Algebraic Fractions Mark Scheme 1 Level IGCSE Subject Maths Exam Board Edexcel Topic Equations, Fmulae and Identities Sub Topic Algebraic Fractions(Algebraic manipulation) Booklet Mark Scheme 1 Time Allowed: Sce: Percentage: 50 minutes / /100 Grade Boundaries: A* A B C D E U >85% 75% 70% 60% 55% 50% <50%
Question Number Wking Answer Mark Notes 1. ( x) +x x( x) oe 8 x +x x( x) 8 x x( x) Accept 8 x x x Single fraction needed as final answer. Total marks. crect expression with crect common denominat 5(x ) + 9(x + ) = (x + )(x ) x 1x 16 (= 0) oe x 7x 8 (= 0) oe (x + 1)(x 8) (= 0) oe (=) x = 1, x = 8 5 gather terms crectly. Accept x f (x + )(x ) crect part quadratic dep on previous oe condone 1 sign err. M If not M then f numerat denominat crect Total marks
. y(x ) xy x(x ) x(x ) 5 LHS may be two separate fractions one single fraction y(x ) xy x(x ) x(x ) x(x ) x(x ) y(x + ) + xy = x(x + ) xy y xy x(x ) x(x ) xy y xy x(x ) x(x ) x(x ) x(x ) (brackets may may not be removed on RHS and denominat) LHS may be two separate fractions one single fraction; if one fraction, numerat on LHS may may not be simplified (implies previous ) (brackets may may not be removed on RHS and denominat) xy y xy x 1x xy y _ xy x( x ) xy y x 1x xy y x( x ) y(x ) x(x ) y(x ) x 1x x(x ) x (brackets may may not be removed on RHS) (implies previous two s) LHS factised crectly - expression in bracket on LHS may may not be simplified x(x ) x 1x x x a fully crect method must be seen in der to award full marks
5. (x ) ( x 1) ( x 1)( x ) (=1) 8 x 7 = ( x + 1)( x ) oe x 9x + (= 0) 5 ( x ) + ( x + 1) = ( x +1)( x ) 8 x 7 = ( x + 1)( x ) oe crect -part quadratic in the fm ax + bx + c (=0) ( x 1)( x ) (=0) x = ½ 9 ( 9) dep on previous Question Wking Answer Mark Notes 6. (x + )(x ) f (x + )(x ) (x )(x ) f (x )(x ) x + x cao Total marks 7. ( x+ 1) (x 1) (x+ 1)( x 1) x+ x+ ( x+ 1)( x 1) x + 7 1 x F expressing both fractions crectly with a common denominat. Allow as two separate fractions. F removing brackets crectly in a crect single fraction. Allow x 1 in denominat. Allow x + 7 ( x+ 1)( x 1) Total marks
Question Wking Answer Mark Notes ( ) ( + ) ( + )( ) ( + )( ) 8. ( ) + ( + ) ( + )( ) (x ) + (x + ) = (x + )(x ) 7x 1 = (x x 6) oe crect single fraction crect removal of denominat to give a crect equation x 9x 11 (= 0) (x 11)(x + 1) (=0) x = 1 x = 5.5 oe 5 crect part quadratic (eg x 9x 11 (= 0) x 9x = 11 x² = 9x + 11 oe) f (x 11)(x + 1) (=0) a fully crect substitution into the quadratic fmula 9±( 9)² 11 9 ± 169 dep on last condone no brackets around 9
Question Wking Answer Mark Notes 9. 5 x x x + factised crectly ( x ) ( x )( x 1) 5 x x 6 ( x )( x 1) 5( x1) ( x) a crect common denominat may be a single ( x )( x 1) ( x )( x 1) fraction two fractions with crect numerats; denominat may be expanded crectly 5x 5 x ( x )( x1) crect single fraction with numerat expanded crectly; denominat may be expanded crectly ( x ) ( x )( x1) Alternative 5( x x ) (x 6)( x ) (x 6)( x x ) (x 6)( x x ) 5x 0x 15 x x 6x 1 (x 6)( x x ) x 18x7 (x 6)( x )( x 1) ( x ) ( x)(x)( x1) (x 1) (x 1) crect factisation of numerat ; denominat may be expanded crectly 5 Accept x a crect common denominat may be a single fraction two fractions with crect numerats; denominat may be expanded crectly crect single fraction with numerat expanded crectly; denominat may be expanded crectly; x x + factised crectly could occur earlier crect fully factised numerat and denominat 5 Accept x Total marks
Question Wking Answer Mark Notes 10. (a) x y B (b) (B1 f ax n y m with two of a = ; n = ; m = 1) (x )(x + ) (x )(x + ) (x )(x + ) f numerat factised x(x ) x(x ) f denominat factised Alternative to (b): x 8 x ( x )( = = x 8x x x x+) xx ( ) x + x x + x 1 1 accept + x In der to use this mark scheme, crect simplification of the iginal fraction must be seen (x )(x + ) x(x ) 1 1 accept + x