4MB1/01R — January 2023 (Edexcel IGCSE Maths): Past Paper

Write 48 seconds as a fraction of 1 day. Give your answer in its simplest form.

Here are the numbers of items that the last 9 people who visited a shop bought. 6 1 13 20 2 4 14 11 20 Find the median of these numbers of items.

Write down a formula for the nth term of the sequence. 7 11 15 19 23

Simplify fully (125a ) 9 3

Given that y = 21x 2 – x dy find dx dy = ……………dx

Given that y = 21x 2 – x dy find dx dy = dx

A = 23 × 34 × 53 × 11 B = 22 × 33 × 54 Find the lowest common multiple (LCM) of 2A and 7B Give your answer as a product of prime factors.

Without using a calculator, and showing all your working, evaluate 2 4 3 +2 3 5 Give your answer as a mixed number in its simplest form.

A farmer keeps cows, pigs and sheep. The ratio of the number of cows he keeps to the number of pigs he keeps is 2 : 3 The ratio of the number of pigs he keeps to the number of sheep he keeps is 7 : 11 The farmer keeps 42 cows. Work out the number of sheep the farmer keeps.

Solve 3(2 – x)² – 75 = 0 Show clear algebraic working. x = ……………Solve 3(2 – x)² – 75 = 0 Show clear algebraic working. x =

Simplify + − 4 x 3x 5 x Give your answer in its simplest form.

A = y w = 21.7 to one decimal place x = 12 to the nearest whole number y = 20 to the nearest ten Find the lower bound for the value of A Show your working clearly.

M varies inversely as the cube of p M = 0.8 when p = 25 Find a formula for M in terms of p

Solve x + 3 2x − 1 + =5 7 4 Show clear algebraic working. x =

The diagram shows a square piece of card from which two semicircles are cut out. 5 cm 5 cm Diagram NOT accurately drawn 15 cm The square has a side of length 15 cm. Calculate the area, in cm² to 3 significant figures, of the piece of card left when the semicircles are cut out cm²

Solve the simultaneous equations 9x + 7y = 3 5x – 4y = 6.4 Show clear algebraic working. x = y =

The diagram shows trapezium ABCD in which AB = 16 cm DC = 20 cm ∠BCD = 68° ∠BAD = ∠CDA = 90° Calculate the area, in cm² to 3 significant figures, of trapezium ABCD cm²

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: A, B, D, C · Figure values: 16, 68°, 20.

The Venn diagram shows the sets D, E and F where the numbers represent numbers of elements. E D E 7 1 3 2 F

Find n(D ∪ E)

Find n(D ∩ E′)

Find n(F′)

Find n([D ∪ F ] ∩ E′)

Make b the subject of a = b−d

In the diagram, ABCD is a trapezium and EDF is an isosceles triangle with DE = DF EDC and GADF are straight lines. ∠GAB = 106° Calculate the size, in degrees, of ∠DEF Give reasons for each stage of your working. ° ∠DEF =

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: F, D, C, E, A, B, G · Figure values: 106°.

A B D C The diagram shows a quadrilateral ABCD

Construct the locus of all points inside the quadrilateral that are 5 cm from D

Using ruler and compasses only and showing all your construction lines, construct the locus of all points inside the quadrilateral that are equidistant from AB and BC

Construct the locus of all points inside the quadrilateral that are 3 cm from BC The region R consists of all the points inside the quadrilateral that are more than 5 cm from D, nearer to BC than to AB and more than 3 cm from BC

Show, by shading, the region R Label the region R

(x + 2) is a factor of 6x 3 + 31x 2 + kx + 30

Use the factor theorem to show that k = 53

Factorise fully 6x 3 + 31x 2 + 53x + 30

⎛ 3 4⎞ ⎛ −2 3⎞ ⎛ 7 x⎞ B= 4 −1 A= 2 −3 C= 2 4

Find 4A – 2B Given the determinant of BC is 20

find the value of x x =

Simplify 7y 0 where y > 0 22 × 152 x × 35 x ( x − 3) × 3x + 3 × 4 x −1

Solve 2x = 813 x =

The diagram shows a solid right square‑based pyramid ABCDE The volume of the pyramid is 1000 cm³ The pyramid is standing with its square base, ABCD, on a horizontal table. The square base has side 10 cm. X is the midpoint of the side AB Calculate the size, in degrees to the nearest degree, of ∠CEX °

Labels in the original figure: E, D, A, X, C, B · Figure values: 10, 10.

B P Diagram NOT M accurately drawn 3a A a O c C The diagram shows a quadrilateral OABC in which → → → OA = a OC = c CB = 3a The point M lies on OB such that OM : MB = 7 : 3 The point P lies on AB such that CMP is a straight line. →

Find, in terms of a and c, simplifying your answer, the vector CM → CM =

Using a vector method, and showing your working clearly, find AP : PB in the form x : y where x and y are integers. Show your working clearly. AP : PB =

Jenny has a shop. One Monday, each of the 40 people who went in Jenny’s shop were asked how long they were in the shop. The table below shows information about the results.

Calculate an estimate for the mean length of time, in minutes, that these people were in the shop

The incomplete table and the incomplete histogram give information about the number of kilometres each of the 40 people had travelled to get to the shop.

None of the people travelled more than 60 km. Frequency density 0 10 20 30 40 50 60 Distance (k kilometres)

Complete the histogram and the frequency table.