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
(a) A rectangle measures 8.5cm by 10.7cm, both correct to 1 decimal place.
Calculate the upper bound of the perimeter of the rectangle.
…………………………………….. cm
(b)
ABDF is a parallelogram and BCDE is a straight line.
AF = 12cm, AB = 9 cm, angle CFD = 40° and angle FDE = 80°.
(i) Calculate the height, h, of the parallelogram.
h = ……………………………………. cm
(ii) Explain why triangle CDF is isosceles.
……………………………………………………………………………………………………………………………
……………………………………………………………………………………………………………………………
(iii) Calculate the area of the trapezium ABCF.
(c)
A, B, C and D are points on the circle, centre O.
Angle ABD = 21° and CD = 12 cm.
Calculate the area of the circle.
…………………………………… \(cm^{2}.\)
(d)
The diagram shows a square with side length 8cm and a sector of a circle with radius 9.5cm
and sector angle x°.
The perimeter of the square is equal to the perimeter of the sector.
Calculate the value of x.
x = …………………………………………
Answer/Explanation
(a) 38.6
(b)(i) 8.86 or 8.863…
(ii) ∠CDF = 100 leading to ∠DCF = 40
Or
∠EDF = 80 leading to ∠DCF = 40
two equal angles’
(iii) 66.5 or 66.45 to 66.47…
(c) 130 nfww or 129.6 to 129.8
(d) 78.4 or 78.37 to 78.41
Question
Amol and Priya deliver 645 parcels in the ratio Amol : Priya = 11 : 4.
(a) Calculate the number of parcels Amol delivers.[2]
(b) Amol drives his truck at an average speed of 50km/h.
He leaves at 0700 and arrives at 1115.
Calculate the distance he drives.
km [2]
(c) Priya drives her van a distance of 54km.
She leaves at 1055 and arrives at 1238.
Calculate her average speed.
km/h [3]
(d) Priya has 50 identical parcels.
Each parcel has a mass of 17kg, correct to the nearest kilogram.
Find the upper bound for the total mass of the 50 parcels.
kg [1]
(e) 67 of the 645 parcels are damaged on the journey.
Calculate the percentage of parcels that are damaged.
% [1]
(f) (i) 29 parcels each have a value of \($\)68.
By writing each of these numbers correct to 1 significant figure, find an estimate for the total value of these 29 parcels.
\($\) [1]
(ii) Without doing any calculation, complete this statement.
The actual total value of these 29 parcels is less than the answer to part (f)(i) because [1]
Answer/Explanation
Ans:
1(a) 473
1(b) 212.5
1(c) 31.5 or 31.45 to 31.46
1(d) 875
1(e) 10.4 or 10.38 to 10.39
1(f)(i) 30 [×] 70 and 2100
1(f)(ii) both numbers rounded up oe