Edexcel IGCSE Maths B Paper 2 June 2023 question paper 4MB1/02R

On Monday, Tisam buys 600 watermelons in India to sell in the UK.

On Tuesday, Tisam splits 200 of the watermelons each into 8 slices.

She sells each slice for £0.60

She sells all the slices by the end of the day.

Work out how much money Tisam receives from the sale of the watermelon slices on Tuesday.

On Wednesday, Tisam sells 60% of the remaining watermelons.

She sells them for £1.40 each.

Work out how much money Tisam receives from the sale of the watermelons on Wednesday.

Tisam gives away for free the watermelons she has left.

Tisam bought the 600 watermelons at a cost of 90 rupees each.

The cost to send the watermelons to the UK was £700

Using an exchange rate of

1 rupee = £0.0097

calculate the percentage profit, to one decimal place, that Tisam makes from the sale of the watermelons.

E is the universal set and A, B and C are three sets.

E = { p, q, r, s, t, u }

A = { p, r, t }

B = { q, r, s }

List the elements of the set A Bʹ

Given that

n(C) = 3

n(A C) = 2

n(B C) = 1

list all the possible sets C

Solve 4x – 3 ≤ 11

On the grid opposite, by drawing suitable straight lines and using shading, show the region R that satisfies the inequalities

Label the region R

Turn over for a spare grid if you need to redraw your inequalities.

Only use this grid if you need to redraw your inequalities.

x = 4.2 × 10⁵ and y = 6 10^–100

Write x as an ordinary number.

Calculate xy

Give your answer in standard form.

Using the values of x and y above, write the following in order of size

Start with the smallest value.

Figure 1 shows a framework of wooden beams, with ADC a straight line.

Calculate, giving your answer to the nearest metre, the length of AC

Calculate, giving your answer to one decimal place, the size, in degrees,

A fourth beam DE is added to the framework.

The point E lies on AB and is such that DE is perpendicular to AB

Calculate the length, in metres to 3 significant figures, of DE

Triangles A and B are shown on the grid opposite.

Describe fully the single transformation that maps triangle A onto triangle B

Triangle A is transformed to triangle C under the translation 81

On the grid, draw and label triangle C

Triangle A is transformed to triangle D under the transformation with the matrix M where

On the grid, draw and label triangle D

Triangle B is transformed to triangle E by a rotation of 180° about the point (0, 1)

On the grid, draw and label triangle E

Find the matrix which represents the transformation that maps triangle A onto triangle E

Turn over for a spare grid if you need to redraw your triangles.

Only use this grid if you need to redraw your triangles.

The diagonals AC and BD meet at the point E

Find as a column vector BC →

The point E has coordinates (6, 4)

Given that AE:AC = 3: 5

find the coordinates of the point A

Given that ABCD is a kite,

find the coordinates of the point D

The function f is such that

State a value that cannot be in the range of the function f

Solve 16 f(x) = x + 8

Show that ff(x) = f^–1(x)

State a value that cannot be in the domain of the function f^–1

Evaluate fff(2)

The curve C has equation

Find, to one decimal place, the coordinates of the stationary point of C

Complete the table of values for y

Give your values of y to one decimal place where necessary.

On the grid opposite, plot the stationary point and plot the points from your completed table. Join these to form a smooth curve.

By drawing a suitable straight line on the grid, find estimates, to one decimal place, of the solutions to the equation

within the range 0 < x 5

Turn over for a spare grid if you need to redraw your curve.

Only use this grid if you need to redraw your curve.

Hugo is learning a new game. Each time he plays the game the possible outcomes are that he may win, draw or lose.

The first time Hugo plays the game the probability that

Show that the probability that Hugo loses the first game is

The second time Hugo plays the game the probability that

Use the information to complete the tree diagram opposite.

Hugo plays the game twice.

Find the probability that he draws both of his games.

Hugo scores points each time he plays.

He scores 3 points if he wins, 2 points if he draws and 1 point if he loses.

After 2 games Hugo has 3 points.

Find the probability that Hugo lost the first game.

Turn over for a spare copy of the tree diagram.

Only use this diagram if you need to redraw your tree diagram.

Figure 3 shows triangle ABC

show that x is a solution of the equation

where k is a constant that should be stated as a simplified surd.

Given that ABC is obtuse

use parts (b) and (c) to find the exac lue of