Cambridge IGCSE-0607/43-May/June 2018

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Gunter keeps chickens.
He records the number of eggs he collects each day for 31 days.
These are the results.
a) Write down the range of the numbers of eggs.
(b) Find the inter-quartile range.
(c) Write down the mode.
(d) Find the median.
(e) Find the mean.
(f) Explain why the mode is not the best measure of average to represent these results.
Flavia makes china cats.
They each cost $22.60 to make.
(a) Flavia sells some of them to Ari.
She makes a profit of 35% on each cat.
Calculate the price Ari pays for each cat.
(b) Ari sells each cat for $43.
Calculate Ari’s percentage profit.
(c) Jean buys 92 of Flavia’s cats.
This is 15% more than the number Ari bought.
Calculate the number of cats that Ari bought.
(d) Jean bought the cats for $32 each.
He sells some of the cats for $45 each.
For the rest of the cats he reduces the price by 5% each day.
Find the number of reductions he has made when the price first falls below $32.
Draw the image of triangle A after a translation by the vector 3
-7 c m. [2]
(b) Draw the image of triangle B after a stretch, factor 3 and the x-axis invariant. [2]
(c) Describe fully the single transformation that maps triangle A onto triangle B.

Hamid records the population density, p persons/km2, in ten regions of the city in which he lives.
He also records the distance, dkm, of each region from the city centre.
The results are shown in the table.
Complete the scatter diagram.
The first four points have been plotted for you.
What type of correlation is shown in your scatter diagram?
(ii) Which region fits this model of correlation least well?
Calculate the equation of the regression line in the form p = md + c.
(ii) Use this equation to estimate the population density of a region 2.4km from the city centre.
(iii) Why would it not be sensible to use this equation to estimate the population density of a region
6.3km from the city centre?
On the diagram, sketch the graph of y = f(x) for values of x between -6 and 6. [3]
(b) Find the co-ordinates of the local maximum.
(c) Find the equations of the three asymptotes to the graph of y = f(x) .
(d) The equation f(x) = k has no solutions.
Find the range of values of k.
Solve f(x) = g(x).
(ii) Solve the inequality f(x) 2 g(x).
A ship sails 80 km on a bearing of 065° from A to B.
It then sails 140km on a bearing of 125° from B to C.
(a) Find AB as a column vector with the components in kilometres.
Find AC as a column vector with the components in kilometres.
The ship sails directly back from C to A.
Using your answer to part (b), calculate
(i) the distance the ship sails from C to A,
(ii) the bearing of A from C.
ABCDEF is a solid triangular prism.
(a) Calculate the volume of the prism.
(b) Calculate the total surface area of the prism.
ABCDEF is made of metal and has a mass of 2170kg.
It is melted down and made into prisms similar to ABCDEF.
Each of these prisms has a mass of 2.17kg.
Calculate the total surface area of each of these smaller prisms.
Rashid takes a language examination that has three tests.
The probability that Rashid passes the Listening and Reading test is 0.9 .
The probability that Rashid passes the Speaking test is 0.8 .
The probability that Rashid passes the Writing test is 0.7 .
(a) Complete the tree diagram to show the probabilities of passing (P) and failing (F) each part.
Listening Speaking Writing
(b) To pass the whole examination Rashid has to pass all three tests.
Calculate the probability that he passes the whole examination.
(c) If Rashid only fails one test, he can take that test again.
Calculate the probability that Rashid needs to take one test again.
Complete the table for the sequence of patterns above.
Find the number of each colour of tiles in
(i) Pattern 15,
(ii) Pattern 20.
Find an expression, in terms of n, for the total number of tiles in Pattern n.
Solve this equation.
Give your answers correct to 1 decimal place.
(iii) Find the time taken for the journey from Rome to Geneva in hours and minutes.
A, B, C and D are points on the circle.
ABX, CDX, AYD and BYC are straight lines.
(a) (i) Explain why triangle ADX is similar to triangle CBX.
(ii) Use part (a)(i) to show that XA # XB = XC #
(c) Find the value of these fractions
f(x) = 2x + 1 g(x) = 4 – 3x h(x) = 2x
– 1
(a) Find h(-2).
(b) Find g-1(x).
g-1(x) =
(c) Find g(f(3)).
(d) Find and simplify g(g(x)).
(e) Find h-1(7).
(f) Write as a single fraction in its simplest form.