Answer Booklet. Based on Latest Math Syllabus

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1 Based on Latest Math Syllabus Answer Booklet onsponge Pte Ltd All rights reserved. No parts of this material may be reproduced, stored in a retrieval system or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the copyright owner.

2 P6 Solutions Note: In all solutions, u represents units Chapter More Than/Less Than Charles +$8 Benedict x x + $7 Charles +$8 +$8 $0 Unit. More Than/Less Than (Model Drawing) Qn L Left R Remained 7% 0 60% Benedict $8 + $8 + $0 $ $ $6 + $ Total number of children [0 (L) 0(R)] Boys Girls u (L) u (L) u(r) 8u (R) 0 Total number of children remained Boys Girls u(r) 0 8 8u (R) Charles at first + $0 ( $6) + $0 $00 Qn % Dennis Karen 80 0 From the model, units 8 unit 8 6 Total number of girls at first Qn G Gave L Left Chocolate Banana Left Chocolate Banana 9u G 6 L u (G) 0u (L) 6 9u (G) 9u (L) 0u 0 Dennis +60 Karen +0 In the end Dennis Karen +8 9 units units unit 8 7 Dennis at first units + 80 ( 7) Qn unit Total chocolate muffins at first 8 units + 6 (8 ) Qn At first Boys Girls +8 60% % of $7 $0 $7 $7 $8 $0 $7 $8 $7 $8 $ Charles x x x $0 Benedict $7 + $8 In the end Boys Girls + 8 units unit 6 8 Total boys at first u + ( 8) + 6 Left Page

3 Qn 6 At first Boys Girls In the end Boys 0 Girls unit + 0 unit 0 8 Number of boys at first units Qn 7 John Janet unit 0 + Total number of stickers John had at first units 96 Qn 8 At first Boys Girls In the end Boys + 0 Girls units + 0 unit 6 No. of boys at first unit Qn 9 (L) Left (R) Remained 8 0 % 0 At first Adults Children Total remained in the end Adults Children Left Left (L) 0 (R) 8u (L) u (R) 0 u(r) u (R) u (R) 0 0 u (R) 0 Qn 9 (Cont.) units unit 0 80 Number of children in the end u Qn 0 Green Blue 6% of total Red Total 6% total % total % total 00% % 6% 6% % Total in bag 00% Qn 80 0 Triangles Squares Rectangles 0 + % of total % of total % of total 8 0% of total 00% 0% 60% 60% of total 00 % of total 7 Total number of triangles Qn Adults 0 Boys Girls + 0 % of total units % of total unit % of total 0 unit 0% of total Remaining 60% of total 0 % of total Total number of adults % of total + 0 ( ) + 0 Qn (S) Spent (R) - Remained 9 6 At first Daniel u(s) 80 0u (R) $88 $8 6 [$8(S) $0(R)] $88 Edwin 9u (S) u(r) Page onsponge Pte Ltd No further reproduction and distribution.

4 Qn (Cont.) In the end Daniel Edwin u $0 7 units $0 $0 $6 unit $6 7 $9 Daniel had at first units + $88 ( $9) +88 $96 Qn At first Alan Kenneth u u $0 + $0 $60 u $0 Total at first u + $0 + u + $0 u + $80 ( $0) + $80 $70 Qn End Girls 0u $0 u $0 $00 $0 0 + $0 Qn 6 (Cont.) $700 - $00 $00 May $700 + $00 $00 Jenny $800 Qn 7 spent Benedict Jeremy Benedict Jeremy spent 8 + $0 $080 8 $960 $0 Each at first Benedict $0 + $080 $00 Jeremy $0 $60 Chapter Patterns Unit. Equal Intervals Qn Diagram $080 $0 Boys No. of dots At first total Girls Boys total Therefore, Total Boys at first 8 (8 0) 0 Qn 6 spent May Jenny spent 0 $ (b) 9 th diagram 6 + (8 ) th diagram 6 + (9 ) Qn Diagram No. of dots (b) 0 th diagram + (9 ) + 8 dots 00 th diagram + (99 ) Qn T P May Jenny $ (b) No. of people around 00 tables (00 ) + 0 Page

5 Qn Fig. No. of squares No. of triangles Perimeter : ; : : : : : : (7 ) No. of sticks (b) Perimeter for Figure (9 ) 0 (c) No. of sticks for figure (99 7) 70 (d) Figure No No. of squares 6 Qn T-shaped array Number of coins st + nd + ( ) 8 + rd + ( ) + th + ( ) th + ( ) 7 6 th + ( ) 0 7 th + (6 ) (b) No. of coins for 00 th array + (99 ) 0 (c) No. of coins for 00 th array + (99 ) 60 Qn 6 nd structure + ( 8) 0 rd structure + ( 8) 8 (b) 0 th structure + (9 8) 8 (c) 00 th structure + (99 8) (d) Structure 0 + ( st structure) Qn 7 Figure (9 ) 6 (b) Figure (89 ) 7 (c) st row dots Figure 9 (Figure 9 th ) Total dots 7 + (8 ) 6 Qn 8 Total seats ( ) + 8 (b) Total seats (0 ) + 8 (c) Total seats (00 ) + 0 (d) Diagram 9 could seat 70 students. : : 8 + (7 7) Qn 9 Block. Perimeter (cm) (b) Perimeter of a 0-T block 0 + (9 ) 86 (c) Perimeter of a 00-T block 0 + (99 ) 06 (d) T block No. of squares 00 Unit. Square Numbers Qn Diagram, n No. of shaded squares, S No. of unshaded squares Total no. of squares, T (b) Total squares in diagram 0 (0 + 9)² 8 (c) Total unshaded squares (9 )² 960 (d) Diagram 8 has 9 shaded squares Qn No. of squares Total Fig. Fig. + Fig Fig (b) Figure 9 since Qn Diagram No. of shaded triangles No. of unshaded triangles Total no. of triangles : : : : ( 6) (b) Diagram 0 + -T -T -T -T 0 8 (c) No. of shaded triangles in diagram (d) Total triangles in Diagram 80 (8 8) 6889 Page onsponge Pte Ltd No further reproduction and distribution.

6 Qn Figure No. of white squares 9 6 No. of coloured squares Total no. of squares (b) 00 Figure no. (c) No. of white squares in Figure (d) Total Qn Length of side of given big square (cm) No. of small black 8 squares No. of small white 0 8 squares Total no. of small 9 6 squares (b) (c) (d) Side cm side has squares Total squares Total white squares ( ) 60 Length of side cm Since 96 Side 8 cm side has 8 squares Total squares 8 8 Total black squares 6 Unit. Sum of Odd Numbers Qn 0 th line ² 00 (b) 0 th line ² 00 (c) 00 th line ² Qn Figure No. of shaded squares 6 6 No. of unshaded squares 0 0 Total no. of squares (b) Figure Figure (c) Figure no. + last digit Figure no. 9 9 The sum (9 + )² 00 (d) Figure no Total sum (9 +)² 600 Qn and 9 (b) Total tiles in bottom layer (9 ) 7 (c) Total tiles (d) Total tiles Qn No. of bricks ² (b) No. of bricks (c) No. of steps (d) 76 No. of steps Unit. Sum Of Consecutive Numbers Qn q (b) (c) No. of handshakes (d) No. of handshakes Qn (b) Maximum no. of intersections 0 (c) Maximum no. of regions + 8 (d) No. of lines No. of line segments Qn 0 Area cm² 80 cm² Perimeter 0 cm 60 cm 0 (b) No. of cubes for figure (c) Area cm² 6 80 cm² Perimeter 90 cm 70 cm Page

7 Unit. Sum of Even Numbers Qn Figure No. of bricks (b) Figure 0 (0 9) + 8 (c) Figure 00 (00 99) Qn Figure No. of circles (b) Figure 0 (0 ) + 9 (c) Figure 90 (90 9) + 89 Qn th line ² (b) Line 9 0² (c) p² 6 p 6 Line Last digit q (line no.) + ( ) + 6 (d) 0 th line sum ² 60 0 Unit.6 Multiples of Sum of Consecutive Numbers Qn Day Day + Day Day ( ) 6 No. of cubes added on Day ( ) + (7 ) + (6 cubes) (b) Total blocks on Day 0 (0 + ) (0 + ) 9 99 (c) Total blocks on Day 0 (0 + ) (0 + ) Qn No. of small triangles 6 No. of sticks 0 0 (b) Figure triangles Sticks ( ) 0 8 Qn (Cont.) (c) Figure (0 000 triangles) Sticks ( ) 000 ( 0 sticks) (d) Since Figure 7, no. of triangles Qn Line (b) Line (0 numbers) (c) 67 th line Qn No. of shaded triangles, and 60 Total no. of triangles 6, No. of unshaded triangles, and 8 (b) No. of shaded triangles in Diagram (c) No. of unshaded triangles in diagram 0 + (0 9) (d) Total triangles in Diagram Qn Total no. of dots; No of small right angled triangles T ;, T0 ; (b) Total dots for figure 0 (c) Total no. of small right angled triangles in figure (d) No, because 0 70 is not a square number. (E.g. 9 is a square number because 7 7 9) Qn 6 s 6, t 0 (b) Number of unshaded rhombuses in Figure 0 (8 + 9 ) 6 Chapter Circles Unit. Composite Figure (Square Quadrant) Qn Area of shaded part square quadrant. cm² Shaded part. cm 8 cm² Qn Area of ( ) ² shaded part square quadrant. cm² Shaded part. cm 86 cm² Perimeter big circle + 0 cm (0 cm) + 0 cm 0 cm Alternatively, area square circle (0 0) cm² ( 0 ) cm² (0 0) (0 0) 86 cm² Page 6 onsponge Pte Ltd No further reproduction and distribution.

8 Qn Area of shaded part square quadrant 8. cm² Shaded part 8. cm² 9 cm² Perimeter big circle ( cm) 9 cm Alternatively, area square circle Qn Area of shaded part 8 square quadrant ( ) cm² ( ²) cm² (0 0) cm² ( ) cm² 9 cm² ( ) cm² ( ²) cm² 0.9 cm² Shaded part 0.9 cm² 8 7 cm² Perimeter circles + () ()() cm Alternatively, area (square circle) [( ) ( )] 7 cm² Qn Area square circle ( ) cm² ( 6²) cm² 0 cm² Perimeter circle + square (6 cm) + ( cm) 9 cm Qn 6 Perimeter big circle (0) 6 cm Area square circle (0 0) cm² (0)² cm² cm² Qn 7 Area square + circles ( ) cm² + ()² cm² 9 cm² Qn 8 Outer perimeter circle + ( cm) ( cm) + 8 cm cm Area of shaded part (squares circle) ( ) ()² cm² Unit. Composite Figure (Rugby ball (Quadrant Triangle)) Qn shaded part quadrant triangle r b h ² ()².9 cm² Qn (Cont.) Shaded part (rugby).9 cm² cm² Qn Radius 7 cm Area circle square circle triangles r ( 7) (7)² ( 7) 6 cm² Qn shaded part quadrant triangle 8 7 [ ] [ 7 ]. cm² Shaded part. cm² 8 8 cm² Qn Area circle square (8)² cm² (6 8) cm² 7 cm² Qn Area (circle square) (circle triangles) [(0)² (0 0)] cm² 8 cm² Qn 6 Area (circle square) (circle triangles) Qn 7 [(8)² (6 8)] cm² 6 cm² Area big circle (0)² cm² cm² Qn 8 Perimeter small circle + big quadrant 7 66 cm Area quadrant triangle [ 6 cm² [ ()²] Unit. Similar Figures Qn Perimeter rs + rb () + (8) 8 cm Area (8)² ()² 6 9 cm² Qn Perimeter big circle (0 cm) 89 cm Page 7

9 Qn (Cont.) Area of small semicircle (0) 7 cm² Diameter (small) : Diameter (big) : Area (small semicircle) : Area (big semicircle) : 9 Area of shaded part 9u u 6u Since u 7 cm² Shaded 6 7 cm² 9 cm² Qn Diameter (S) : Diameter (M) : Diameter (B) : 8 : : : Area (S) : Area (M) : Area (B) : : 9 Shaded part 9u u u u Area of small semi-circle 6. Area of shaded 6. cm² cm² Perimeter of shaded part big circle (6 cm) 8 cm Qn Perimeter of shaded part circles (B) r (8) 0 cm Diameter (S) : Diameter (B) : Area (S) : Area (B) : r Area of small circle () (unit) 0. cm Area of shaded part u u 0. cm 0 cm Qn Radius (S) 0 cm cm Radius (B) Diameter (S) + Radius (M) 0 cm + 0 cm 0 cm Perimeter of shaded part circles (big) (0 cm) 80 cm (b) Radius (S) : Radius (M) : Radius (B) : 0 : 0 : : Area (S) : Area (M) : Area (B) : : 6 Shaded part 6U U U U 0U Fraction shaded Qn 6 Diameter (S) : Diameter (M) : Diameter (B) : : Area (S) : Area (M) : Area (B) : : 6 Shaded part 6u u ( )u 8u Diameter (S) 7 8 cm Radius 9 cm Qn 6 (Cont.) Area of small circle u (9)² 8 cm² Area of shaded part cm² Qn 7 Perimeter big circles (9 cm) cm Diameter (S) : Diameter (M) : Diameter (B) 6 : : 8 : : Area (S) : Area (M) : Area (B) : : 9 Area of (small) ()² 8. cm² Area of (shaded) 9u u u 8. cm² Qn 8 Perimeter quadrant + semicircle + 6 semicircle (big) + 6 (6 cm) + 6 cm 66 cm 6 Area of (quadrant) 0. cm² Area of (semicircle) 00.6 cm² Shaded 0. cm² 00.6 cm² 0 cm² Qn 9 Perimeter big semicircle + small circle big circle ( cm) 8 cm () Area of small semicircle 90. cm² Area of shaded part u u u u 90. cm² 80 cm² Qn 0 Perimeter of shaded big semicircle + small circle + cm big circle + cm (6 cm) + cm cm Area of small semicircle u (8) 6 cm Area of shaded part u u u u 6 0 cm² Qn Perimeter of shaded (8 + quadrant + semicircle) (8 + big semicircle) (8 + (8)) cm Page 8 onsponge Pte Ltd No further reproduction and distribution.

10 Qn (Cont.) Area of small semicircle u () cm². cm² Area of shaded part u. cm² 0 cm² Qn Perimeter big circle (9 cm) 7 cm Area big semicircle (9) cm² 7 cm² Unit. Cut And Paste Qn There are equal semicircles formed by the equal sides of the isosceles triangle. Since the small unshaded part overlaps on both semi circles, we could cut and paste the remaining shaded semicircle onto the remaining unshaded semi circle to form a sector. Area of shaded part area of sector 60 ()² 60 7 cm² Qn r Area of shaded part big semicircle () 6 cm² Qn Area of shaded part square (8 8) cm² 6 cm² Perimeter of shaded Perimeter of semicircle (8 cm) + 6 cm cm Qn Perimeter of shaded part circle + 0 cm ( cm) + 0 cm cm Area of shaded part square circle Qn (0 0) cm² ()² cm² cm² Area of shaded part area of sector 0 (0)² cm² 60 0 cm² Qn 6 Area of shaded part rectangle (8 9) cm² 6 cm² Qn 7 Area of shaded part area of triangle ( 6 8) cm² 6 cm² Qn 8 Perimeter r (0 cm) + 0 cm 7 cm Qn 9 Area of shaded part (square circle) + triangle (6 6) cm² (8)² cm² + (6)(8) cm² 6 cm² + 6 cm² 6 cm² 9 cm² Qn 0 () Square quadrant ()² cm² cm² 0.9 cm² Area of region Z 0.9 cm². cm² Shaded area semi-circle Region Z Qn () cm². cm² cm² Area of shaded part large semicircle small circles Qn rugby quadrant triangle (8) cm² (8)(8) cm² 8. cm² Shaded area big circle rugby (0) cm² 7 ()(0)² cm² cm² (8)² cm² (8.) cm² 6 cm² Qn Area of shaded big semi triangle + rectangle(after cut N paste) () cm² (8)(0) cm² + ( 7) cm² 66 cm² Shaded area is 66 cm² Unit. Overlapping Method Qn Area of small semicircle + medium semicircle + Area of triangle (.) cm² + (6) cm² + ( ) cm² 96. cm² Shaded area total area big semicircle cm² Page 9

11 Qn Region A square quadrant (8) (8 8) cm² cm².7 cm² Shaded area 0 8 cm².7 cm² 66 cm² Qn Region A rectangle small quadrant ( ) cm² () cm² 60 cm² 9.6 cm² 0. cm² Shaded area big quadrant Region A () cm² 0. cm² 7 cm² Qn Triangle 8 cm triangle 6 cm Area of circle 6 6. cm cm 6..7 cm Area of shaded.7 cm 6 cm.7 cm Area of shaded parts.7 cm 7. cm Qn Area of Region A rectangle quadrant () (8 ) cm² cm² 9. cm² Shaded region Big semicircle ( region A) (8) cm² ( 9.) cm² 6 cm² Qn 6 Area of unshaded part squares (7. 7.) cm² Perimeter of unshaded part circles + radius ()(7. cm) + ( cm) cm Qn 7 Areas X + A quadrant small semicircle () (7) cm² 77.0 cm² Areas Y + A square quadrant () ( ) cm². cm² cm² cm² Difference between X and Y 77 cm². cm² cm² Qn 8 Areas X + A quadrant (0) cm². cm² Areas Y + A square quadrant (0 0) cm² (0) cm² 8.8 cm² Difference between X and Y. cm² 8.8 cm² 8 cm² Chapter Speed Unit. - Journey By Parts Qn D (0 km) D km S 80 km/h S 60 km/h T 0 80 h T h Distance travelled 0 km + 0 km 0 km (b) Time travelled h + h h h min 8. a.m..0 p.m. He started his journey at 8. a.m. Qn Total distance travelled (60 km/h h) + (0 km/h h) 0 km + 0 km 0 km (b) Average speed for the journey 0 km h Qn Since journey 60 km journey 0 km Total journey 60 km + 0 km 00 km 6 km/h Time taken to complete st 0 km part of journey 0 km h Time taken to complete nd 60 km part of journey 80 km h Total time taken h Average speed for whole journey 00 km h 0 km/h Page 0 onsponge Pte Ltd No further reproduction and distribution.

12 Qn Total distance 70 km/h h 0 km Distance ( st part) 0 km 0 km Speed ( st part) 0 km h 6 km/h Qn journey 0 km/h h 0 km journey 0 km Journey 00 km Total time taken 00 km h 0 km/h Qn6 To find the average speed for the whole journey, we must first find the total distance from Town A to B. Distance ( st h) km/h h 8 km Distance 8 km Distance km Whole distance km 60 km Average speed for whole journey 60 km h 0 km/h Unit. Journey In Opposite Direction Qn In min, A + B jogged 0 km. Time taken to meet 000 m 0 m min Distance Andy travelled 00 m/min min 00 m Qn In hour, Mr Tan and Mr Krishnan travelled 0 km Time taken to meet km 0 km h h later 9 a.m. 0.0 a.m. They will meet at 0.0 a.m. Qn In hour, Tommy and Jerry travelled 0 km 0 km Time taken to meet 0 km h h later 8.0 a.m. 0.0 a.m. They will meet at 0.0 a.m. Qn Distance (Janet) 80 km/h h 60 km Distance (Tommy) 0 km 60 km 0 km Speed (Tommy) 0 km 7 km/h Qn In 0 min, Benedict jogged. km Alan. Alan Benedict units units unit m Speed (Alan). km h.6 km/h Unit. Common Distance Or Time Qn Time (Alex) : Time(Calvin) : Speed (Alex) : Speed (Calvin) : Speed difference 8 km/h ( unit) Speed (Alex) 8 km/h km/h Qn Time (car A) : Time (car B) h : Speed (car A) : Speed (car B) : Speed difference 0 km/h Speed (car A) 0 km/h 600 m more than 00 m Qn Speed (Jason) : Speed (Carl) : 8 Time (Jason) : Time (Carl) 8 : Time difference h ( units) unit h h : Time (Jason) 8 h h Qn Speed (Yen Ming) : Speed (Leon) 70 : 00 7 : 0 Time (Yen Ming) : Time (Leon) 0 : 7 Time difference u u h h 600 Page

13 Qn (Cont.) Time (Leon) 7u 7 h h h later 0. a.m. p.m. Qn T : T : S : S : Speed difference u 0 km/h Distance T S or T S h 0 or h 0 80 km Qn 6 S : S : T : T : Total time 9u min u 6 min T u 6 min min Qn 7 TA : TB 0 : : 6 SA : SB 6 : Speed difference u 9 km/h Speed (A) 6u 6 9 km/h Qn 8 Ronnie, of journey h; TJ : TR : SJ : SR 9 : 8 Qn 9 9 of journey 8 : 9 Sc : SL 7 : 6 9 : 7 When time is the same, DC : DL 9 : 7 9u 7u h; Journey 9 A km B The car covered ( km 8km) more than the lorry from the time they left the towns to the time they passed each other units 8 km unit km Distance from A to B 6 units 6. 8 km Chapter Simultaneous Unit. Simultaneous (Fraction of Different Quantities Qn 8 of boys + of girls of boys + 7 of girls 6 h Qn (Cont.) (Multiply by 7) 7 8 of boys + 7 of girls (6 7) boys + 7 girls 7 of boys 8 Boys 8 96 Qn 7 of English + of Chinese 8 7 of English + of Chinese 0 English + Chinese 00 7 of English English Chinese Qn 7 of men + 9 of women 0 7 of men + 9 of women of men + 9 of women 0 9 But men + women 90 Extra 7 men 0 men 7 Number of men at first 7 7 Qn circle + rectangle square circle + rectangle 6 square Circle + rectangle circle square Circle : Square : u + rectangle 7 Rectangle 7u u 7 square Circle : Square : Rectangle : : Qn of circle + of rectangle of square of circle + rectangle 9 of square Circle + rectangle squares of circle of square of circle 0 of square Page onsponge Pte Ltd No further reproduction and distribution.

14 Qn (Cont.) Circle : Square : 0 u + rectangle 0u Rectangle u Circle : Square : Rectangle : 0 : Qn 6 Z : X : Y + u (u) Y u Y + Z 6 X x Y + Z 6 X Y + Z X Z X Z : X : Y : : u cm² Total area of figure Area (X + Y + Z) Shaded Area u + u + u u 9u 9 6 cm² Qn 7 A + B A + B 0 C Since u 00 u 00 Bernard 00 Qn 8 girls Girls boys 0 boys 0 Girls + Boys 70 Difference boys + 6 boys 80 boys 80 boys 60 Boys 60 0 boys Chapter 6 Percentage Unit 6. Percentage Of Different Bases Qn Boys % Girls 00% Adults 0 00 % % Difference between adults and boys % % 9% 9% 6 % 7 Total % + 00% + % 99% There were 9 people at the fun fair altogether. Qn At first, pears 0% oranges 60% Left, oranges 70% of 60% 7 60% % 0 End, pears increase 60% of 0% 6 0 0% % Total pears % + 0% 6% Total in the end % + 6% 06% 6% of fruits % of fruits Total at first 00% There were 00 fruits in the box at first. Qn Adults 80% Children 0% Female 0% of 80% 0 80% % Male 80% % 6% Girls 60% of 0% 6 0 0% % Boys 0% % 8% Boys Girls % 8% % % of audience 0 % of audience 0 00% of audience 000 (b) The number of children and men remained the same, Children + male 76% 76% of audience 760 If 80% of remaining people 760 % of remaining people 9. 0% of remaining people Woman at first 0 Women who left Page

15 Qn At first, pears 60% (u) 7 u apples 0% (u) 7 u End, pears 0% (u) 6u apples 70% (7u) u Since the number of apples remained unchanged, the units for apples were made the same in both scenarios. Decrease in pears u 6u u u u Apples u There are applies in the basket. Qn Fixed 0% (u) 0u Unfixed 00% (u) u Fixed 80% (u) 7 8u Unfixed 0% (u) 7 7u Transfer 8u 80 pieces u 0 pieces Total u 0 0 pieces Qn 6 Daryl + Chelsia 7% (u) u John % (u) u Chelsia + John 60% (u) u Daryl 0% (u) 8u Chelsia : Daryl : John 7 : 8 : Difference between Daryl and John u $8 u $8 $6 Total at first 0u 0 $6 $0 The amount of money shared was $0. Qn 7 Roy spent of his money left with Dennis spent of his money left with At the end Dennis Roy s money D R D R D 6 R Total u $660 u $60 Dennis at end u $60 $80 Qn 8 0% of A 0% of B A 0 B 6 A 0 B of his money of his money Qn 8 (Cont.) A : B 6 : 0 C is 0% of A + B C 6u 8u Removed 8u u (in C) A : B : C 6 : 0 : 6 u u No. of oranges in A 6 8 Qn 9 $0 Money 0% books remainder of remainder Remainder 7 of total $0 of total of total $0 7 $ Total $ $80 She had $80 at first. 60% left ( ) % total ( total) of total Qn 0 % + $0 (book) Money 60% + $0 (CD) 7% - $0 remainder 0% $0 (left) $6 0% remainder $0 + $6 $8 0% remainder $ Remainder $ $0 7% total $0 $0 7% total $0 % total $80 Total $80 $0 Qn First bags, selling price % of $80 00 $80 $00 rd bag, selling price 60% of $ $80 $8 Amount of money $00 + $8 $8 She received $8 from selling the three bags. Qn Jenny 80% Daryl 00% Jenny left 80% of 80% 6% Page onsponge Pte Ltd No further reproduction and distribution.

16 Qn (Cont.) Daryl (end) 6% 8% Increase (Daryl) 8% 8% of cards 6 % of cards Jenny at first, 80% of cards Qn Red 0% (6u) 8u Blue 00% (u) u Red 90% (9u) 8u Green 00% (0u) 0u No. Value Total Red 8u 6u Green 0u 00u Blue u u Total 8u 8u 7 u Red balls, 8u 8 7 Qn Jason : Susan At first 7% u : u 00% Change End (0%) 6p : p 6 (00%) Jason Susan u 0 u 9u 0 6 u Jason at first, u 7 Qn Amos 0% Daniel 00% 0% of Amos s 0% 6% 0 Amos, 0% 6% 8% Daniel, 00% + 6% 6% of Daniel s 6% % End Amos, 8% + % 8% Daniel, 6% % 0% Difference 6% 6% of total % of total 6 Amos at first, 0% of total 0 0 Amos had 0 sweets at first. Chapter 7 Pie Chart Qn 7 00% 0% 60 0% of the students like oranges. 0 (b) Pear students like pears. Qn u u 0 Percentage of cricket (b) 70 of total of total 60 of total 80 Qn (b) u u Spiders, u %.89% 88 % of housewives who dislike spider % Qn 6u u 0 0 % teachers 60 00%.6% (b) 0 of total 0 of total 0 Qn u u TV sets 7u 0 Diff º 0 º Radios º 60º 60º 60 0 (b) Total (c) Irons sold u % of iron sold 60 00%.% Qn 6 Total angle sector Amount spend 0 60 $800 $0 (b) Fare 0% (6u) Miscellaneous 00% (u) u u 0 Miscellaneous u u 0 0 $800 $0 60 Page

17 Qn 7 % of girls who chose diet coke 6 00% % 60 (b) 90% of total Total number of girls, 60 8 Qn (b) u u 6 Chinese, u 6 08 (c) 6º 90º 6º 6º º Total, Qn 9 Total, 6u u 0 u 00 % of girls 00 00% 7.78% 60 (b) u Difference between boys and girls (0 ) 0 Qn 0 6u u 0 0 % of students who walk to school 00%.6% 60 (b) 0% of total i) Cars, 00% of total 6 students ii) Bus, 0% of total 00 students Qn 0 0% of Others % on other expenditure 00% 7.78% 60 (b) Amount spent on souvenir $8000 $000 Qn 60 yrs old and above : 0-9 yrs old : : 0 9 yrs old : 0 9 yrs old : Total u + u + u u u 60º 0º 0º u 0º 60 years old and above, units 0º Fraction of people 60 years old and above (b) Chapter 8 Algebra Unit 8. Introduction to Algebra Qn Breadth w cm Length w cm Perimeter (w + w) 8w cm (b) Area w w 7 cm² Qn Annie b years old Mother b b years old Father (b + ) years old years time, father (b + + ) years old (b + 8) years old Qn Gary years old Nathaniel w years old Daniel w years old Qn years ago, Age difference k years Since age difference remains the same throughout, John (k + ) + (k + ) years old Qn apples + oranges 0 cents apple + orange w cents apples + oranges w cents apple (0 w) cents $ 0 w or $ 0 w 00 0 Qn 6 Notebook u Pen $ + u $T CD $ + $ + u $0 + u ($T) T 0 Notebook $ Qn 7 x cm Total perimeter u X cm x u cm Shortest length, u x x cm (b) Since X cm; Shortest 6 cm nd shortest, u 8 cm Area of triangle 6 8 cm² Qn 8 Total score 78(x) 78x points Total new score 80(x + ) (80x + 80) points Next test 80x x (80 + x) points Page 6 onsponge Pte Ltd No further reproduction and distribution.

18 Qn 9 Siti Lilian $K $6 Janet + k + $ k 6 6 k 0 k 0 Siti ( 0 k ) 0 k 0 08 K 8, Siti $6.0 Qn 0 Total units 6 units+ k units (6 + k) units $0 U 0 k 6 k Amount by Mrs Lee k units $ 0 k 6k Qn box of chocolates $(w + ) (b) Amount of money Mrs Lim have 6(w + ) w or (w + ) + 6w + w or w $(w + ) Qn 80% of cost $n 0% of cost $ 8 n n n 00% of cost 0 $( ) 8 Qn Total chairs (p) + 8 6p + 8 (b) Total chairs 6(8) Qn Total work to be done w 0 0w Total days taken with additional workers 0 w w w Qn Cost of pen $ m calculators $m 8 pens 8 ( m) Total cost $m + $6m $m 0 w (0 days) w Unit 8. Solving Simple Linear Equations Involving Whole Number Coefficient Qn J p 0 E p p p 0 p 0 Janice has 0 sweets. Qn J w E w + E (end) w + w + w + w + 0 w 0 6 Jason at first 6 Qn D $m T $(m + 8) C $( m + ) Total $( 9 m + 60) 9m $78 $60 $8 m $ D $8 Qn J (now) (x + ) years old B (now) (x + ) years old J (in years time) (x + ) years old B (in years time) (x + 7) years old x + + x x x Joy (now) ( + ) years old 0 years old Chapter 9 Revision of Key Constructs Qn Square : Round Square : Oval : : Square : Round : Oval : 8 : 9 (b) Round : Square + Oval 0% 70% : 7 9 : Increase in round cookies 0 Square cookies 0 0 Qn Cost of a child s ticket 0 00 $ $7 Number Value ($) Total cost ($) Adults 60% (u) u Children 0% (u) 7 u 6u 6u 670 u Tickets for adults, u 0 60 Page 7

19 Qn $0 tickets : $ tickets : 6 : Number Value ($) Total amount ($) U 0 0u U 0u 70u 70u $600 u $ u of adult tickets 80 $0 $800 Qn Area of square cm² Area of triangle CDE cm² Difference in square and triangle CDE difference in shaded area 00 cm² 0 cm² 0 cm² Qn 0% of total $000 0% of total $00 Mr Soon s salary, 00% of total $00 (b) Difference currently $00 New difference $90 % increase in salary % increase in difference % 8% Qn 6 Difference in income $0 Difference in savings $0 $600 $70 Number of months Clayton take to save $ months (b) Alvin s monthly income $ 0 + $00 $90 Qn 7 80 Roses 7 threw remainder 6 7 left total left 6 7 of remainder total Remainder of total 80 sold 0 of total Total number of roses 0 0 Total number of roses left 0 60 Qn 8 Total cost Keychain $ $8 $ 0 Mug $ 8 u of key chains cost $0. u of key chains cost $0. u of mugs cost $. Difference in u $ $0 $7 No. of items in u $7 $ mugs cost $. mug cost $ 6 $7 Qn 9 A 60% (u) u B + C 00% (u) u B % (u) 8u A + C 00% (u) 8 u A : B : C : 8 : 7 Difference between A and B u u u Total in box 0u 0 80 Qn 0 In day, Imran can paint house. Hence in days, he can paint of the house (Imran painted alone as John rested on these days). In day, John can paint house. Hence, in days, he can paint of the house (John painted alone as Imran rested on these days.) Remaining part of the house for both to paint together house Number of days for both ( + 60 ) Total number of days Qn A : B 0% of B 0% of u u : u u u u u : u % figure unshaded u u 6 00% 66 % or 66.67% u u u 9 60 Page 8 onsponge Pte Ltd No further reproduction and distribution.

20 Qn Case : + 0 red beads Ratio Red : Blue : Case : +0 red beads + 0 blue beads : () : 6 Blue changed by units, u 0 beads u 0 beads Red beads, u 0 0 Number of beads Qn 80% male 90% female 8 0 male 9 0 female 7 7 male female Total 90u + 80u 70u 70u 70 members u member Total this year, u members Qn Performers 0% 70% of 70% 7 70% 9% 0 (70) male Spectators 70% 70% 9% % female Difference 8% of total 00 % of total 0 Performers + female spectators (remains constant) % % 0% 60% 60% of total 760 0% of total 0 0% of total 00 male spectators left Number of male that must leave (9 0) Qn Total number of rectangles in Figure () 7 (b) Figure 0 ( shaded rectangle) Unshaded rectangles 00 (c) Figure ( shaded rectangle) Unshaded rectangles Qn 6 $8 $66 $768 $768 $8 Pants $8 + $66 $0 Shirts $8 u of pants cost $0 u of shirts cost $8 u of pants cost $0 u of shirts cost $96 Difference in u $ Qn 6 (Cont.) No. of items in u $ 9 6 Total shirt + pants bought 7u 6 Qn 7 Item No. of Boxes Item Total Blue Red + 0 0Red + 0 Red Red 0 0Red Comparing the total of items (plates vs cups) Cups Plates Red 0 Red Red 60 Number of Red boxes 60 0 Number of Blue boxes + Total Plates Qn 8 Lim Zhang 6 9 Lim Zhang Lim : Zhang 9u : u p : p Lim Zhang ( )u u 00 u 0 Total ducks u 0 60 Qn 9 Total shaded area cm² Since AB BE but AB BC Therefore EB BC CF 60 cm 0 cm Qn 0 Initial extra 6 0-cent $ After using eight 0-cent coins, 8 0-cent $ $ $ $ Difference in value of 0-cent coins and 0-cents coin $7.0 + $ $8.0 u u Page 9

21 Qn 0 (Cont.) Difference in value of one 0-cent coin and one 0-cent coin $0.0 $0.0 $0.0 $8.0 $0.0 8 At first, he had 8 0-cent coins and cent coins. Qn Green : Blue u : u 0u : u Green markers sold, % of 0u 0u u Number Value ($) Total ($) Green u 60u Blue u 60u 0U 0u 80 u 80 0 Green markets at first, 0u 0 80 Qn Yeo 0% (6u) Yeo : Lim : Tang Lim 00% (u) 0u : u : 8u Tang 60% (u) 6 u 6u +9u Yeo 00%(u) 6 7u : 9u : 7u 0% of 8u 9u p 9u p u Difference between Lim and Tang 8u 8u 96 u 96 8 Mrs Yeo gave Miss Tang u of books 6 Qn Terry loses 9, Alex left 9 Terry : Alex : 0u : u +8u 8u 8 : 7 (b) At first T : A 8 : 7 nd stage T : A 0 : Since 9 9 of Terry 0u of Terry u 9 of Terry 8u Finally T : A : : 0 Transfer u u 7 Terry in the end u Qn No. of shaded tiles 0 No. of plain tiles 6 Qn Assume all delivered successfully, Total earned $ 00 $00 Amount refunded $ 00 $900 $000 No. of parcels damaged $000 ($ +$) 7 No. of parcels delivered successfully 00 7 Qn 6 Area of unshaded part 7 ( + 7) Shaded 66 cm² quadrant + square unshaded + (7 7) cm² Qn 7 Spent Anna 0% Isabel $0 Kenneth 80% Anna Total amount spent $60 $70 $70 0% of Anna + $0 $70 0% of Anna $0 % of Anna $ 00% of Anna $00 Isabel + Kenneth at first $60 $00 $0 Qn 8 Total (Alan + Charles) 0 0 Total (Charles + Gavin) 9 90 Difference between Alan + Gavin 0 Gavin u Alan 7u Qn 8 (Cont.) Difference, u 0 u Gavin, u Charles 90 6 Qn 9 Square X u u Rectangle Y u Difference 6u 9u Unshaded X u u Difference 6u Unshaded Y u 8u Decrease each, u 7 cm² Area (Square X), u 7 cm² 8 cm² Length of square 9 cm (b) Shaded () 0 Plain Total Page 0 onsponge Pte Ltd No further reproduction and distribution.

22 Qn 0 AFG o DFE 80 o AFD BFC FBC 7 Qn Find the ratio of speed for the remaining journey from home to school. Original speed, S : Increased speed, S 0 : 0 : Since the distance for the remaining journey is the same, the ratio of the time taken to complete the rest of the journey is opposite to the speed. Original time, (T ): New time, (T ) : Difference in time, u min + min min u min 0 min Total distance ( 0) m + (0 m/min 0 min) 880 m Qn Alfred Benedict Alfred Benedict spent spent Amount Alfred received $0 + $80 $00 (b) u $80 $0 $60 u $0 Benedict $0 $0 Qn Aaron Lucy 6 + Aaron Lucy $80 6 u u Lucy at first + 6 Qn A u A : B : C : J B + C + J u : : 6 : B u A + C + J u $0 6 Qn (Cont.) C u Difference u $ A + B + J 7u Cost of present 0u 0 $ $80 Qn A u A : B : C : D B + C + D u : : : B u C + D 6u C u Difference u $00 D u u $00 Total sum u $00 $000 Qn 6 Number Value ($) Total ($) On time 8u 6 08u Late u 8u 6u 6u 0 u 0 Number of parcels delivered on time, 8u (b) Amount did not collect u 0 $(6 ) $80 Qn 7 W u W : X : Y : Z X + Y + Z u : : : X u Y + Z u Y u Difference u $ Z u u $8 Total cost of present, u $8 $96 Qn 8 of Joel s of Matthew s 6 0 of Joel s 6 of Matthew s 9 Joel 0u Difference Matt 9u u $ Ben u u $7 J : M : B 0 : 9 : (b) Total savings, u $7 $68 Qn 9 A u 0 A : B : C B + C u 0 0 : : 9 B u 7 A + C 7u 7 u $ Total cost of present 70u 70 $ $80 Qn 0 A, 0% of total u 9 A : B : C B + C, 00% of total u 9 9 : 7 : B, % of total 7u A + C, 00% of total 0u u 8 u 9 Total 7u 7 9 Page

23 Qn W C Total no. of students who like either or both types of food Number of students who do not like Western or Chinese Percentage % % Qn A : B B : C : : : 6 6 : 9 Summary A : B : C : 6 : 9 Since all triangles have the same height, area ratio base ratio area of triangle D 9u + u 6u 7u 7u 70 cm² u 0 cm² Area of rectangle (9u + u) 6u cm² Qn Perimeter (6 ) + (x + 0) + (x + 0) ( + x) m Cost 0( + x) $( x) Qn Perimeter of circle (0 cm) 0 cm Perimeter of figure 0 +(0 0) cm + 0 cm (80 + 0) cm Qn D E : D F : D G 00 : 80 : 60 : : Since time is the same, S E : S F : S G : : D F : D G : : For every unit that Faith travelled, George would travel u. Faith would complete the race in 0 m, so if u 0 m, u 0 m m When Faith completed the remaining 0 m, George would have travelled another m. Distance George was from finishing line 0 m m m Qn 6 Total cost Watch Clock $6780 $6780 $80 $980 u of clocks cost $980 u of watches cost $800 u of clocks cost $660 u of watches cost $960 Difference in u $00 u $00 ( items) $ Total number of watches and clocks, 8u 8 items 96 items Qn 7 Area of shaded part ( ) cm² ( ²) cm² cm² 7 cm² 60 cm² Qn 8 When both have the same height, Ratio of volume ratio of base area Base Area (A) : Base Area (B) ( ) : (0 ) : Volume of water in Tank A 70 cm 70 cm is to be shared between Tank A and Tank B in the ratio : respectively. u 70 cm u 70 cm cm Volume of water transferred to tank B, u 88 cm Qn (left) Calvin Elizabeth Left behind Calvin u Elizabeth 6 9 U (gave) $980 $980 9u (gave) 0u u 8 u Total sweets Calvin had at first u Qn 0 Total numbers Total 6 numbers Total 7 numbers th number 90 $80 0U (left) 88 u (left) 0 Page onsponge Pte Ltd No further reproduction and distribution.

24 Qn B : C : of A + of B A + B 0 C Since u 00 u 0 B + C, 9u Number of sweets Annie had at first Qn Since triangle A, B and C have the same height, ratio of their areas is equal to ratio of their bases. Area A : Area B : Area C Base A : Base B : Base C, so, Base A (YQ) : Base C (QZ) : Area A : Area C : Difference ( )u u u cm² Area B, u 8 cm² Sample Examination Paper Booklet A. (). (). (). (). () 6. () 7. () 8. () 9. () 0. (). (). (). (). (). () h min days. 7 km. $7. 9, 0,,,,, Ans: 9 N 8, N 6 Number 6 80 of number 0 Ans : 0 of red 6 of red 6 8 red u of blue of blue blue 8u Ans: Average D (7%) u D : C : J C (00%) u : 6 : D (80%) u J (00%) u u u 7 u 7 D 8 Sample Examination Paper Booklet B. Area of shaded part cm 8 cm 6 cm². Z (Alt ) Z 9. 8% of original $d 7 7 d % of original $ 7. d 0d 00% of original $ 0 $ 7 7. Difference $0 End, Imran (0%) u Jason (00%) u Difference, u $0 Amount each spent $00 $0 $80 6. U Janet Tony u $90 + $60 + $90 $0 u $0 Janet at first, u $90 ( 0) 90 $70 7. c + d 80 (sum of angles in a triangles) a + b 80 ( interior exterior ) a + b + c + d 0 8. Area of shaded part 0 cm 0 cm 00 cm² 9. Total (A + B) $00 $0 00 Total (B + C) $800 $7600 Difference, u $0 00 $7600 u $00 U $90 $800 Benson $7600 ( 00) $00 0 FBE 90 DFC ( interior exterior ) DFC (b) BDF 8 7 $60 +$90 Page

25 .. Total Before Pears u u Oranges u 6u After Pears u Oranges u Difference in oranges u u 8 Total number of fruits, 9u 9 8 of total + $0 7 of total $0 of remainder + $ of remainder $ $ of remainder $ + $ $8 of remainder $8 $6 Remainder $6 $80 of total $0 $80 of total $90 of total $90 $0 Total amount of money at first $0 $0. In h, Mr Tan would paint 6 of the house. In h, Mr Tan + Krishnan would paint of the house. Krishnan would paint 6 of the house in h. To paint the whole house, Krishnan would take h.. S : S T : T : : 9u min u 6 min T (home to nearby park) u 6 min. Area big semicircle 6. At first Chocolate Banana (0) 7 cm² 8u (gave) (0)² u (gave) small circles (gave) 6(left) u (left) 60 u(left) 6. (Cont.) Left Chocolate Banana 6 7u u Chocolate pies at first 0u Number of shaded triangles in Figure () 66 (b) Number of unshaded triangles in Figure () 7 (c) Total number of triangles in Figure Sample Examination Paper Booklet A. (). (). (). (). () 6. () 7. () 8. () 9. () 0. (). (). (). (). (). () m.. of total h of total 8 Total at first y apples + oranges $.0 apple + orange $0.8 Compare apples + oranges $.70 orange 0 cent Ans: 0 cents or $ $6 ($7) $ Total 0 + (0) + (60) + (0) + (0) 0 0. u Gerald Tommy u(left) u (left) u $60 + $0 $00 u $0 Gerald u + $60 $0 + $60 $0 Sample Examination Paper Booklet B. Total sweets 0 + w 60 + w Total needed for each student to receive 6 sweets Extra sweets needed 0 60 w 80 w u 6 $0 $0 +$ Page onsponge Pte Ltd No further reproduction and distribution.

26 . st watch $0 $0 Loss $ nd watch 0 00 $0 $80 Profit $0 Overall loss $. BCD 80 o 0 o 0 o (interior angles in a parallelogram) BCE 0 o 0 o 0 o (b) ACE 60 o 0 o 0 o 0 o 60 o (angles in a quadrilateral). Volume of solid cm cm. Number Value (legs) Total Legs Chickens u u Horses u u 8u 8u u 8 9 Chickens, u Square Rectangle Unshaded : shaded Shaded : Unshaded : : 8 : Fraction of figure unshaded Since all triangles share the same height, area ratio will be equal to base ratio : 6 : 7 : : 7 7u 6 cm² u 8 cm² Total unshaded, 0u 80 cm² 8. cups u u $8 of total of total 0 of total of total of total $8 + U $8 + 0 ( ) of total $8 7 0 of total $8 of total of total $8 7 0 $ Total $ 0 $0 9. Volume u u u cm u u u 7 cm u cm Area of base unit unit ( ) ( ) cm² 0. John u u Sister u 8u Difference u 6u In yrs time, John u 9u Sister u u Difference u 6u Increase each 7u years u years John is now years years old. S : S T : T 0 : 6 : : 6 u min u min T (home to nearby park), 6u 6 0 min. 0% wife 00% 60% himself (remainder) Increase 0 wife 00 0% % 0% himself 0% % 78% Increase (wife), % of total $60 % of total $0 Income before, 00% of total 00 $0 $000. 0% of total + 0% jewellery box Total 0% remainder + $0 CD 70% of total $0 0% remainder $0 left 0% remainder $ + $0 $6 Remainder $6 $8 70% of total $0 $8 70% of total $68 0% of total $ 00% of total $ 0 $0 $. P small circle + big semicircle + cm (6) + () + 99 cm (b) Area square small circle big semicircle ( ) (6)² () 7 cm². Elias : Roy (0%) u : 0U (00%) +0 + (80%) p : p (00%) Elias Roy u 0 0u 00 u 0 u 0 6 Elias at first, u 6 8 Page

27 6. At first Boys Girls +8 In the end Boys 0 Girls 6 8 u Number of boys at first Total unshaded in Figure (b) Total unshaded in Figure (c) (Figure No.) (Figure No. + ) Therefore Figure. Page 6 onsponge Pte Ltd No further reproduction and distribution.

28 While every care has been taken to compile this answer booklet, errors may still arise in the course of compilation and production. If you notice any error, kindly write to so that we can review it.