P5 Maths SA Grade AAA Paper 2 Word Problems - Nanyang. Word Problem Worksheet & Solutions Difficulty: AAA P5 Mathematics SA2 2016

Transcription

1 Word Problem Worksheet & Solutions Difficulty: AAA P5 Mathematics SA

2 Show your working clearly in the space provided for each question and write your answers in the spaces provided. 6. The length of rectangle ACBD is m. Its breadth is 21 5 m shorter than its length. Find the perimeter of rectangle ABCD in metres. Express your answer as a mixed number in its simplest form. Breadth = = = = m Perimeter of ABCD = ( ) x 2 = m Ans: m 7. The number of children who visited the National Museum was 6 times the number of adults. The number of boys was twice the number of girls. There were 60 fewer adults than girls. How many children visited the National Museum? Let g = number of girls Number of children = 2g + g = 3g Number of adults = 3g 6 = ½ g Number of girls minus adults = g ½ g = ½ g = 60 g = 60 x 2 = 120 Number of children = 3g = 3 x 120 = 360 Ans: 360 children 2

3 8. A rectangular tank measuring 30 cm by 12 cm by 16 cm was completely filled with water. After some water was poured out from the tank, the height of the water decreased from 16 cm to 11 cm. How much water was poured out from the tank? Area of base = 30 x 12 = 360 cm 2 Reduction in height = = 5 cm Volume of water poured out = 360 x 5 = 1800 cm 3 = 1.8 l Ans: 1.8 l 9. Mr Lee measured and recorded the mass of Ashley, Bala, Chin Hin and Dave. The average mass of these 4 children was 49 kg. The next day, Mr Lee realized that he had recorded Ashley s mass wrongly. Ashley s recorded mass was 8 kg more than her actual mass. What was the correct average mass of the 4 children? Average of 4 children s mass = 49 kg Error in Ashley s mass = - 8kg Effect of Ashley s error on the average = -8 2 = -2 kg Correct average mass of 4 children = 49 2 = 47 kg Ans: 47 kg 3

4 10. In the square grid below, DE and EF are straight lines. a) DE and EF from the two sides of a four-sided figure DEFG. EF is parallet to DG and EF = DG. Complete the drawing of the four-sided figure DEFG. b) Which one of the following is the special name given to the four-sided figure DEFG: parallelogram, rectangle, rhombus or trapezium? a) b) DEFG is a parallelogram Ans: (a) as shown in figure (b) parallelogram 4

5 11. At first, Zhi Lie, Eva and Lisa had some sweets in the ratio 5 : 3 : 4 respectively. Zhi Lie had 190 sweets. Then he gave his sweets to Eva and Lisa. After receiving the sweets from Zhi Lie, Eva and Lisa had the same number of sweets. How many sweets did Eva received from Zhi Lie? Ratio of sweets of Zhi Lie, Eva and Lisa 5 : 3 : 4 Zhi Lie had 5u = 190 sweets u = = 38 After receiving Zhi Lie s sweets, ratio of Eva and Lisa (3 + 3) : (4 + 2) 6 : 6 Eva received 3u sweets = 3 x 38 = 114 Ans: In the figure below, rectangle PQRS is made up of 8 identical rectangles. QR = 16 cm and SU = UY. Find the area of triangle SQU. Breadth of identical rectangles = 16 4 = 4 cm Length of SY = 3 x 4 = 12 cm Length of SU = 12 2 = 6 cm Area SQU = ½ x 16 x 6 = 48 cm 2 Ans: 48 cm 2 5

6 13. There were some red, blue and green beads in a box. 1 9 of the beads were blue. The ratio of the number of red beads to the number of green beads was 3 : 5. There were 288 fewer blue beads than green beads. a) Find the ratio of the number of read beads to the number of blue beads to the number of green beads in the box. b) How many green beads were there? Fraction of blue beads = 1 9 Ratio of number of red beads to number of green beads 3 : 5 Ratio of number of red, green, blue beads 3 : 5 : 1 3u : 5u : u Green minus blue beads = 5u - u = 4u = 288 u = = 72 a) Ratio of number of red, blue, green beads 3 : 1 : 5 b) Number of green beads = 5u = 5 x 72 = 360 Ans: (a) 3 : 1 : 5 (b) Mdm Asfa bought some egg tarts and cheese tarts. She paid a total of $168 for the tarts. 40% of the tarts bought were cheese tarts and the rest were egg tarts. Each egg tart cost $6 and each cheese tart cost $3. How many cheese tarts did she buy? Let number of cheese tarts = u Number of egg tarts = x u = 3 2 u Total cost = 3u u x 6 = u = 168 Number of cheese tarts = u = = 14 Ans: 14 6

7 15. In the figure below, ABCD is a trapezium and ADEH is a rhombus. AD is parallel to BC and DE = DF. HDC and DGF are straight lines. DAH = 38 o and GDH = 47 o. a) Find ADC. b) Find DFE. ADE = = 142 o ADH = = 71 o ADC = = 109 o HDE = 71 o FDE = = 24 o DFE = (180-24) 2 = = 78 o Ans: (a) 109 o (b) 78 o 7

8 16. The table below shows the rates charged for the use of water in a country. First 30 units Next 30 units After 60 units $0.97 per unit $1.12 per unit $2.00 per unit (a) (b) Mr Tan and his family used 30 units of water in January. How much did they pay for the usage of water in January? Mrs Sahin and her family paid $ for the usage of water in February. How many units of water did they use in February? a) Water bill for Mr Tan in January = 30 x 0.97 = $29.10 b) Cost of first 30 units = $29.10 Cost of next 30 units = 30 x 1.12 = $33.60 $ = Usage after 60 units = = 50 units Total water usage for Mrs Sahin in February = = 110 units Ans: (a) $29.10 (b) 110 units 17. Vera, Leroy and Tarita each donated some money to charity. The amount of money donated by Vera was ½ of the total amount of money donated by Leroy and Tarita. The amount of money donated by Leroy was 1 of the total amount of money donated by 3 Vera and Tarita. Vera donated $168. How much did Leroy donate? Let amount donated by: Vera = V Leroy = L Tarita = T V : L + T 1 : 2 u : 2u Total = 3u = 3 X 168 = $504 L : V + T 1 : 3 p : 3p p + 3p = 504 4p = 504 Leroy s donation = p = = $126 Ans: $126 8

9 18. A rectangular tank measuring 48 cm by 18 cm by 26 cm was filled with 18.8 litres of water as shown in the Figure 1. When three identical wooden blocks were put into the tank, 794 ml of water overflowed from the tank as shown in Figure 2. Find the volume of one such wooden block. Volume of full tank = 48 x 18 x 26 = cm 3 = l Increase in volume to full tank = = l Total volume increase = ml = 4458 ml Volume of one wooden block = = 1486 m l Ans: 1486 m l 9