IGCSE Foundation Sheets 4-Answers -...

For use only in Whitgift School IGCSE Foundation Sheets 4-Answers

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IGCSE Foundation

Sheet F4-1 F4-10-1 Similar Shapes - Answers 1.

(a) 1

2k = , =x 2.5cm

(b) 5

12k = , =x 4.8m

(c) 4

3k = , =x 3.75cm

(d) 8

5k = , =x 2.5cm

(e) 3k = , =x 4.5m 2. 8cm x 10cm 3. 16cm

4. 15mm x 21mm

5.

(a) 6

5k =

(b) =x 14.4cm

6.

(a) 5

4k =

(b) =x 10cm 7. 16cm x 20cm 8.

(a) 2

3k = , =x 4.5cm

(b) 4

5k = , =x 15mm

9. 20cm by 25cm 10. 216 2cm

11. 56mm by 71mm



Sheet F4-2 F4-10-2 Similar Shapes - Answers

1. 3.75cm

2.

(a) 15cm

(b) 16cm

(c) 33.75cm

(d) 14mm

3. 4.8cm

4. 1.6cm

5. not similar

6. 16m

7. 12m

8.

(a) =x 25cm, =y 8cm

(b) =x 3cm, =y 6.6cm

(c) =x 6cm, =y 7cm

(d) =x 14cm, =y 12cm

9. 11.25cm



Sheet F4-3 F4-10-3 Similar Shapes - Answers 1. =x 31.5cm, =y 24cm 2. =x 18mm, =y 49mm 3.

(a) LRS (b) 208cm (c) 336cm (d) 84.1cm

4. not similar 5.

(a) =x 4cm, =y 15cm (b) =x 33cm, =y 8cm

6. (a) – (b) – (c) corresponding angles are equal (d) =x 13.5cm (e) =y 10cm



Sheet F4-4 F4-10-4 Similar Shapes - Answers 1.

(a) 36.9

(b) 30mm

(c) –

(d) 36.9

(e) –

(f) –

(g) 5

24 3

y=

(h) 40mm

(i) 32mm

2.

(a) 5/3

(b) 23/9

(c) not similar

(d) ADE

(e) =x 13.8cm, =y 1.2cm

3.

(a) –

(b) –

(c) –

(d) 10

6 8

x=

(e) =x 7.5cm

(f) =y 4.5cm

4. 2.5cm

5.

(a) 12.5cm

(b) 15cm

6. 4.8cm



Sheet F4-5 F4-10-5 Similar Shapes - Answers

1.

(a) DBA or EBA

(b) CAB or EAB

(c) –

(d) 6.4cm

(e) 6.25cm

2.

(f) 90-θ and θ

(g) –

(h) 65

(i) –

(j) 104

(k) 169

(l) Pythagoras

3.

(m) right

(n) wrong

(o) right

4. All equilaterals

5.

(p) 100mm

(q) 55mm

(r) 70mm

6.

(s) –

(t) –

(u) 10

10 10

x

x=

−

(v) –

(w) 1.62

7. 4cm



BLANK PAGE



Sheet F4-6 F5-02a-c-01 Rotations - Answers 1.

2.

3. (a)

(b) 90 clockwise direction about (1,0)

1R 2R

3R

4R

1T 2T

3T 4T

1F

2F

3F



Sheet F4-6 F5-02a-c-01 Rotations – Answers (cont.) 4.

(f) Centre of rotation is (1, 0) 5.

(d) 90 clockwise direction about (1,-1).

1F 5F

4F

3F

2F

1Q

2Q

3Q



Sheet F4-7 F5-02a-c-02 Centre of Rotations - Answers 1. (a) See graph

(b) (2, -1) (c) See graph

2. (a) See graph

(b) (-1, 1) (c) See graph

A1

B1

C1

A2

B2

C2

T1

T2

A1

B1

C1 A2

B2

C2 T2

T1



Sheet F4-7 F5-02a-c-02 Centre of Rotations – Answers (cont.) 3. (a) See graph

(b) (1, 3) (c) See graph

4. (a) See graph

(b) (0, 2) (c) See graph

C1

A1

B1

D1

A2

B2 C2

D2

S2

S1

C1

A1

B1

D1

A2

C2 D2

B2

S1

S2



Sheet F4-8 F5-02a-c-03 Centre of Rotations - Answers 1. (a) See graph

(b) (-2, 3) (c) Se graph (d) See graph (e) See graph

2. (a) See graph

(b) (-1, 1)

(c) See graph

A1

B1

C1

T1

A2

B2

C2

T2

A4

C4

B4

T4

A3

C3

B3

T3

A2

B2

C2

D2

S2

C1

A1

B1

D1

S1

C3

A3

B3 D3 S3



Sheet F4-9 F5-02a-c-04 Rotations and Reflections - Answers 1. (a) 6y x= − (b) - (c) (2.5, 3.5)

−2 2 4 6 8

2

4

6

x

y

2.

(a) 1x = (b) y x= (c) See above

S1

S3

S2

S4

y x=

1x =

2y =



Sheet F4-10 F5-02d-f-01 Reflections - Answers 1.

2.

(e) Reflection in 1x = − 3. (a) 1x = −

(b) 0y = (c) y x= −

1T 2T

3T

4T 5T

1T 2T

3T

4T 5T



BLANK PAGE



Sheet F4-11 F5-02d-f-02 Reflections - Answers 1.

2.

PTO

F1

F2

F3

F4

T1T2

T3

T4

T5



Sheet F4-11 F5-02d-f-02 Reflections – Answers (cont.) 3.

(d) A reflection in the line 6y x= − 4.

(e) Rotation of 180° about the point (1, -1)

T1

T2

T3

T4

T1

T2 T4

T3



Sheet F4-12 F5-02d-f-03 Rotations and Reflections - Answers 1.

−8 −6 −4 −2 2 4 6 8

−8

−6

−4

−2

2

4

6

8

x

y

(a) -

(b) 11

7

−⎛ ⎞⎜ ⎟⎝ ⎠

2.

−8 −6 −4 −2 2 4 6 8

−8

−6

−4

−2

2

4

6

8

x

y

(d) 10

6

−⎛ ⎞⎜ ⎟⎝ ⎠

(e) ( )6, 4−

(f) ( )2, 2−

PTO

T1

T2

T3

T4 T5

T6

P1

P2 P3

P4



Sheet F4-12 F5-02d-f-03 Rotations and Reflections – Answers (cont.)

3.

−6 −4 −2 2 4 6

−5

−4

−3

−2

−1

1

2

3

4

x

y

T1

T2

T3

T4



Sheet F4-13 F5-02g-h-01 Translations and Enlargements - Answers

1.

(b) (i) 8

9

⎛ ⎞⎜ ⎟−⎝ ⎠

(ii) 7

2

−⎛ ⎞⎜ ⎟−⎝ ⎠

(iii) 9

7

−⎛ ⎞⎜ ⎟−⎝ ⎠

(e) 13

12

−⎛ ⎞⎜ ⎟−⎝ ⎠

(f) 13 9 4

12 7 5

− − −⎛ ⎞ ⎛ ⎞ ⎛ ⎞= +⎜ ⎟ ⎜ ⎟ ⎜ ⎟− − −⎝ ⎠ ⎝ ⎠ ⎝ ⎠

2.

(c) 7

1

−⎛ ⎞⎜ ⎟−⎝ ⎠

(d)- (e) (7, 7)

T1

R1

S2

S3

R2

S1

T2

T3

T1

T2

T3

T4



BLANK PAGE



Sheet F4-14 F5-02j-l-01 Centre of Enlargements - Answers 1-3

4-5

4. (d) 2, (0, 3) 5. (d) 1.5, (1, 0)

PTO

A B

C

D

P

E F

G

Q

J K

L M

R

A B

C D

E

F

G H

P Q

R

X Y

Z

A' B'

C'

D'

J' K'

L' M'

E' F'

G'



Sheet F4-14 F5-02j-l-01 Centre of Enlargements – Answers (cont.)

6-8 6. (a)-(d) see graph (e) scale factor ½ (f) centre (6, 4) 7. (a)-(d) see graph (e) scale factor 1

3 (f) centre (3, 5) 8. (a)-(d) see graph

A'

A B

C

P

B'

C' E F

G

L M

N

Q

L' M'

N'

R S

T

H

I

J

K

H'

I'

J'

K' X



Sheet F4-15 F5-02j-l-02 Centre of Enlargements - Answers 1&2

3-5

5b (2, 1) scale factor 3 6 (a) 3 (b) (2, 0)

A B

C D A′

B′

C′ D′

G′E F

G

F′ E′

P

Q

A B

C D A′ B′

C′ D′

G′ E

F

G

F′E′

P

H I

J

Q



Sheet F4-16 F5-02j-l-03 Centre of Enlargements - Answers 1.

2.

(f) Centre (4, 1) and scale factor -2.

A B

C

D A′ B′

D′

C′ A′′

B′′

C′′

D′′

T1

T2

T3

T4

T5



Sheet F4-17 F5-02j-l-04 Transformations - Answers

1. (a) See graph (b) 11

12

⎛ ⎞⎜ ⎟⎝ ⎠

(c) 11

12

−⎛ ⎞⎜ ⎟−⎝ ⎠

(d) &(e) See graph

(e) See graph (f) 5

10

⎛ ⎞⎜ ⎟−⎝ ⎠

2.

(a) See graph (b) -

PTO

T1

T2

T3

T4

R1

R2

T1

T2

T3 T4 T5

T6



Sheet F4-17 F5-02j-l-04 Transformations – Answers (cont.)

3. (a)-(d) See graph (e) 90 anticlockwise rotation about (0, 7) (g) 5y =

T

A B

C

T1

A1

C1

B1

T2

A2 B2

C2

A3

B3

C3

T4

A4 B4

C4



Sheet F4-18 F5-02j-l-05 Enlargements - Answers 1. 2.4mm 2. 5km 3. 500m 4. (a) 3600cm

(b) 60 5. (a) AB = 3cm, AC = 4cm, BC = 5cm

(b) 36cm 6. 1:25000 7. 1:500000 8. (a) AB = 5cm, AC = 13cm, BC = 12cm

(b) 60cm (c) 2 (d) Both are 90 .



Sheet F4-19 F6-02-1 Averages - Answers 1.

(a) Mean 5 Mode 3 Range 12 (b) Mean 22.3 Mode 22 Range 23 (c) Mean 1.1 Mode 1.06 Range 0.34 (d) Mean 8 Mode 9 Range 12 (e) Mean 47 Mode 47 Range 11 (f) Mean 113 Mode 119 Range 17 (g) Mean 88 Mode 88 Range 14

2. (a) 1.6 and 1.06

(b) Mean increased but median unchanged. 3. (a) 3.51

(b) 3 (c) Mode is 3 and range is 5

4. (a) 1.20 days

(b) 0 days (c) 1 day

5. Mean is 37.0 and median is 37 6. (a) 110g

(b) 25g (c) 110g (d) They are all the same

7. Mean 5, Median 4.5 8. (a) (i) Range 10 Median 15

(ii) Range 50 Median 115 (iii) Range 0.5 Median 2.4 (b) (i) Mean 14.2 (ii) Mean 117 (iii) Mean 2.35



Sheet F4-20 F6-02-2 Grouped Mean - Answers 1. (a)

Weight, x (g) 125 135 145 155 165 175 Frequency 25 19 23 16 12 5

(b) 143.6g (c) “140-”

2. (a) 42.5g

(b)

Weight, x (g) 42.5 47.5 52.5 57.5 62.5 67.5 Frequency 43 31 39 28 19 15

(c) 52.3g (d) “50-”

3. (a)

Time taken, x (min) 57 62 67 72 77 82 Frequency 21 17 22 16 13 11

(b) 67.8min

4. (a) 13.5

(b)

Age, x (year) 13.5 18.5 23.5 28.5 33.5 38.5 Frequency 46 34 51 29 22 18

(c) 23.5g (d) “21-25”

5. (a) 55.4g (b) 53.9cm



BLANK PAGE



Sheet F4-21 F6-02-3 Grouped Mean - Answers 1.

(a)

Milk intake (Midpoint) 20 45 80 125 175 250 400 No. of students 3 7 25 55 23 15 2

(b) 137ml (c) “100-” (d) “100-”

2. (a) Price of good

(£) Frequency

10 2 25 8 35 19 45 37 55 62 65 51 80 29 110 9 140 2

(b) £58.70

3. (a) 13 (b)

Number of Correct Answers (x) 13 18 23 28 33 38 Frequency 2 11 31 37 24 12

(c) 27.5 (d) Don’t know actual number of correct answers for each student. (e) 59th value

(f) 26-30 (g) 26-30

4. (a) 7

(b) Number of Points (x) 7 12 17 22 27 32

Frequency 18 12 7 5 2 3 (c) 13.8 points (d) “10-14” (e) “5-9”



Sheet F4-21 F6-02-3 Grouped Mean – Answers (cont.) 5. (a) 142.5cm

(b)

Height, h (cm) 142.5 147.5 152.5 157.5 162.5 167.5 Frequency 40 45 94 97 85 57

(c) 156cm (d) “155-”

6. (a) A child is 5 until the moment before their sixth birthday. (b) 3.5 (c) 12.1 years (d) “6-10”



Sheet F4-22 F6-03-1 Probability-Introduction - Answers

1. (a) 1

6

(b) 1

2

(c) 1

3

(d) 1

2

(e) 2

3

2. (a) 7

12

(b) 1

4

(c) 5

12

(d) 3

4

3. (a) 0.9

(b) 0.18 (c) 0.46

4. (a) 1

4

(b) 1

13

(c) 1

52

(d) 2

13

5. 52

365

6. (a) 1

5

(b) 8

15

PTO



Sheet F4-22 F6-03-1 Probability-Introduction – Answers (cont.)

7. (a) 9

49

(b) 24

49

(c) 1

7

(d) 11

49

8. (a) 1

4

(b) 1

12

(c) 2

3

(d) 7

12

9. (a) 2p, 3p, 4p

(b) 0.1

(c) 3

5

10. (a) 0.15

(b) 0.4 (c) 0.55



Sheet F4-23 F6-03-2 Probability-Estimation - Answers

1. (a) No

(b) Yes 2. (a) 50

(b) (ii) 85 3. (a) 300

(b) 100 (c) 300

4. 130 5. 200 6. 4 7. (a) 100

(b) 200 (c) 100

8. 130 9. 160



Sheet F4-24 F6-03-3 Probability-Mutually Exclusive - Answers

1. 0.05 2. (a) 0.55

(b) 0.7 (c) 0.45

3. (a) 0.1

(b) 0.9 (c) 0.75

4. (a) 1

3

(b) 5

6

5. (a) 0.6

(b) 132 6. (a) 3p

(b) 6p (c) 0.1 (d) 0.7

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