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

The nth term of a sequence is given by 6n² 5

Find the difference between the 2nd term and the 4th term of the sequence.

Find the Highest Common Factor (HCF) of 60 and 165

Show your working clearly.

Factorise fully 6af 30 f²

Without using a calculator and showing all your working, calculate

Give your answer as a mixed number in its simplest form.

Solve the inequality 5x 3x + 15

Calculate 4 2. 10⁷² 5 5. 10⁷⁵

Give your answer in standard form.

The price of a holiday is reduced by 4% in a sale.

Haniya pays $600 of the sale price when she books the holiday.

She pays the remainder of the sale price in 4 equal monthly payments of $180

Calculate the price of the holiday before the sale.

The straight line L₁ has equation y + 4x = 5

The straight line L₂ is parallel to L₁ and passes through the point (2, ‒6)

Find the equation for L₂ in the form y = mx + c

Quadrilateral A and quadrilateral B are drawn on a grid.

Quadrilateral B is the image of quadrilateral A under a single transformation.

Describe fully this single transformation.

Without using a calculator and showing your working clearly, find the value of the integer a so that

Write down the value of a⁰ where a > 0

Simplify fully 2w² 11w⁵

A, B, C and D are points on a circle.

EDF is the tangent to the circle at the point D

Angle BDF = 75°

Calculate, giving your reasons, the size, in degrees, of BCD

v= 8.91 to 3 significant figures.

u = 5.82 to 3 significant figures.

t = 9 to 1 significant figure.

Calculate the lower bound, to 3 significant figures, of a

Show your working clearly.

The diagram shows a regular pentagon ABCDE and three sides, FE, EG and GH, of a regular n-sided polygon.

AB is horizontal.

EG is vertical.

Calculate the value of n

The diagram shows a sphere of radius r cm and a right circular cone with base radius r cm and vertical height 20 cm.

The volume of the sphere is 1.5 times the volume of the cone.

Find the value of r

P is inversely proportional to the square root of W

P = 1600 when W = 1.96

Find the value of W when P = 800

Quadrilateral A is transformed to quadrilateral B under a reflection in the line y = − x

Quadrilateral C is the image of quadrilateral A under the matrix N

Find the matrix N

The diagram shows two mathematically similar solids A and B

The volume of solid A is 1125 cm³

The volume of solid B is 576 cm³

Given that

surface area of solid A + surface area of solid B = 3198 cm²

calculate the surface area of solid B

The quadrilateral ABCD is a scale drawing of Simon’s garden.

There is a tree at the point X and a tree at the point Y

Construct the locus of all points inside the quadrilateral that are 10 metres from C

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

Construct the locus of all points inside the quadrilateral that are 6 metres from AB

Simon is going to place a light in the garden so that it is closer to X than to Y, more than 6 metres from AB and more than 10 metres from C

Show, by shading, the region where Simon can place the light.

Label the region R

Sarah records the number of visits to the cinema that each of the 19 students in her class made in June. The table below shows her results.

Write down the mode of the number of visits to the cinema.

Find the median number of visits to the cinema.

Bhaskor joins Sarah’s class.

The mean number of visits to the cinema, after Bhaskor joins the class, for the 20 students in June is 1.7

Calculate the number of visits to the cinema Bhaskor makes in June.

The diagram shows a sketch of the speed-time graph of part of a cyclist’s journey along a straight horizontal road.

Calculate the deceleration, in m/s², for the last 2 seconds of this part of the cyclist’s journey.

At time t = 0 seconds, the speed of the cyclist is u m/s

The cyclist travelled a total distance of 65 m in the 8 seconds.

Calculate the value of u

The bar chart gives information about the number of pieces of music downloaded last month for each of 30 students in a class.

Calculate the percentage of students who downloaded more than 8 pieces of music last month.

Calculate an estimate for the mean number of pieces of music each student downloaded last month.

Show your working clearly.

Use the factor theorem to show that x 1 is a factor of 18x³ 9x² 17x 10

Factorise fully 18x³ 9x² 17x 10

Show clear algebraic working.

A particle P is moving along a straight line that passes through the point O The displacement, x metres, of P from O at time t seconds (t 0) is given by

At time t seconds, the velocity of P is v m/s

Find an expression for v in terms of t

The particle P comes to instantaneous rest at the point A

Find, in metres, the distance OA

The diagram shows a pyramid ABCD with a horizontal triangular base ABC

ADB 60 DCA DCB 90

Calculate the length, in cm to one decimal place, of AB

Calculate the area, in cm² to 3 significant figures, of triangle ABC