IGCSE Higher Sheets 5-Answers - Weeblyrunnymedemathematics.weebly.com/uploads/4/0/6/7/... · IGCSE Higher Sheets 5-Answers Copyright IGCSE Higher Sheet H5-1 3-01-1 Linear Sequences

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IGCSE Higher

Sheet H5-1 3-01-1 Linear Sequences - Answers

1.

12

12

3 31 1 1 12 4 2 8 2 4

13, 15 41, 51 43, 50(a) (b) (c)

(d) 38, 47 (e) 42, 49 (f ) 3, 3

(g) 3, 0 (h) 93, 91 (i) 7, 13

( j) 19, 23 (k) 19, 26 (l) 3, 4

(m) 1 , 1 (n) , (o) 3 , 4

− −− −

2.

1 12 2

1 12 2

9 31 1 1 14 4 8 8 4 4

2 3 10 9 7 8(a) (b) (c)

(d) 9 7 (e) 7 7 (f )

(g) 18 3 (h) 103 2 (i) 23 6

( j) 1 4 (k) 7 16 (l) 1 4

(m) (n) (o)

n n n

n n n

n n n

n n n

n n n

+ − +

− + +− − −

− − −+ − −

3. (a) 6 1n −

(b) 239 (c) 80

4. (a) 7 4n −

(b) 493 (c) 102

5. (a) 24 5n−

(b) -91 (c) 74

6. (a) 1 2n− −

(b) -31 (c) 143

7. (a) 3 1n +

(b) 451 (c) 334 8. (a) 1089 7n−

(b) 389 (c) 156




1. (a) 37 2n− (b) 18 2. (a) 47 3n+

(b) 12th

3. (a) 20 5n+ (b) 45 (c) 14

4. (a) 32.75 0.75n− (b) 18.5 (c) 19th from bottom

5. (a) 34750 250n+

(b) 12 6. (a) £2.40

(b) 21 (c) 0.8 0.2n+ (d) 99p




1. (a) 4 3n − (b) 69 (c) 29

2. (a) 11 3n − (b) 129 (c) 23 3. (a) 5 2n −

(b) 43 (c) 103

4. (a) 7 27n +

(b) 111 (c) 46

5. (a) 46 8n−

(b) 104 11n− (c) 20

6. (a) 8

n

(b) 7

8

(c) 41st term 7. (a) £12,100

(b) £1050 (c) A

8. (a) 3 23 6 38a d a d+ = + = (b) 8, 5a d= =



Sheet H5-4 3-02a-1 Functions - Answers

1. (a) 6 (b) 1 (c) -4 (d) 2

2. (a) 3 (b) 5 (c) -1 (d) 10

3. (a) 2 (b) 2 (c) 5 (d) 10 or -10

4. (a) 0 (b) 1.5 (c) 3 (d) 1

5. (a) -8 (b) 7 (c) -8.75 (d) -2 or 4

6.

(a) -5 (b) 3 (c) 4 (d) 2

7. (a) 1 (b) 0 (c) 4 (d) 1.875 (e) 0.5



Sheet H5-5 3-02a-2 Functions - Answers

1. (a) 20 (b) 6 (c) 2 (d) 2 or 3

2.

(a) 4 (b) 5 (c) 3.5 (d) -1

3. (a) 0 (b) 0.724 (c) 0.849 (d) 2

4.

(a) 6

(b) 0

(c) 1.875

(d) 0

(e) 0, 1, 2− −



Sheet H5-6 3-02c-1 Functions - Answers

1. (a) { }1 , 4 ,9 , 16

(b) { }0, 1 , 4

(c) { }7, 9, 11, 13

(d) { }0, 1, 2, 3

(e) { }8, 1, 1, 8− −

(f) { }1, 2, 3, 4, 6, 12, 24

(g) { }4, 10, 14, 8, 6, 5− − .

(h) { }: 1x x ≥

(i) { }: 0 1x x< ≤

2. (j) 0 (b) 1

(c) 2 (d) 1

2

(e) 2 or -2 (f) { }: 0x x <

(g) { }: 1x x < (h) 0

(i) { }: 2x x < (j) 1 or 2



Sheet H5-7 3-02d-1 Functions - Answers

1. (f) 1 (g) 6 (h) 9 (i) 2 (j) 4

2. (k) 1.5 (l) -3 (m) -1 (n) -1.75

3. (o) -2 (p) -1.75 (q) 22

4. 8 5. 2 or -16 6.

(r) 18 (s) -43 (t) -18 (u) 2 (v) -8 (w) 1




1. 3

g( )2

xx

−=

2. (a)

(i) 2

(ii) 1

(iii) 14

(b) 2

5

y −

(c) ( )1 2f

5

xx− −

=

(d)

(i) 2

(ii) 1

(iii) 14

3. (a)

(i) 1

(ii) 2

(iii) 1−

(b) 1

1x

y=

−

(c) ( )1 1f

1y

y− =

−

(d)

(i) 1

(ii) 2

(iii) 1−




1.

-1

-1

-1

-1

-1

-1

-1

-1

-1

-1

(a) f ( ) 2

4(b) f ( )

34 1

(c) f ( )3

13(d) f ( )

2

4(e) f ( )

3

(f ) f ( ) 1

3 1(g) f ( )

23

(h) f ( )5

7 5(i) f ( )

2

9 5( j) f ( )

3 2

y y

y y

yy

yy

yy

y y

yy

yy

yy

y

yy

y

= −

=

+=

=

−=

= −

−=

−=

+=

−+

=−

2.

(a) All

(b) All

(c) All

(d) 0

(e) All

(f ) 1

(g) All

(h) All

(i) 2

( j) 1.5

y

y

y

y

y

y

y

y

y

y

≠

>

≠≠




1.

-1 -1

-1 -1

-1 -1

-1 -1

-1 -1

4(a) f ( ) 2 (b) f ( )

34 1 13

(c) f ( ) (d) f ( )3 2

4(e) f ( ) (f ) f ( ) 1

33 1 3

(g) f ( ) (h) f ( )2 5

7 5 7 5(i) f ( ) ( j) f ( )

2 3 2

yy y y

yy y

y

yy y y

y yy y

y yy y

y y

= − =

+= =

−= = −

− −= =

+ += =

− −




3. (a)

(i) 5 (ii) 1

(iii) 7 (iv) 3

(v) 9 (vi) 3

(vii) 19 (viii) 1.5

(ix) 4 (x) 1

(xi) 9 (xii) 0.25

(xiii) 25 (xiv) 49

−

(b) f(g(2)) 9= and g(f (2)) 25= . (c) f(g( 1)) 3− = and g(f ( 1)) 1− = . (d) f(g(3)) 19= and g(f (3)) 49= . (e) f(g(0.5)) 1.5= and g(f (0.5)) 4= .

4. (a)

(i) 2 (ii) 11

(iii) 5 (iv) 7

(v) 17 (vi) 62

(vii) 32 (viii) 28

(ix) 6 (x) 21

(xi) 11 (xii) 9

(xiii) 56 (xiv) 26

(xv) 34 (xvi) 0

−

−

−

−

(b) f(g(1)) 17= and g(f (1)) 11= . (c) f(g(4)) 62= and g(f (4)) 56= . (d) f(g(2)) 32= and g(f (2)) 26= . (e) f(g( 2)) 28− = − and g(f ( 2)) 34− = − .

5.

(a) 1 11f ( ) and g ( ) 7

3

xx x x− −+= = −

(b) ( )( )1 16g f 4

3− = − .

(c) ( )( ) ( )( )1 1f g 7 =5 and g f 2 8− − =






1. (a) f ( 1) 4x x+ = + .

(b) f (3 2) 6 5x x+ = + .

(c) ( )( ) 2f g 1x x= − and ( )( ) ( )2g f 1x x= − .

(d) ( )( ) ( )2f g 2 1 1x x= + − and ( )( ) ( )2g f 2 1 1x x= − + .

(e) ( )( ) 5 1f g 2

5

xx

+= + and ( )( )g f 11x x= + .

(f) ( )( )f g x x= and ( )( )g f x x= .

2. 11 3. (a) ( )( )g f 6 4x x= − .

(b) 5

4. (a) ( )21x +

(b) 2 or -4 5.

(a) –

(b) ( )1 1f

3

yy− +

=

(c) - 6.

(a) 12.5 (b) 10 (c) 10

7. (a) 2 and 0.

(b) ( ) ( )1 2 1 1f 2 and gx x x

x− −= + = .

PTO



Sheet H5-11 3-02d-5 Functions - Answers (cont.)

8.

(a) ( ) ( )1 1-1 5 3f and g

2

x xx x

x− − +

= = .

(b) 0x ≠ for ( )1g x− .

9.

f( )y x=

1f ( )y x−=




1.

(a) 7 (b) 4 (c) 0

2.

(a) 2

(b) 2 1

1

y

y

+−

3.

(a) 9

(b) ( )21x +

(c) 3 or -5 4.

(a) -1 (b) 6 (c) { }: 0x x <

(d) ( )22y −

5.

(a) 6 9x +

(b) 73−



BLANK PAGE



Sheet H5-13 3-03a-1 Graphs of Quadratics - Answers

1. (a)

x 0 1 2 3 4 5 6 y 1 -4 -7 -8 -7 -4 1

(b) - (d)

(d) (2, -7)

2. (a)

x -3 -2 -1 0 1 2 3 4 5 y 11 4 -1 -4 -5 -4 -1 4 11

(b) & (c)

(d) 5y = (e) -2.2 or 4.2x x= = (f) -5 at 1x =

PTO



Sheet H5-13 3-03a-1 Graphs of Quadratics – Answers (cont.)

3. (a) x -6 -5 -4 -3 -2 -1 0 1 2 y -11 -4 1 4 5 4 1 -4 -11

(b) & (c)

(d) 3.7 or 0.3x x= − = (e) 5 at -2x =

4. (a) 2, 3x x= − = −

(b) Not whole number solutions (c)

x -6 -5 -4 -3 -2 -1 0 1 y 11 5 1 -1 -1 1 5 11

(d)

(e) 1.4 or 3.6x x= − = −



Sheet H5-14 3-03a-2 Graphs - Answers 1. (a)

x 0.5 1 2 3 4 5 10 15 20 y 19.5 8 3 2 2 2.4 6.2 10.8 15.6

(b), (c)

(d) About 0.5 (e) 0.52 (f) About 1.9 (g) 1.93

PTO



Sheet H5-14 3-03a-2 Graphs – Answers (cont.) 2. (a)

x 3 5 10 20 30 40 50 60 70 80 90 100 y 30 55 70 70 63 55 46 37 27 18 8 -2

(b)-(c)

(d) About -0.9 (e) -0.92 (f) About 72 (g) 71.7

PTO



Sheet H5-14 3-03a-2 Graphs – Answers (cont.)

3. (a), (b), (e)

(c) (1, 1) (d) (2, 1) (f) 2.5

4. (a)

x -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 y -1 3.4 5 4.6 3 0.9 -1 -1.9 -1 2.4 9

(b) - (d)

(e) 4



BLANK PAGE



Sheet H5-15 3-03c-1 Graphs - Answers

1. (a)

x -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 y -1 1.6 2 0.9 -1 2.9 -4 -3.6 -1 4.6 14

(b) - (d)

(d) About 8

2. (a)

x -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 y -12.4 -5 -1.1 0 -0.9 -3 -5.6 -8 -9.4 -9 -6.1 0 10.1 25

(b) - (c), (e)

(d) 4.6 (f) 4.2

PTO



Sheet H5-15 3-03c-1 Graphs – Answers (cont.)

3. (a) x 1 2 3 4 5 10 15 25 30 y 91 2 -13.7 -18.5 -20.2 -18.8 -14.5 -4.8 0.1

(b) & (c)

(d) 1 and 21.6

(e) About -21

4.

(a) 15y = (b) -5.9 or 2.9

(c) 10 2y x= − (d) -6.8 or 1.8 (e) 2 3 2 5 5x x x+ − = + (f) 5 5y x= + (g) -1.8 or 3.8



Sheet H5-16 3-03c-2 Graphs - Answers

1.

(a) 3y = (b) 4.1 (c) 3 24 1 10x x− + = − (d) -1.4

2.

(a) 7y = (b) 0.8 or 6.2

(c) 5

14 2x xx

+ = −

(d) 0.4 or 4.3 PTO



Sheet H5-16 3-03c-2 Graphs – Answers (cont.)

3.

(a) 2.3 ( 5y = ) (b) 1.9 ( 8 2y x= − ) (c) -1.7 or -0.5 or 2.2 ( 2 1y x= − )

4.

(a) 2.2 ( 2y = − ) (b) -2.1 or 0.3 or 1.9 ( 3y x= − ) (c) 1.5 ( 5 4y x= − )



Sheet H5-17 3-03d-1 Straight Lines - Answers

1. AB: 4 BC:-4 AC:-2 2.

(a) 2.5 5.5

(b) 0.8 0.6

(c) 1.5 2

(d) 5.5 2.5

y x

y x

y x

y x

= += − −= −= − +

3. Write the following as equations involving only integers (e.g. 632 =+ yx ):

(a) 3 4 6

(b) 2 8

(c) 24 8 3

(d) 15 3 10

y x

y x

y x

y x

= −− == −= +

4.

A 4

B 2

1C 2

2D

y x

y

y x

y x

= −=

= − +

= −

5. (a) 4, 0x y= = (b) 2, 2x y= = − (c) 4, 4x y= − =



BLANK PAGE




1.

2. (a) (-1, -1)

(b) (2, -1) (c) (-2, -3) (d) (4, 4)

PTO

2 1y x= + y x=

12

2y x= −

8y x= −

5 3y x= −



Sheet H5-18 3-03d-2 Straight Lines – Answers (cont.)

3.

4. (a) (2, 2)

(b) (4, 2) (c) (1, 5) (d) (6, 0)

5. 3 14y x= −

8 3y x= −

6y x= −

11

2y x= +

1

2y x=

6y x= +




1. 31(a) : (b) :2 4

: 2 : 2

72: :5 2

AB AB

AC AC

BC BC

−

− −

2.

3. (a) (i) (3, -1)

(ii) (5, 2) (iii) (2, 4) (iv) (-1, 7)

(b) 2 4y x y x= + = − PTO

2y x= 2y x= +

4y x= −

6y x= −

5 2y x= − 6y = −




4.

−8 −6 −4 −2 2 4 6 8

−8

−6

−4

−2

2

4

6

8

x

y

5. (a) (2, 3)

(b) 1

2 2 22

y x y x= + = +

3 5y x= −

12

2y x= +

14

2y x= −

8 2y x= −

6y x= −

12

2y x= +

2 2y x= +






BLANK PAGE




1. (a) 2 (b) 4 (c) 2 (d) 3 (e) 0 (f) infinite

2.

3.

(a) 4, 4

(b) 2, 2

(c) 1, 4

(d) 2, 6

(e) 2, 2

x y

x y

x y

x y

x y

= == == == == − = −

PTO

y x=

8y x= −

6 2y x= −

2 3 12y x+ = −

4 5 20y x− = −




4.

5.

(a) 6, 8

(b) 2, 0

(c) 2, 4

(d) 4, 2

(e) 4, 1

x y

x y

x y

x y

x y

= == − == == − = −= − =

6y x= −

2 2x y+ = −

4 8y x− =

2 4y x= −

2y x= +

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IGCSE Higher Sheets 5-Answers - Weeblyrunnymedemathematics.weebly.com/uploads/4/0/6/7/... · IGCSE Higher Sheets 5-Answers Copyright IGCSE Higher Sheet H5-1 3-01-1 Linear Sequences