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

Rory buys and sells jewellery.

Rory buys a necklace for $180

He sells the necklace for $230

Calculate, to 3 significant figures, Rory’s percentage profit.

Rory sells a bracelet for $203

This price represents a 16% profit on his cost price.

Calculate the cost price of the bracelet.

Rory travelled by plane from New York to Dubai to buy some jewellery.

The total flight time for the journey was 12 hours 48 minutes.

The average speed for the journey was 860 km/h

Calculate the total distance, in kilometres, travelled by the plane.

Rory bought some earrings for a total cost of 91 750 dirhams.

Using the exchange rate,

calculate the total cost of the earrings in dollars.

Write 76 000 000 in standard form.

Write 8.310^–4as an ordinary number.

Calculate (310¹⁴⁷) (610¹²²)

Give your answer in standard form.

Write 1.610⁴¹as a product of its prime factors.

Show your working clearly.

Figure 1 shows a solid right circular cone.

The radius of the base of the cone is 8 cm.

The volume of the cone is 320πcm³

The total surface area of the cone is kπcm²

Calculate the value of k

Trapeziums P and Q are drawn on the grid opposite.

Describe fully the single transformation that maps trapezium P onto trapezium Q

On the grid, draw and label trapezium A

Trapezium P is transformed to trapezium B by a rotation of 90° clockwise about the point (5, 2)

On the grid, draw and label trapezium B

Trapezium C is the image of trapezium Q under the transformation with matrix M where

On the grid, draw and label trapezium C

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

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

Figure 2 shows right triangular prism ABCDEF

AB = 5 cm DF = 8 cm AF = 7 cm CBA = 90°

Calculate the volume, in cm³ to the nearest whole number, of the triangular prism.

Figure 3 shows a shaded shape made by removing triangle PTQ from rectangle PQRS

QR = 12 cm SR = 25 cm PTQ = 90° TQR = 20°

Calculate the perimeter, in cm to the nearest whole number, of the shaded shape.

Ted has two boxes of buttons, Box A and Box B

There are 20 buttons in Box A and 20 buttons in Box B

There are 13 white buttons in Box A

There are 9 white buttons in Box B

Ted takes at random a button from Box A and a button from Box B

Complete the probability tree diagram.

Calculate the probability that Ted takes at least one white button.

Ted also has a bag of buttons.

There are 30 buttons in the bag.

There are x white buttons in the bag.

Ted takes at random a button from Box A, a button from Box B and a button from the bag.

The probability that of the 3 buttons Ted has, 2 of the buttons are white is

Work out the value of x

Show clear algebraic working.

The function g is defined as

Find the value of x that must be excluded from the domain of g

Solve g(x) = 5

The function f is defined as

Express the inverse function f^–1 in the form f^–1:x ...

Complete the table of values for y = x³ – 5x – 3

On the grid opposite, plot the points from your completed table and join them to form a smooth curve.

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

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

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

Solve the inequality 5y – 7 2y – 13

Hence, represent on the number line at the top of the next page, the values of y

Solve the inequality 4x² + 4x – 35 < 0

Hence find the values of x for which

–5 –4 –3 –2 –1 0 1 2 3 4 5

Show your working clearly.

find the value of x, giving your answer as a fraction in its simplest form. Show your working clearly.

A curve C and a straight line L are drawn on a grid.

C has equation y = 5x² – 16x – 5

L has equation y + 5x = 7

Find the coordinates of the points of intersection of C and L

Show clear algebraic working.

P is the point on the curve with equation y = 5x² – 16x – 5 with x coordinate 2

The line Q is the tangent to the curve at the point P

The line Q crosses the x‑axis at the point X and the y‑axis at the point Y The point M lies on Q and is such that XM = MY

Calculate the coordinates of the point M

Give your coordinates as exact values.

Figure 4 shows a regular hexagon ABCDEF

find the perimeter, in cm, of the hexagon.

Figure 5 shows a shape AGHIJKLBCDEF made from a regular octagon GHIJKLBA and the regular hexagon ABCDEF from part (a).

Work out the length, in cm to one decimal place, of the straight line KF