SEKOLAH MENENGAH KEBANGSAAN CHERANG RUKU 16700 PASIR PUTEH

KELANTAN

Disediakan Oleh Abd Laziz Ghani

1. Calculate the values of m and n that

satisfy the simultaneous linear equations:

4m + n = 2 and 2m – 3n = 8

2. Calculate the values of m and n that satisfy the simultaneous linear equations:

21

m - 3n = 10

5m + 6n = -8

3. Calculate the values of m and n that

satisfy the simultaneous linear equations: 2m – n = 7

m – 2n = 5

4. Calculate the values of p and q that satisfy the simultaneous linear equations: p + 2q = 6

23

p – q = -7

5. Calculate the values of m and n that

satisfy the simultaneous linear equations:

4m - 3n = 7 and m + 6n = 4

6. Calculate the values of p and q that satisfy the simultaneous linear equations: 2p - 3q = 13

4p + q = 5

Selesaikan persamaan berikut:

a) 2

1)3x(x −= x + 6

(b) (w – 1)2 – 32 = 0

(c) 2a2 = 3(1 + a) + 2

(d) p1

3p5p2

+

+= 4

(e) 2

3t2

= 7t – 4

(f) 3x(2x – 1)+ 8x = 1

1.

DIAGRAM 1 Diagram 1 shows a solid formed by joining a

cuboid and a half-cylinder. Using π = 722

,

calculate the volume, in cm3, of the solid. [4 marks]

2.Diagram 3 shows a solid formed from a cone and hemisphere.

DIAGRAM 3 The diameters of the cone and the hemisphere are 21cm each. The volume of

the solid is 4 042.5 cm3. Using π = 722

,

calculate the height of the cone in cm. 3. Diagram 4 shows a solid formed by joining a right pyramid and a cuboid.

DIAGRAM 4 The volume of the solid is 1 100 cm3. Calculate the height of the pyramid.

4. Diagram 5 shows a solid formed by joining a cone and a cylinder.

DIAGRAM 5 The diameter of the cylinder and the diameter of the base of the cone are both 7 cm. The volume of the solid is 231 cm3 . By

using π = 722

, calculate the height, in cm,

of the cone.

5. Diagram 6 shows a solid cylinder of height 20cm and diameter 14 cm. A cone with radius 7 cm and height 9 cm is taken out of the solid. Calculate the volume in cm3 of the remaining solid.

(Use π = 722

).

`[4 marks]

DIAGRAM 6

6. Diagram 7 shows a solid formed by combining a right prism with a half cylinder on the rectangular plane DEFG.

DIAGRAM 7

DE = 14 cm, EJ = 8 cm, °=∠ 90DEJ and the height of the prism is 6 cm. Calculate the

volume, in cm3, of the solid. (Use 722

=π )

C

B

A

O

60

A B O

210o

B′

A′

1. In diagram 1, OABC is a sector of a circle with centre O and radius 14 cm.

DIAGRAM 1

By using 722

=π , calculate

(a) perimeter, in cm, the shaded area. area, in cm2, the shaded area. (b) area, in cm2, the shaded area.

2. In Diagram 2, the shaded region represents the part of the flat windscreen of a van which is being wiped by the windscreen wiper AB. The wiper rotates through an angle of 210o about the centre O.

Given that OA = 7 cm and AB = 28 cm.

DIAGRAM 2

Using π = 722

, calculate

(a) the length of arc BB′ ,

(b) the ratio of arc lengths , AA′ : BB′

the area of the shaded region.

3. In diagram 3, ABCD is a rectangle.

FIGURE 3

CF is an arc of a circle with center E where E is a point on the line DC with EC = 7 cm.

Using 722

=π , calculate

(a) the length, in cm, of arc CF (b) the area, in cm2, of the shaded region

4. Diagram 4 shows two sector of circle ORQ and OPS with centre O.

By using π = 722

, calculate

(a) the perimeter for the whole diagram in cm,

(b) area of the shaded region in cm2.

C

B A

D E

F

14 cm

21 cm

F

O P Q

R

S

150° 7 cm

12 cm

DIAGRAM 4

1 On the graph provided, shade the region which satisfies the three inequalities 123 +−≤ xy , 4−>y and 4−≤ xy .

[3 marks] Answer: 2. On the graph, shade the region that satisfies all three inequalities : y > x, x + y ≤ 5 and x ≥ 0. [ 3 marks ] Answer :

y

5

4

3

2

1

0

1 2 3 4 5 x

y

x

y = −3x+12

O

y = x−4

x + y = 5

y

3. Find the three inequalities which satisfy the shaded region in the diagram below.

4. Draw the line 2x + y=6. Hence, shade the region which satisfies the three inequalities y > 3, 2x + y ≥ 6 and x + y ≤ 6.

x

10

2x+y =10

5 10

2x + 5y= 20

y

x 3 6

3

y + x=6

y=3

6

1. The Venn diagram in the answer space shows the universal set ξ, sets P, Q and R. The universal set ξ = P ∪ Q ∪ R. On the diagram in the answer space, shade the region for (a) P ∩ Q, (b) P ∩ ( Q ∪ R )’.

[3 marks] Answer: (a) (b)

2. The Venn diagram in the answer space shows sets J ,K and L. In the answer space, shade (a) J ∩ L’ (b) (K ∪ L)∩ J’

[3 marks] Answer: (a) (b)

ξ

ξ

P Q

R

P Q

R

J K

L

J L

4. If ξ = {x : 1 ≤ x ≤ 10 , x is an integer}

E = {x : x is a multiple of 4} F = {x : x is a factor of 20}

(a) List all the elements in set E, (b) Find ( )∪n E F .

[3 marks]

3 The Venn diagram in the answer space shows set P, set Q and set R with the universal set ξ = P ∪ Q ∪ R.

On the diagram in the answer space, shade (a) P ∪ Q ∩ R (b) P ∩ ( Q ∪ R) ′

a)

(b)

5. (a) Given that ξ = { x: x is an integer and 7 ≤ x ≤ 15}, A = { x: x is a multiple of 3 }, B = {x : x is an odd number} and C = { x: 10 ≤ x ≤ 13 }.

(a). List the elements of the set C ′ . (b). Find n(A ∪B).

R Q

P

Q

P R

1..(a) State whether the following statements is true or false. (i) 8 + 2 = 10 and 2 < -3 (ii) All square numbers are even numbers. (b) Complete the following argument. Premise 1 : If 3t = 0, then t = 0. Premise 2 : _________________________________ Conclusion :3t ≠ 0 (c) State the converse of the following statement and hence, determine whether its converse is true or false.

2.(a) State whether each of the following statement is true or false. (i) 42 = 8 or = -2 (ii) a ⊂ { a, b, c } and -3 > -7 (b)Write down premise 1 to complete the following argument. Premise 1 ___________________ Premise 2 : 6 x p ≠ 42 Conclusion : p ≠ 7 (c) Form a general conclusion by induction for the number sequence 11, 23, 43, 71, … which follow the pattern

11 = 4(12) + 7 23 = 4(22) + 7 43 = 4(32) + 7 71 = 4(42) + 7 ……………… ………………

3.(a) State whether the following statement is true or false. b) Write down two implications based on the following statement:

(c) Complete the premise in the following argument: Premise 1 :_______________________

Premise 2 : ≠ 3 Conclusion : x ≠ 9

4.(a) State wheather each of the following statements is true or false.

(i) 23 = 6 or = 3.5

(ii) ( -4 ) x ( -5 ) = 20 and -4 > -2 b)Complete the premise in the following argument: Premise 1 : If the determinant of a matrix = 0, then the matrix does not have an inverse. Premise 2 :___________________ Conclusion :Matrix A does not have an inverse. (c)Write down two implications based on the following sentence. A ⊂ B if and only if A ∩B = A’

x3 = 64 if and only if x = 4

-2 ( 3 ) = 6 or -4 > -5

P3 = 8 if and only if p = 2

x

27

3 8−

5.(a)Determine whether each of the following sentences is a statement. (i) 9 is a prime number. (ii) Solve the equation 2x(x – 2) = 0 (b)Fill in the suitable quantifier to make the following statement become true. (c)Complete the following argument. Premise 1 : If p is a positive integer, then 4p is a multiple of 2 Premise 2 : ____________________ Conclusion : 4p is a multiple of 2.

6.State whether each of the following statement is true or false (i) -22 = -4 or ( -3 )3 = -9 (ii) and (b) Complete the following argument. Premise 1 :________________ Premise 2 : xn + x is not a quadratic expressions. Conclusion : n ≠ 2. (c) Write down two implications based on the following sentence.

7.(a) State whether the following sentence is a statement or a non-statement. Give a reason for your answer. (b) State whether each of the following statements is true or false. (i){ 0 } is an empty set or is an empty set. (ii){ } is and empty set and is also an empty set. (c ) Complete the following argument. Premise 1 : if y > 3, then 5y > 15. Premise 2 : 5y > 15. Conclusion:________________

(a) Is the sentence below a statement or non-statement? (b) Write down two implications based on the following sentence: (c) Make a general conclusion by induction for the following number pattern : 2 = (0)2 + 2 3 = (1)2 + 2 6 = (2)2 + 2 11 = (3)2 + 2

816 21

=5125 2

1

=−

1 – m > 2 if and only if m < -1

2 + 7 = 1 + 6

φφ

3 and 4 are factors of 8

x is an even number if and only if only if x can be divided by 2

…. Prime number are odd numbers

1.(a) Given matrix M = , find the value of k if matrix M has no inverse. (b) Given the matrix equations and

(i) Find the value of h (ii) Hence, find the value of x

and y.

2.Given the matrix P is , (a) Find the matrix Q so that PQ = (b) Hence, calculate the values of h and k, which satisfy the matrix equation:

4.Given matrix P = and matrix PQ =

(a) Find the matrix Q. (b) Hence, calculate by using the

matrix method, the values of m and n that satisfy the following simultaneous linear equations :

4m + 5n = 7 6m + 8n = 10

4. (a) Given that find matrix A.

(b) Hence, using the matrix method, find the value of r and s which satisfy the simultaneous equations below. -r + 2s = -4 -3r + 5s = -9

− 24

6k

−=

−

−14

8567

yx

−

=

14

75681

hyx

−−

5834

−−

=

−−

117

5834

kh

1001

8654

1001

,1001

5321

=

−−

A

5. (a)Given that G = and the inverse matrix of G is find the value of m and of n.

b) Hence, using matrices, calculate the value of p and of q that satisfies the

following equation :

6. It is given that matrix P = does not have an inverse matrix.

(a) Find the value of k. (b) If k = 1, find the inverse

matrix of P and hence, using matrices, find the values of x and y that satisfy the following simultaneous linear equations.

2x + 5y = 13 x - 2y = -7

7. (a)Find matrix M such that

(c) Using matrices, calculate the values of x and y that satisfy the following matrix equation.

(a) Find the inverse of matrix . (b) Hence, using matrices, calculate the values of d and e that satisfy the following simultaneous equations :

2d – e = 7

5d – e = 16

n

m2

3

,2

34141

−

−m

−

=

8

1qp

G

− 252

k

=

56

3142

yx

=

3142

3142

M

−−

2513

1. The diagram below shows the straight lines PQ and SRT are parallel.

DIAGRAM 1

Find

(a) the gradient of the line PQ.

[ 2 marks ] (b) the equation of the line SRT.

[ 2 marks ] (c) the x- intercept of the line SRT. [ 1 mark ]

2. The diagram below shows that the straight line EF and GH are parallel.

DIAGRAM 2

Find (a) the equation of EF. [ 3 marks ] (b) the y - intercept and x - intercept of EF.

6. The diagram below shows that EFGH is a trapezium.

DIAGRAM 6

Find

(a) the value of z. [ 2 marks ] (b) the equation of the line EF. [ 2 marks ] (c) the x - intercept pf the line EF. [ 1 mark ]

8. The diagram below shows that PQR and RS are straight lines.

DIAGRAM 8

Given that x-intercept of PQR and RS are -8 and 6 respectively.

(a) Find the gradient of PQR.

(b) Find the y-intercept of PQR.

[ 2 marks ] (c) Hence, find the gradient of RS.

1. Diagram 1 shows a cuboid with base TUVW.

Calculate the angle between plane PRV and plane QRVU.

2 Diagram 3 shows a right prism with horizontal rectangle base. Right triangle RSW

and UTV are the uniform cross section of the prism. Calculate the angle between plane SRV and plane RSTU.

[4 marks]

R

Q

S

P

T U

V W

5 cm

12 cm

4 cm

DIAGRAM 1

5 cm

T

U

V

W

S

R

10 cm 12 cm

DIAGRAM 2

3 Diagram 3 shows a cuboid PQRSDEFG with a horizontal square base PQRS.

DIAGRAM 3

J is the midpoint of DG. QR = RS = 12 cm and FR = 8cm. Calculate the angle between the plane JRS and the plane RSGF.

[4 marks]

4. Diagram 4 shows a cuboid with a rectangular base PQRS.. M and N are midpoints of TU and PQ respectively.

DIAGRAM 4

(a) Calculate the length of SN

(b) Calculate the angle between the line SM and the plane TUVW

(c) Name the angle between the plane SRUM and the plane PQUT

Q

R

S

P

E

D

G F

J

P

24 cm

7 cm

5 cm

T M U

Q

R

N

W

S

V

1. Diagram 1 shows a velocity-time graph for a particle.

velocity ( m s-1) 20

(a) State the time, in s, the particle moves with constant velocity. (b) Calculate the accleration, in m s-2, of the particle in the last 5 seconds. (c) Find the value of u if the total distance travelled after 15 seconds is 190

m. 2. Diagram 2 shows a displacement – time graph for the journey of a car from town A

to town C passing town B and then back to town A.

DIAGRAM 2 (a) Calculate the speed in km/h for the journey from town A to town B.

(b) State the time taken for the car to stop at town C.

(c) Calculate the average speed in km/h for the total distance of the car.

15 25 30 time (s)

u

O

DIAGRAM 1

Time (min) 0 20 55 64 95

B

Displacement (km)

45

60

A

C

3. Diagram 3 shows the distance-time graph of the journeys taken by Ali and Fuad. DIAGRAM 3 The straight line OB represents Ali’s journey from town X to town Y, while the straight line FG represents Fuad’s journey from town Y to town X. Ali and Fuad uses the same route. (a) State the distance, in km, of town Y from town X. (b) Find the time Ali and Fuad meet each other during their journey. (c) Find the distance when they meet from town Y. (d) Calculate Fuad’s speed.

Distance (km)

Time

105

60

O 0700 0730 0800 0830 0900 0930

F

G

B

4. Diagram 4 shows the speed-time graph of a particle for a period of 17 seconds.

(a) Calculate the value of u, if the total distance traveled in the first 8 seconds is 164 meters.

(b) State the length of time, in s, that particle move with uniform speed. (c) Calculate the rate of change of speed, in m s 2− , for a period of 20 second.

Time (s)

Diagram 4

Speed (m/s)

0

u

8 12

25

20

1.Diagram 1 show twelve labelled cards which are placed in an empty box. Diagram 1 (a) If a card is chosen at random from the box, calculate the probability that the

card labelled ‘L’ is chosen. (b) If a card is chosen at random from the box, calculate the probability that the

card labelled ‘L’ or the card labelled ‘C’ are chosen. 2.Table 1 which is incomplete shows, the probability of spending the weekend among two classmate Azmi and Faizal.

Table 1 Calculate the probability that (a) Azmi going shopping (b) They both doing the same activities

Probability Students Gardening Fishing Shopping Azmi

61

43

Faizal

52

101

21

3. A coin is tossed and a dice is rolled simultaneously. By listing the sample of all the possibleoutcomes of the event, find the probability that Sekeping syiling dan sebiji dadu dilambung serentak. Dengan menyenaraikan Semua kesudahan yang mungkin, cari kebarangkalian

(a) a tail and an even number are obtained ,

bunga dan nombor genap diperolehi , (b) a head or a number greater than 4 are obtained.

kepala atau nombor lebih besar daripada 4 diperolehi.

P

C

C I O L E

S T E D A

4. Diagram 4, shows seven cards labelled with letters in boxes E and box F. Rajah 4, menunjukkan tujuh kad huruf di dalam kotak E dan kotak F. Box E Box F Kotak E Kotak F A card is picked at random from box E and than a card is picked at random from box F. Satu cad dipilih daripada satu kotak E dan kemudian satu kad dipilih seacra rawak daripada kotak F. By listing a sample space of all possible outcome of even, find the probability that Dengan menyenaraikan ruang sample bagi semua kesuahan peristiwa yang mungkin, cari kebarangkalian

a) both card are labeled with same latter, kedua-dua kad ditanda dengan huruf yang sama,

b) only one of the cards labeled with the latter P are the picked. Hanya sekeping kad yang dilabel dengan huruf P yang dipilih.

5. Diagram 5 shows the cards in a box A and box B. Rajah 5, menunjukkan kad dalam kotak A dan kotak B. A B Diagram 5 A card picked at random from box A and than a card is picked at random from box B. Satu kad dipilih secara rawak daripada kotak A dan kemudian satu kad pula dipilih secara rawak daripada kotak B. By listing the sample of all the possible outcome of event, find the probability that Dengan menyenaraikan semua sample bagi semua kesudahan peristiwa yang mungkin, cari kebarangkalian

a) a card labeled X, or a card with the number 8, satu kad bertanda X atau kad yang bernombor 8 dipilih,

b) both card are labelled with a number. kedua-dua kad berlabel dengan nombor.

U P S R

P M R

3 X Y

8 S T 5

PART II(Paper 2) 1. The data in Diagram shows the donations, in RM, of 40 people to a charity fund.

12 48 27 43 33 40 18 29 41 30 45 35 56 16 24 49 32 31 53 13 22 42 38 21 47 32 46 17 37 44 38 23 47 35 40 28 35 43 58 26

a) Based on the data in Diagram 4 and using a class interval of RM10, complete Table 4 in the answer space.

b) By using a scale of 2 cm to RM10 on the x-axis and 2 cm to 5 persons on the y-axis, draw an ogive based on the data. c) From your ogive in b),

i) find the third quartile, ii) explain briefly the meaning of the third quartile.

Donation (RM) Frequency Cumulative frequency 10-19

20-29

2. The data in Diagram shows the mass, in kg, of 40 pupils in a class. 36 55 46 45 55 35 39 59 41 50 50 39 41 52 40 41 38 39 33 45 48 52 35 51 40 42 47 36 41 36 49 32 42 40 37 44 48 48 43 43

a) Based on the data in Diagram 5 and using a class interval of 5 kg, complete Table 5 in the answer space.

b) From the table in a), i) State the modal class,, ii) Calculate the estimated mean mass of the pupils.

c) By using a scale of 2 cm to 5 kg on the x-axis and 1 cm to 1 pupil on the y-axis, draw a frequency polygon based on the data.

Mass(kg) Frequency Midpoint 30-34

1. a) Complete Table 4 in the answer space for the equation y = x2

b) For this part, use a graph paper. By using a scale 2 cm to 1 unit on the x-axis and 2 cm to 1 units on the y-axis,

draw the graph of y = x2

for -4 ≤ x ≤ 4.

c) From your graph, find

a. the value of y when x = -1.5, b. the value of x when y = 1.2.

d) Draw a suitable straight line on your graph to find all the values of x which

satisfy the equation x2

= 43

x - 2 for -4 ≤ x ≤ 4.

State these values of x. Answer: a)

X -4 -2.5 -2 -1 -0.5 0.5 1 2 2.5 4 Y -0.5 -0.8 -2 -4 4 2 1 0.5

Table 1 2. a) Complete Table 2 in the answer space for the equation y = x2 – 5x + 4.

b) For this part, use a graph paper. By using a scale 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, draw the graph of y = x2 – 5x + 4 for 0 ≤ x ≤ 8.

c) From your graph, find

a. the value of y when x = 4.5, b. the value of x when y = 21.75

d) Draw a suitable straight line on your graph to find all the values of x which

satisfy the equation x2 – 7x + 3 = 0 for 0 ≤ x ≤ 8. State these values of x.

a)

X 0 1 2 2.5 3 4 5 6 7 8 Y 4 0 -2 -2 4 10 18 28

Table 2

1. (a) Diagram 2(i) shows a solid prism. Hexagon ABCDEF is the uniform cross section of the prism. The base ALGF is on the horizontal plane.

The sides BA, CD and EF are vertical whereas the sides BC and DE are horizontal. Draw in full scale, the plan of the solid prism.

F G

H E

D I

J

K B

C

A L

2 cm

4 cm

4 cm

4 cm

8 cm

5 cm

DIAGRAM 2(i)

(b) A solid prism with triangle AFM as its uniform cross section is joined at the vertical plane ABCDEF to form a combined solid as shown in Diagram 2(ii).

Draw in full scale, (i) the elevation of the combined solid on a vertical plane parallel to GF as

viewed from X.

(ii) the elevation of the combined solid on a vertical plane parallel to AF as viewed from Y.

6 cm

DIAGRAM 2(ii)

Y

M

F G

H E

D I

J

K B

C

A L

2 cm

4 cm

4 cm

X

Q N

4 cm

2. (a) Diagram 4(i) shows a solid right prism. The base BCDF is on a horizontal plane. Triangle ABC is the uniform cross section of the prism.

Draw in full scale, the elevation of the solid right prism on a vertical plane parallel to BF as viewed from X.

Diagram 4(i)

E

A

C

B

F

D

8 cm

6 cm 7 cm

10 cm

X

(b) A cuboid is joined to the solid in Diagram 4(i) at a vertical plane APGC to form a combined solid as shown in Diagram 4(ii).

Draw in full scale,

(i) the plan of the combined solid, (ii) the elevation of the combined solid on a vertical plane parallel to HM as

viewed from Y.

E

A

C

B

F

D

3 cm 7 cm

Diagram 4(ii)

G

H

M

L

I

N

K

J

11 cm

6 cm

10 cm

Y

2. (a) Diagram 3 shows the point K on a Cartesian plane. DIAGRAM 3 The transformation R represents a 90 0 anticlockwise rotation about the center

(3, 2). The transformation T represents a translation

32

. State the coordinates

of the image of the point K under the following transformations. (i) R (ii) RT [3 marks] Answer: (a) (i) (ii)

y

x 0

4

2

2 4 6

-2

-4

-2 -4

K

(b) Diagram 4 shows three quadrilateral EFGH, ABCD and OFJK on a Cartesian plane. EFGH is the image of ABCD under the transformation U and OFJK is the image of EFGH under the transformation V . DIAGRAM 4 (i) Describe completely the transformation,

(a) U, (b) V. [6 marks]

(ii) Given that the shaded area is 120 unit 2 , find the area of ABCD.

y

x O

4

2

2 4 6

-2

-4

-2 -4

A

B

C

D

H

E F

G

J K

2

-2 -4 0 2 4

-2

-4

2. (a) Diagram 2 shows two points, M and N, on a Cartesian plane. y

N x M DIAGRAM 2

Transformation Y is a translation

−−

33

.

Transformation P is a reflection in the x-axis. (i) State the coordinates of the image of point N under transformation Y. (ii) State the coordinates of image of point M under the following transformation:

(a) Y2 (b) YP [3 marks]

Answer: (a) (i) (ii) (a) (b)

(b) Diagram 2 shows three trapezium ABCD, EFGH and PQRS on a Cartesian plane. 6 4 2 O 2 4 6 8 10 DIAGRAM 2 Trapezium ABCD is the image of trapezium PQRS under transformation M. Trapezium EFGH is the image of trapezium ABCD under transformation N. (i) Describe in full transformation : (a) M (b) N [6 marks] (ii) Calculate the area of trapezium EFGH, if the area of trapezium ABCD is 25 unit2. [3 marks] Answer: (b) (i) (a) (b) (ii)

A B

C D

P Q

R

S F G

H E

1 (a) Diagram 1(i) shows a solid right prism with the rectangular base QRXW lying on a horizontal plane.Pentagon PQRST is the uniform cross section of the prism.

Rectangle STUY is a horizontal plane whereas rectangle PTUV is an Inclined plane.

The sides PQ and SR are vertical. Draw in full scale, the plan of the solid right prism.

2 cm

8 cm

R X

Y S

Q

P V

T U W

8 cm

5 cm

3 cm

DIAGRAM 1(i)

(b) Another solid prism with uniform cross section ABC is joined to the prism in Diagram 1(i) at the vertical plane EFUYXW to form a combined solid as shown in Diagram 1(ii). It is given that BX = 3 cm and AB = 5 cm.

Draw in full scale,

(iii) the elevation of the combined solid on a vertical plane parallel to XR as viewed from G.

(iv) the elevation of the combined solid on a vertical plane parallel to RQ as

viewed from H.

8 cm

R X

Y S

Q

P V

T U W

8 cm

5 cm

DIAGRAM 1(ii)

4 cm B C

A

F E

G

H

2. (a) Diagram 2(i) shows a solid prism. Hexagon ABCDEF is the uniform cross section of the prism. The base ALGF is on the horizontal plane.

The sides BA, CD and EF are vertical whereas the sides BC and DE are horizontal. Draw in full scale, the plan of the solid prism.

F G

H E

D I

J

K B

C

A L

2 cm

4 cm

4 cm

4 cm

8 cm

5 cm

DIAGRAM 2(i)

(b) A solid prism with triangle AFM as its uniform cross section is joined at the vertical plane ABCDEF to form a combined solid as shown in Diagram 2(ii).

Draw in full scale, (v) the elevation of the combined solid on a vertical plane parallel to GF as

viewed from X.

(vi) the elevation of the combined solid on a vertical plane parallel to AF as viewed from Y.

6 cm

DIAGRAM 2(ii)

Y

M

F G

H E

D I

J

K B

C

A L

2 cm

4 cm

4 cm

X

Q N

4 cm

3. (a) Diagram 3(i) shows a solid right prism. Trapezium ABCD is its uniform cross section. The base ADEF is on a horizontal plane. Draw in full scale, the elevation of the solid right prism on a vertical plane parallel to AF as viewed from X.

F

E

A

B G

H C

D

6 cm

4 cm

DIAGRAM 3(i)

4 cm

7 cm

X

(b) A half-cylinder with radius 3 cm and height 6 cm is joined to the solid in Diagram 3(i) at a vertical plane ABLKD to form a combined solid as shown in Diagram 3(ii).

Draw in full scale,

(i) the plan of the combined solid, (ii) the elevation of the combined solid on a vertical plane to EF as viewed

from Y.

F

E

A

B G

H C

D

6 cm

4 cm

DIAGRAM 3(ii)

7 cm M

K

6 cm

Y