Cambridge CIE IGCSE Past Papers and solutions.

Questions and Worked Solutions for IGCSE 2021 0580/43 Oct/Nov Paper 4.

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IGCSE 2021 0580/43 Oct/Nov Questions (pdf)

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- The diagram shows three triangles, T, A, and B, drawn on a 1cm
^{2}grid.

(a) Describe fully the single transformation that maps triangle T onto triangle A.

(b) (i) Describe fully the single transformation that maps triangle T onto triangle B.

(ii) Calculate the distance that each point of triangle T moves when it is mapped onto triangle B - (a) A, B and P are points on a circle, centre O and angle OBA = 38°.

Find angle APB.

CDEF is a cyclic quadrilateral and FC = FE.

TU is a tangent to the circle at C and angle TCF = 50°.

Find

(i) angle EFC,

(ii) angle CDE. - The diagram shows a prism.

The cross-section of the prism is a trapezium with CD parallel to AB and AC = BD.

AB = 10 cm, CD = 4 cm and the height of the trapezium is 5cm.

The volume of the prism is 525cm^{3}.

(i) The prism is made of iron.

1cm^{3}of iron has a mass of 7.8 g.

Calculate the mass of the prism.

Give your answer in kilograms.

(ii) Calculate the length of the prism.

(iii) Calculate the total surface area of the prism

(iv) In a mathematically similar prism, the height of the trapezium is 10cm.

Calculate the volume of this prism.

(b) A cuboid measures 10cm by 4cm by 6cm.

Each side is measured correct to the nearest centimetre.

Complete the inequality for the volume, V, of this cuboid.

- (a) Solve the simultaneous equations.

You must show all your working - (a) $500 is invested at a rate of 3% per year.

Calculate the total interest earned at the end of 7 years when

(i) simple interest is paid,

(ii) compound interest is paid.

(b) The value of a car decreases exponentially by 10% each year.

The value now is $6269.40 .

Calculate the value of the car 3 years ago - (a) Calculate AD

(b) Calculate angle BAC and show that it rounds to 40.42°, correct to 2 decimal places

(c) Calculate the area of the quadrilateral ABCD.

(d) Calculate the shortest distance from B to AC. - (a) Amir buys 3 cakes that cost c cents each and 2 loaves of bread that cost (2c - 11) cents each.

He spends a total of $5.87 .

Find the value of c.

(b) A bottle of water costs $w.

A bottle of juice costs $(w + 1).

Alex spends $22 on bottles of water and $42 on bottles of juice.

The number of bottles of water is equal to the number of bottles of juice.

Find the value of w

(c) Alicia walks a distance of 9km at a speed of x km/h.

She then runs a distance of 5km at a speed of (2x + 1) km/h.

The total time Alicia takes is 2.5 hours.

(ii) Work out Alicia’s running speed.

You must show all your working. - (a) Jean asks 600 people to choose their favourite sport.

The pie chart shows some of this information.

(i) Show that 100 people choose tennis.

(ii) Work out how many people choose rugby

(iii) 125 people choose cricket and the rest choose swimming.

Complete the pie chart to show this information

(b) The heights of some plants are measured:

- smallest height = 0.6cm
- range = 8.1cm
- median = 5.2cm
- lower quartile = 3.4cm
- interquartile range = 4.1cm.

On the grid, draw a box-and-whisker plot to show this information

- f(x) = x(x - 1)(x - 2)

(a) Find the coordinates of the points where the graph of y = f(x) crosses the x-axis - a) Sarah spins a fair four-sided spinner numbered 0, 1, 1 and 3.

(i) What number is the spinner most likely to land on?

(ii) Sarah spins the spinner twice.

Find the probability that it lands on the number 1 both times.

(b) Scott takes an examination.

The examination is in two parts, a theory test and a practical test.

Both parts must be passed to pass the examination.

The probability that Scott passes the theory test is 0.9 .

The probability that Scott passes the practical test is 0.8 .

Find the probability that

(i) Scott passes the examination,

(ii) Scott passes the theory test or the practical test but not both. - f(x) = 2x - 1

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