IGCSE Higher Sheets 5-Answers - Weeblyrunnymedemathematics.weebly.com/uploads/4/0/6/7/... · IGCSE...
Click here to load reader
Transcript of IGCSE Higher Sheets 5-Answers - Weeblyrunnymedemathematics.weebly.com/uploads/4/0/6/7/... · IGCSE...
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
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
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
Sheet H5-2 3-01-2 Linear Sequences - Answers
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
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
Sheet H5-3 3-01-3 Linear Sequences - Answers
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= =
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
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
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
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− −
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
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
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
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
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
Sheet H5-8 3-02d-2 Functions - Answers
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−
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
Sheet H5-9 3-02d-3 Functions - Answers
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
≠
>
≠≠
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
Sheet H5-10 3-02d-4 Functions - Answers
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
= − =
+= =
−= = −
− −= =
+ += =
− −
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
Sheet H5-9 3-02d-3 Functions - Answers
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− − =
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
Sheet H5-11 3-02d-5 Functions - Answers
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
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
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−=
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
Sheet H5-12 3-02d-6 Functions - Answers
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−
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
BLANK PAGE
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
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
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
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= − = −
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
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
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
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
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
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
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
BLANK PAGE
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
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
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
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
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
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
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
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= − )
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
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= − =
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
BLANK PAGE
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
Sheet H5-18 3-03d-2 Straight Lines - Answers
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= −
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
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= +
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
Sheet H5-19 3-03d-3 Straight Lines - Answers
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 = −
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
Sheet H5-19 3-03d-3 Straight Lines – Answers (cont.)
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= +
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
Sheet H5-20 3-03d-4 Straight Lines - Answers
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
BLANK PAGE
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
Sheet H5-21 3-03d-5 Straight Lines - Answers
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− = −
For use only in Whitgift School IGCSE Higher Sheets 5-Answers
Copyright www.pgmaths.co.uk
Sheet H5-21 3-03d-5 Straight Lines – Answers (cont.)
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= +