Edexcel IGCSE Maths B Paper 1 January 2019 question paper 4MB1/01

A shop sells a tablet computer for $230

The shop increases the price of the tablet computer by 5%

Calculate the price of the tablet computer after this price increase.

Factorise fully 9x²y + 12xy²z

The diagram shows a curve drawn on a grid.

By drawing a suitable straight line on the grid, find an estimate, to one decimal place, of the gradient of the curve at the point when x = 1

Write 340 000 000 in standard form.

Calculate, giving your answer in standard form, (210⁹⁹) ÷ (510¹¹⁰)

Given that, for all values of x,

find the value of a, the value of b and the value of c.

a =

b =

c =

AOC and BOD are diameters of a circle, centre O.

Prove that triangle ABC and triangle DCB are congruent.

In the diagram, ABC is a triangle with point D on AB and point E on AC such that DE is parallel to BC.

ABC = 40 AED = 110 BAC = x

Find the value of x.

Give reasons for each stage of your working.

x =

The diagram shows the position of a rock R, a boat B and a lighthouse L. The bearing of L from R is 156

Calculate the bearing of R from L.

Given that the bearing of B from R is 072 and that RB = RL,

calculate the bearing of L from B.

The diagram shows a shape ABCDE made from a rectangle R and a semicircle S. The side DB of the rectangle is the diameter of the semicircle.

Given that AB = 9 cm and that the area of S = 2πcm²

find the area of R.

Find the matrix B.

A solid cone has a mass of 1200 g, to 2 significant figures.

The area of the base of the cone is 38.5 cm², to 1 decimal place.

The height of the cone is 5.0 cm, to 2 significant figures.

Given that

calculate the upper bound of the density of the cone.

Give your answer to 3 significant figures.

ABCD and PQRS are two similar quadrilaterals.

The side AD of length (2x + 4) cm is the longest side of quadrilateral ABCD. The side PS of length 4(x² – 4) cm is the longest side of quadrilateral PQRS. The area of the quadrilateral ABCD is 10 cm²

Show that the area, in cm², of the quadrilateral PQRS is a(x – b)²

where a and b are integers to be found.

Cod that have a length less than 35 cm are returned to the sea.

Calculate an estimate, to one decimal place, of the percentage of cod caught that were returned to the sea from the boat last month.

The width of a rectangle is x metres.

The length of the rectangle is 7 m longer than the width of the rectangle.

Find the set of values of x for which the area of the rectangle is less than 44 m² Show clear algebraic working.

Josh asks the students in his form how many hours they played sport last week.

The table shows information about his results.

Number of hours (t)	Frequency
0 t 1	9
1 t 2	8
2 t 3	5
3 t 4	7
4 t 6	3
6 or more	0

Find the class interval that contains the median number of hours.

Calculate an estimate, to 3 significant figures, for the mean number of hours that the students in Josh’s form played sport last week.

hours

Find f (2)

Find the range of f.

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

The function g is defined by g:x 4x – 5

Express the composite function fg in the form fg(x) =...

The diagram shows a pyramid with triangular base OAC. The edges OA, OB and OC of the pyramid are perpendicular to each other.

OA = 7 cm OB = 12 cm OC = 5 cm

Calculate the volume, in cm³, of the pyramid.

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

Solve the simultaneous equations

x² = 10 – y²

x + 2y = 5

Show clear algebraic working.