Question
(a) Manjeet uses 220 litres of water each day.
She reduces the amount of water she uses by 15%.
Calculate the number of litres of water she now uses each day.
………………………………….. litres
(b) Manjeet has two mathematically similar bottles in her bathroom.
The large bottle holds 1.35 litres and is 29.7cm high.
The small bottle holds 0.4 litres.
Calculate the height of the small bottle
…………………………………….. cm
(c) Water from Manjeet’s shower flows at a rate of 12 litres per minute.
The water from the shower flows into a tank that is a cuboid of length 90cm and width 75cm.
Calculate the increase in the level of water in the tank when the shower is used for 7 minutes.
…………………………………….. cm
Answer/Explanation
(a) 187
(b) 19.8
(c) 12.4 or 12.44…
Question
Two rectangular picture frames are mathematically similar.
(a) The areas of the frames are \(350 cm^{2) and \(1134 cm^{2}\). The width of the smaller frame is 17.5cm.
Calculate the width of the larger frame.
(b) A picture in the smaller frame has length 15cm and width 10.5cm, both correct to the nearest 5mm.
Calculate the upper bound for the area of this picture.
(c) In a sale, the price of a large frame is reduced by 18%. Parthi pays $166.05 for 5 large frames in the sale.
Calculate the original price of one large frame.
(d) Parthi advertises a large frame for a price of $57 or 48.20 euros. The exchange rate is $1= 0.88 euros.
Calculate the difference between these prices, in dollars and cents, correct to the nearest cent.
Answer/Explanation
7(a) 31.5
7(b) 163.9375 or \(163\frac{15}{16}\) final answer
7(c) 40.5[0]
7(d) $2.23 final answer
Question
The diagram shows a company logo made from a rectangle and a major sector of a circle.
The circle has center O and radius OA.
OA = OD = 0.5cm and AB = 1.5 cm.
E is a point on OC such that OE = 0.25cm and angle OED = 90°.
(a) Calculate the perimeter of the logo.
cm [5]
(b) Calculate the area of the logo.
cm2 [3]
(c) A mathematically similar logo is drawn.
The area of this logo is 77.44cm2.
(i) Calculate the radius of the major sector in this logo.
cm [3]
(ii) A gold model is made.
This model is a prism with a cross-section of area 77.44cm2.
This gold model is 15mm thick.
One cubic centimeter of gold has a mass of 19 grams.
Calculate the mass of the gold model in kilograms.
kg [3]
Answer/Explanation
Ans:
6(a) 5.83 or 5.832 to 5.833
6(b) 1.21 or 1.208…
6(c)(i) 4[.00…]
6(c)(ii) 2.20704