M g k or M g k AO M 4 k oe or (k = 75).5 M implies first M M 75 g A k accept M with k = 75 stated elsewhere in question g b ( g ) 75 9 oe or 75 AO M 5 A 7 a AO B b AO B c g() = 6 AO M 0.75 oe A 8 correct length scale factor AO M eg 84 or or M for complete method 78 A Pearson Edexcel International GCSE in Mathematics (Specification A) Sample Assessment Materials 9

8 9 E, B, D, A AO B All correct B for correct B for correct 0 a AO M A oe, eg b or oe AO M Allow 0.6(666...) rounded or truncated to at least dp M for or or oe or oe or ' ' Accept fractions evaluated , 7 A oe, e.g. 40 rounded or truncated to at least dp or Pearson Edexcel International GCSE in Mathematics (Specification A) Sample Assessment Materials

9 sin 47 sin M LN AO M Or method using a right angled triangle to find length MX (MX is perpendicular to LN) MX sin M LN sin sin M Or cos 8.5sin 47.8 MLN = 6.7(7...) A LMX= 6. LMN = or 06(.606 ) sin("06") M LMN = 6. + (80 (90+47)) or 06(.606 ) M A Accept an answer that rounds to 56. or 56.4 unless clearly obtained from incorrect working. a (x 4x ) + 9 or AO M (x 4x + 9 ) ((x ) ) + 9 or M ((x ) + 9 ) (x ) + A b explanation AO B E.g. Because minimum is at (, ) Pearson Edexcel International GCSE in Mathematics (Specification A) Sample Assessment Materials

10 BC BA AC or AO M 9 4 or 7 '7 ' ' ' M dep 50 oe A accept 7.07(06 ) 4 AO M method to rationalise M correct expansion of brackets 4 B may be seen before expansion shown 4 A answer from fully correct working with all steps seen 5 (v = ) t 5 t 8 AO M for out of terms differentiated correctly t 0t 8 = 0 A correct equation (t + )(t 4) = 0 M for method to solve quadratic 4 4 A t = 4 only Pearson Edexcel International GCSE in Mathematics (Specification A) Sample Assessment Materials