Question
The diagram shows a circular disc with radius 6 cm.
In the centre of the disc there is a circular hole with radius 0.5 cm.
Calculate the area of the shaded section.
Answer/Explanation
Ans: 112 or 112.3 to 112.33
Question
The diagram shows a cube of side length 8cm.
(a) Calculate the length of the diagonal BS.
BS = ………………………………….. cm
(b) Calculate angle SBD.
Angle SBD = …………………………………………
Answer/Explanation
Ans:
(a) 13.9 or 13.85 to 13.86
(b) 35.1 to 35.5[4…]
Question
ABCD is a kite.
The diagonals AC and BD intersect at X.
AC = 12cm, BD = 20cm and DX:XB = 3:2 .
(a) Calculate angle ABC.
(b) Calculate the area of the kite.
Answer/Explanation
Ans:
(a) 73.7 or 73.73 to 73.74
(b) 120
Question
The diagram shows a rectangle ABCE.
D lies on EC.
DAB is a sector of a circle radius 8cm and sector angle 30°.
Calculate the area of the shaded region.
Answer/Explanation
Ans: 1.38 or 1.39 or 1.384 to 1.389
Question
The base of a rectangular tank is 1.2 metres by 0.9 metres.
The water in the tank is 53 centimetres deep.
Calculate the number of litres of water in the tank.
Answer/Explanation
Ans: 572.4
Question
The diagram shows a rectangular garden divided into different areas.
FG is the perpendicular bisector of BC.
The arc HJ has centre D and radius 20m.
CE is the bisector of angle DCB.
Write down two more statements using loci to describe the shaded region inside the garden.
The shaded region is
• nearer to C than to B
• ……………………………………………………………………………………………………………………………………
• ……………………………………………………………………………………………………………………………………
Answer/Explanation
Ans:
More than 20m from D oe
Nearer to CD than to CB oe
Question
The scale on a map is 1 : 20 000.
The area of a lake on the map is 1.6 square centimetres.
Calculate the actual area of the lake.
Give your answer in square metres.
…………………….. \(m^2\)
Answer/Explanation
Ans:
64 000
Question
A company makes solid chocolate eggs and their shapes are mathematically similar.
The diagram shows eggs of height 2 cm and 6 cm.
The mass of the small egg is 4 g.
Calculate the mass of the large egg..
Answer/Explanation
Since, the eggs are similar in shapes
So ratio of their heights are 2:6 = 1:3
Also ratio of their volumes are 1:27
Since,eggs are mathematically similar, So, their volumes are proportional to the cube of their heigths
So, Let the mass of larger egg be M.
Therefore, \((6cm\div 2cm)^3\)=\(M\div 4g\)
Simplifying ,
\(3^3=M\div 4g\)
M= 27. 4g
M= 108g
Question
The top of a desk is made from a rectangle and a quarter circle. The rectangle measures 0.8m by 1.4m. Calculate the surface area of the top of the desk.
▶️Answer/Explanation
1.62
Question
The diagram represents a rectangular gate measuring 1.5m by 3.5m. It is made from eight lengths of wood. Calculate the total length of wood needed to make the gate.
▶️Answer/Explanation
24.3(0788…)
Question
A semicircle of diameter 6 cm is cut from a rectangle with sides 6 cm and 8 cm.
Calculate the perimeter of the shaded shape, correct to 1 decimal place.
▶️Answer/Explanation
31.4 cao