Edexcel Jan 2020 IGCSE, 4MA1/2HR questions (pdf)
- (a) Write 517 × 52 as a single power of 5
(b) Write 800 as a product of its prime factors. Show your working clearly.
- The table gives information about the amount of money, in £, that Fiona spent in a grocery store each week during 2019
Work out an estimate for the total amount of money that Fiona spent in the grocery store during 2019
- Three tins, A, B and C, each contain buttons.
Tin A contains x buttons.
Tin B contains 4 times the number of buttons that tin A contains. Tin C contains 7 fewer buttons than tin A. The total number of buttons in the three tins is 137
Work out the number of buttons in tin C.
- The diagram shows a rectangle and a diagonal of the rectangle.
Work out the length of the diagonal of the rectangle.
Give your answer correct to 1 decimal place
- A plane takes 3 hours 36 minutes to fly from the Cayman Islands to New York. The plane flies a distance of 2470 km.
Work out the average speed of the plane in km/h.
Give your answer correct to the nearest whole number.
- Use ruler and compasses only to construct the perpendicular bisector of the line AB. You must show all your construction lines.
- Solve the simultaneous equations
3x + 5y = 6
7x – 5y = –11
Show clear algebraic working
- Hamish buys a new car for $20 000
The car depreciates in value by 19% each year.
Work out the value of the car at the end of 3 years.
Give your answer to the nearest $.
- The diagram shows a box in the shape of a cuboid.
The box is put on a table.
The face of the box in contact with the table has length 1.2 metres and width x metres.
The force exerted by the box on the table is 27 newtons.
The pressure on the table due to the box is 30 newtons/m2
Work out the value of x.
- The table shows information about the surface area of each of the world’s oceans.
(a) Work out the difference, in square kilometres, between the surface area of the Atlantic Ocean and the surface area of the Indian Ocean. Give your answer in standard form.
The surface area of the Pacific Ocean is k times the surface area of the Arctic Ocean.
(b) Work out the value of k.
Give your answer correct to the nearest whole number.
- (a) Write down the integer values of x that satisfy the inequality –2 < x ≤ 4
The region R, shown shaded in the diagram, is bounded by three straight lines.
(b) Write down the three inequalities that define the region R.
- The diagram shows two congruent isosceles triangles and parts of two congruent regular polygons, X and Y.
The two regular polygons each have n sides.
Work out the value of n.
- The diagram shows a prism ABCDEFGH in which ABCD is a trapezium with BC parallel to AD and CDEF is a rectangle.
BC = 7 cm AD = 12 cm DE = 10 cm
The height of trapezium ABCD is h cm
The volume of the prism is 608 cm3
Work out the value of h.
- Max kept a record of the marks he scored in each of the 11 spelling tests he took one term.
Here are his marks.
18 5 7 12 11 18 15 16 17 13 14
Find the interquartile range of the marks.
15 (a) Complete the table of values for y = x2 - x/2 - 3
(b) On the grid, draw the graph of y = x2 - x/2 - 3 for values of x from –3 to 3
- Cody has two bags of counters, bag A and bag B.
Each of the counters has either an odd number or an even number written on it.
There are 10 counters in bag A and 7 of these counters have an odd number written on them. There are 12 counters in bag B and 7 of these counters have an odd number written on them.
Cody is going to take at random a counter from bag A and a counter from bag B.
(a) Complete the probability tree diagram.
(b) Calculate the probability that the total of the numbers on the two counters will be an odd number.
Harriet also has a bag of counters.
Each of her counters also has either an odd number or an even number written on it.
Harriet is going to take at random a counter from her bag of counters.
The probability that the number on each of Cody’s two counters and the number on
Harriet’s counter will all be even is 3/100
(c) Find the least number of counters that Harriet has in her bag. Show your working clearly.
- Some students in a school were asked the following question.
“ Do you have a dog (D), a cat (C) or a rabbit (R)?”
Of these students
28 have a dog
18 have a cat
20 have a rabbit
8 have both a cat and a rabbit 9 have both a dog and a rabbit x have both a dog and a cat
6 have a dog, a cat and a rabbit
5 have not got a dog or a cat or a rabbit
(a) Using this information, complete the Venn diagram to show the number of students in each appropriate subset.
Give the numbers in terms of x where necessary.
Given that a total of 50 students answered the question,
(b) work out the value of x.
(c) Find n(C' ∩ D')
- APB and CPD are chords of a circle. AP = 9 cm PB = 6 cm CP = 8 cm
Calculate the length of PD.
- (a) Solve
Show clear algebraic working.
(b) Solve the inequality 5y2 – 17y ≤ 40
- The diagram shows two similar vases, A and B.
The height of vase A is 9 cm and the height of vase B is 13 cm.
surface area of vase A + surface area of vase B = 1800 cm2
calculate the surface area of vase A.
- (a) Simplify fully
(b) Find an expression for n in terms of y.
Show clear algebraic working and simplify your expression.
- The first term of an arithmetic series S is –6
The sum of the first 30 terms of S is 2865
Find the 9th term of S.
- Express 7 – 12x – 2x2 in the form a + b(x + c)2 where a, b and c are integers.
- L1 and L2 are two straight lines.
The origin of the coordinate axes is O.
L1 has equation 5x + 10y = 8
L2 is perpendicular to L1 and passes through the point with coordinates (8, 6)
L2 crosses the x-axis at the point A.
L2 intersects the straight line with equation x = –3 at the point B.
Find the area of triangle AOB.
Show your working clearly.
- N is a multiple of 5
A = N + 1
B = N – 1
Prove, using algebra, that A2 – B2 is always a multiple of 20
- The diagram shows trapezium OACB.
N is the point on OC such that ANB is a straight line.
Find ON as a simplified expression in terms of a and b.
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