January 2019 · Paper 1 (4MB1/01) (Edexcel IGCSE Maths): Exam Questions

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.

$

The nth term of a sequence is given by 5n2 - 2

Find the first 3 terms of this sequence.

,

,

The lengths of the sides of a triangle are in the ratios 4 : 5 : 6

The perimeter of the triangle is 80 cm.

Find the length of the longest side of the triangle.

cm

Factorise fully 9x2y + 12xy2z

Make x the subject of y = 8

(

1

)

w

Simplify fully (

2

)

xy

2

4

y

x

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

Solve the inequality 5x + 4 < 20 − 3x

Represent, on the number line below, your solution of the inequality in part (a).

The points O, A, B and C are such that OA⃗ = (−2 4), OB⃗ = (5 −3) and AC⃗ = (−1 −1)

Find |BC⃗|

Write 340 000 000 in standard form.

Calculate, giving your answer in standard form, ($2 \times 10^{99}$)$\div$($5 \times 10^{110}$)

Calculate, giving your answer in standard form, (2 × 1099)$\div$(5 × 10110)

Given that, for all values of x,

– 3x + 21 = a(x - b)2 + c

2x2

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

a =

b =

c =

A

Diagram NOT

accurately drawn

O

B

D

C

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

Prove that triangle ABC and triangle DCB are congruent.

A

B

Diagram NOT

accurately drawn

3.6 cm

85°

O

The diagram shows a sector OAB of a circle, centre O.

OA = OB = 3.6 cm

Angle AOB = 85°

Calculate the perimeter, in cm to 3 significant figures, of the sector OAB.

cm

A

x°

Diagram NOT

D

accurately drawn

B

110°

40°

E

C

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 =

A car travelled at an average speed of 96 km/h for 11

2 hours and then travelled at an

average speed of 56 km/h for 21

2 hours.

Calculate the average speed of the car for the whole journey.

km/h

N

N

Diagram NOT

accurately drawn

B

R

N

L

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,

N

N

Diagram NOT

accurately drawn

B

R

N

L

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 L from B.

°

D

E

R

S

C

9 cm

A

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 = 2$\pi$ cm²

find the area of R.

cm²

1

1

2

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

density = mass

volume

calculate the upper bound of the density of the cone.

Give your answer to 3 significant figures.

g/cm³

Diagram NOT

Q

accurately drawn

B

P

R

A

C

(2x + 4) cm

4(x2 - 4) cm

D

S

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.

The lengths of cod caught by fishermen in a small fishing boat last month were measured.

The incomplete table and histogram below give information about the length of each cod caught last month.

Complete the table and the histogram.

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.

Calculate an estimate, to one decimal place, of the percentage of cod caught that were

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.

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

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

The table shows information about his results.

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

The function f is defined by f : x ↦ 4 + 3

x x > 0

Find f

The function f is defined by f : x ↦ 4 + 3

x x > 0

Find the range of f.

The function f is defined by f : x ↦ 4 + 3

x x > 0

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

The function g is defined by g : x ↦ 4x - 5

The function f is defined by f : x ↦ 4 + 3

x x > 0

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

B

12 cm

5 cm

O

C

7 cm

A

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.

cm³

B

12 cm

5 cm

O

C

7 cm

A

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

cm²

Solve the simultaneous equations

x2 = 10 - y2

x + 2y = 5

Show clear algebraic working.

A curve has equation y = x3 - 4x2 + 2x

Find the x coordinate of each of the points on the curve at which the gradient of the

tangent to the curve is 2