Edexcel IGCSE Maths B Paper 1 January 2023 question paper 4MB1/01R

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

6 = 2³3⁴5³11

B = 2²3³5⁴

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

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.

Give your answer in its simplest form.

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

Show clear algebraic working.

The diagram shows a square piece of card from which two semicircles are cut out.

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.

Solve the simultaneous equations

x + 7y = 3

5 x – 4 y = 6.4

Show clear algebraic working.

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

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

Find n(D E)

Find n(D E′)

Find n(F′)

Find n([D F] E′)

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.

20

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

21(x + 2) is a factor of 6x³ + 31x² + kx + 30

Use the factor theorem to show that k = 53

Factorise fully 6x³ + 31x² + 53x + 30

22

find the value of x

Simplify 7y⁰where y 0

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

The diagram shows a quadrilateral OABC in which → → →

OA = a OC = c CB = 3 a

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 →

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.

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.

Time (t minutes)	Frequency
0 t 5	10
5 t 15	7
15 t 25	5
25 t 30	6
30 t 40	12

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.

Distance (k kilometres)	Frequency
0 k 10	4
10 k 15
15 k 30
30 k 60	6

None of the people travelled more than 60 km.

Complete the histogram and the frequency table.