iGCSE Mathematics (0580) :C5.1 Use current units of mass, length, area, volume and capacity in practical situations iGCSE Style Questions Paper 3

Question

(a) The diagram shows the position of town A and town B, on a map.

(i) Measure the length, in millimetres, of the line AB.
(ii) Measure the bearing of town B from town A.
(b) A triangular fi eld has sides of length 550m, 300m and 400m.
(i) Construct the triangle, using a ruler and compasses only.
Use a scale of 1 cm to represent 50m.
The side of length 550m has been drawn for you.

(ii) By making a suitable measurement on your diagram, calculate the area of the fi eld.
Give your answer in square metres.

Answer/Explanation

Answer:

(a) (i) 44 – 46
(ii) 231 – 235

(b) (i) Fully correct drawing with arcs
52250 to 60500 nfww

Question

The scale drawing represents the positions of 3 towns, A, B and C.
The scale is 1 centimetre represents 4 kilometres.

(a) Measure the bearing of B from A.

Answer/Explanation

Ans: 106 to 110

(b) A transmitter is placed near to the 3 towns.
(i) The transmitter is equidistant from A and B.
Using a straight edge and compasses only, construct the locus of points equidistant from A and B.

Answer/Explanation

Ans: Correct bisector of AB constructed with 2 pairs of arcs.

(ii) The transmitter is also on the bisector of angle ABC.
Using a straight edge and compasses only, construct the bisector of angle ABC.

Answer/Explanation

Ans: Correct bisector of angle ABC with arcs

(iii) Mark the position, T, of the transmitter on the scale drawing.

Answer/Explanation

Ans: T marked at intersection of their bisectors 

(c) Work out the actual distance, in kilometres, of town A from T.

Answer/Explanation

Ans: 24.4[km] to 26.0[km] 

(d) The signal from the transmitter has a range of 30 kilometres in all directions.
On the scale drawing, construct the locus of points 30 kilometres from T.

Answer/Explanation

Ans: Circle, radius 7.5(±0.2)cm centre T.

(e) Would the signal from the transmitter reach town C ?
Give a reason for your answer.

Answer/Explanation

Ans: No It is outside the circle. oe

Question

(a) Write down
(i) two factors of 12,

Answer/Explanation

Ans: At least two of 1, 2, 3, 4, 6, 12 

(ii) the next prime number after 19,

Answer/Explanation

Ans: 23 

(iii) the cube root of 64,

Answer/Explanation

Ans: 4 

(iv) two million five hundred and seven in figures,

Answer/Explanation

Ans: 2 000 507 

(v) two multiples of 75,

Answer/Explanation

Ans: e.g. 75, 150

(vi) the value of π correct to 5 significant figures.

Answer/Explanation

Ans: 3.1416 

(b) Write as a percentage.

(i) 1.63

Answer/Explanation

Ans: 163

(ii) \(\frac{3}{40}\)

Answer/Explanation

Ans: 7.5

(c) (i) Write 63521.769 correct to 1 decimal place.

Answer/Explanation

Ans: 63521.8 

(ii) Write 63521.769 correct to the nearest hundred.

Answer/Explanation

Ans: 63500 cao

(d) (i) Change 234mm into metres.

Answer/Explanation

Ans: [0].234 

(ii) Change 876m2 into square centimetres.

Answer/Explanation

Ans: 8 760 000

Question

(a) The grid shows part of the net of a cuboid.
Complete the net.

Answer/Explanation

Ans: correct net drawn 

(b) The volume of another cuboid is 60cm3.
Each side is a whole number of centimetres long.
Write down a possible set of dimensions for the cuboid.

Answer/Explanation

Ans: 

60,1,1 or 30,2,1 or 20,3,1 or
15,4,1 or 15,2,2 or 12,5,1 or
10,6,1 or 10,3,2 or 6,5,2 or
5,4,3

(c) Each side of a cube has length 2cm.
Work out the total surface area of the cube.
Give the units of your answer.

Answer/Explanation

Ans: 24 cm2

(d) Change 9cm2 into mm2.

Answer/Explanation

Ans:  900 mm2

(e) The diagram shows a triangle.

(i) Calculate the length AB.

Answer/Explanation

Ans: 7.55 or 7.549….. m

(ii) Use trigonometry to calculate angle ACB.

Answer/Explanation

Ans: 43.3 or 43.34 

(f)  

The diameter of the large circle is 13cm.
The radius of the small circle is 2cm.
Calculate the shaded area.

Answer/Explanation

Ans:  120 or 120.16 to 120.2 cm2

Question

The diagram shows the positions of two villages Dormouth, D, and Greenton, G.
The scale is 1 centimetre represents 20 kilometres.

(a) Find the distance, in kilometres, from Dormouth to Greenton.

Answer/Explanation

Ans: 126

(b) Measure the bearing of Dormouth from Greenton.

Answer/Explanation

Ans: 240

(c) Foxhill is 84 km from Dormouth.
The bearing of Foxhill from Dormouth is 105°.
Mark the position of Foxhill on the diagram. Label it F.

Answer/Explanation

Ans:Correct position on diagram 

(d) A straight road joins Dormouth to Foxhill.
A car drives from Dormouth to Foxhill at a constant speed of 54km/h.
Calculate the time it takes to complete the 84km journey.
Give your answer to the nearest minute.

Answer/Explanation

Ans: 1 hour and 33 min 

(e) Change 54 km/h to m/s .

Answer/Explanation

Ans: 15

Question 

 

 

Question

(a) Ten students take a physics examination and a mathematics examination.
Their scores are recorded in the table below.

(i) Complete the scatter diagram.
The first six points have been plotted for you.

Answer/Explanation

Ans: 4 points correctly plotted 

(ii) What type of correlation is shown by the scatter diagram?

Answer/Explanation

Ans: positive 

(iii) On the grid, draw a line of best fit.

Answer/Explanation

Ans: correct ruled straight line 

(iv) Another student scored 52 in the mathematics examination.
Use your line of best fit to estimate this student’s score in the physics examination.

Answer/Explanation

Ans: 74

(b) This graph can be used to convert between pounds (lb) and kilograms (kg).

Use the graph to convert
(i) 50 pounds to kilograms,

Answer/Explanation

Ans: 22 < Ans ≤ 23 

(ii) 275 kilograms to pounds.

Answer/Explanation

Ans: 590 ≤ ans ≤ 620 

Question

The diagram shows a field in the shape of a trapezium.
AB = 150m, BC = 90m and CD = 120m.
Angle ABC = angle BCD = 90°.
(a) Calculate the area of the field.
\(……………………………………..m^{2}\)
(b) (i) Show that AD = 95m, correct to the nearest metre .
(ii) A fence is built around the perimeter of the field.
It costs \($48\) to build each 5-metre section of the fence.
Calculate the cost of building this fence.
\($ …………………………………………\)

Answer/Explanation

(a) 12150
(b)\((i)AD=\sqrt{90^{2}+(150-120)^{2}}\)
=94.9 OR 94.8
(ii) 4368

Question

(a) A baker puts some cakes in the oven at 5.50 pm.
The cakes take 20 minutes to bake.


Complete the clock diagram to show the time when the cakes are baked.
(b) A recipe uses 550 g of flour to make 8 cakes.

(c)
Work out the amount of flour needed to make 360 cakes.
Give your answer in kilograms.
……………………………………… kg
Work out which bag of flour is the best value.
Show all your working.
Bag …………………………………………
d) One cake costs 24 cents to make.
The baker sells each cake for 65 cents.
Calculate the percentage profit the baker makes on each cake.
……………………………………….%
(e) The baker asks some customers if they like lemon cake (L) and if they like chocolate cake (C).
The Venn diagram shows the results.


(i) Complete the statement.
n(E) = ……………..
(ii) Work out the fraction of the customers who like lemon cake or chocolate cake but not both.
………………………………………….
(iii) Use set notation to complete the statement.
{Jai, Nera} = …………………..
(iv) What does the Venn diagram show about Taj?
……………………………………………………………………………………………………………………………

Answer/Explanation

(a) 10 past 6 shown on clock face diagram
(b) 24.75
(c) B
With correct comparisons made of
the 3 bags with suitable accuracy
shown
(d) 171 or 170.8…
(e)(i) 12
(ii)\( \frac{3}{4}\) or equivalent fraction.
(iii) L ∩C
(iv) Correct statement

Question

The diagram shows a rectangle and two semicircles with diameters AC and BD.
This diagram is a scale drawing of a running track.
AC = BD = 60m
AB = CD = 120m

    (a) (i) Complete the statement.

1 centimeter represents ___ meters. [2]

(ii) Work out the total length of the running track in meters.

 ___ m [3]

(iii) Shreva walks at 1.4m/s.

Work out how long it will take her to walk once around the track.
Give your answer in minutes and seconds, correct to the nearest second.

___ minutes ___ seconds [3]

    (b) Talan completes one lap of the track every 80 seconds.

(i) Work out how many laps he can complete in one hour.[2]

(ii) Naima completes one lap of the track every 88 seconds.
Talan and Naima start running from point A on the track at the same time.
They each complete a number of laps of the track.

Work out the smallest number of laps they each complete before they are both at point A again at the same time.

Talan completes ___ laps and Naima completes ___ laps. [3]

Answer/Explanation

Ans:

9(a)(i) 15

9(a)(ii) 428 or 429 or 428.4 or 428.5 or 428.49 to 428.52

9(a)(iii) 5 minutes 6 seconds

9(b)(i) 45

9(b)(ii) 11, 10

Question

The diagram shows a rectangular field, PQRS.
QR = 120m, PQ = 50m and P is due North of Q.
Bill and Said run from P to R.
Bill runs along the sides PQ and QR.
Said runs directly from P to R.
(a) Calculate how far
(i) Bill runs,

Answer/Explanation

Ans: 170

(ii) Said runs.

Answer/Explanation

Ans: 130

(b) Bill takes 34 seconds to reach R.
Calculate Bill’s average speed.

Answer/Explanation

Ans: 5

(c) Said runs at 4m/s.
Who arrives at R first and by how many seconds?

Answer/Explanation

Ans: Said by 1.5 secs 

(d) (i) Use trigonometry to calculate the size of the angle marked y.

Answer/Explanation

Ans: 67.4° 

(ii) Find the bearing of R from P.

Answer/Explanation

Ans: 113° or 112.6° 

(e) Calculate the area of the field in square kilometres.
Give your answer in standard form.

Answer/Explanation

Ans: 6 × 10–3

Question

 Mr and Mrs Clark and their three children live in the USA and take a holiday in Europe.
(a) Mr Clark changes \(\$500\) into euros when the exchange rate is euro 1= \(\$1.4593\).
Calculate how much he receives.
Give your answer correct to 2 decimal places.

(b) Tickets for an amusement park cost €62 for an adult and €52 for a child.
Work out the cost for Mr and Mrs Clark and their three children to visit the park.

(c) Mr Clark sees a notice:

(d) Mrs Clark buys 6 postcards at €0.98 each.
She pays with a €10 note.
Calculate how much change she will receive.

(e)Children under a height of 130 cm are not allowed on one of the rides in the park.
Helen Clark is 50 inches tall.
Use 1 inch = 2.54 cm to show that she will not be allowed on this ride.

Answer/Explanation

(a) euro 1=\(\$1.4593\)

using unitary method, 

\(\$1.4593\)=euro 1

Therefore, \(\$500\)= \(\frac{1}{1.4593}\times 500\)

= 342.6300

After rounding it off to 2 decimal places,

324.63

(b) Tota cost= 3. (cost for child)+(2. cost for adult)

= 3.(52)+2.(62)

=156+124

=280 euro 

(c) Percentage=\(\frac{Actual cost}{Calculated cost}\times 100\)

 = \(\frac{200}{280}\times 100\)

 = 71.4

(d) Total cost of postard = 6\(\times\)0.98

= \(5.88 euro\)

 Change she will receive = \(10 euro\)- \(5.88 euro\)

= \(4.12 euro\)

(e) Height in cm of Helen clark :

1 inch = 2.54 cm 

So, 50\(\times \) 2.54cm 

= 127.00 cm 

Therefore, the height of Helen Clark is 127 cm 

As , her height is 127 cm which is less than 130cm , So she would not be allowed in the park

Question

             

The diagram shows a block of stone in the shape of a prism of length $42 \mathrm{~cm}$. The cross-section is a trapezium $A B C D$. $A B=19 \mathrm{~cm}, A D=10 \mathrm{~cm}, D C=13 \mathrm{~cm}$ and angle $A D C=90^{\circ}$.
(a) Calculate
(i) the perimeter of the rectangular face $A B F E$,

(ii) the area of the cross-section ABCD,

(iii) the volume of the block of stone.

(b) The mass of 1 cubic centimetre of the stone is 4 grams. Calculate the mass of the block. Give your answer in kilograms.

▶️Answer/Explanation

(a) (i) 122

(ii) 160

(iii) 6720 or their (a)(ii) × 42 evaluated

(b) 26.88 or their (a)(iii) × 0.004 evaluated or 26.9

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