4MB1/01 — January 2019 (Edexcel IGCSE Maths): Past Paper

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 9x 2 y + 12xy 2z

Make x the subject of y = w

Simplify fully 4 xy 2

y –2 –1 O 1 2 3 x –1 –2 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). −5 −4 −3 −2 −1 0 1 2 3 4 5 x

The points O, A, B and C are such that OA = ( −2 4 ), OB = ( 5 −3 ) and AC = ( −1 −1 ) Find |BC| |BC| =

Write 340 000 000 in standard form.

Calculate, giving your answer in standard form, (2 × 1099) ÷ (5 × 10110 )

Given that, for all values of x, 2x 2 – 3x + 21 = a(x – b)² + c 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.

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: A, O, B, D, C.

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° D Diagram NOT accurately drawn B 40° 110° 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=

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Use the text description to work through it.

A car travelled at an average speed of 96 km/h for 1 hours and then travelled at an average speed of 56 km/h for 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 …………… , ……………

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 = 2π cm² find the area of R. cm²

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: E, D, R, S, C, A, B · Figure values: 9.

A= BA = 1 3 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 mass density = volume calculate the upper bound of the density of the cone. Give your answer to 3 significant figures. g/cm³

• 1. 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.

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: Q, B, P, A, R, C, D, S · Figure values: 2 · Other figure text: (2x + 4) cm, 4(x² – 4) cm.

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. Length (l cm) Number of cod 5 < l ≤ 25 30 25 < l ≤ 40 75 40 < l ≤ 50 100 50 < l ≤ 60 155 60 < l ≤ 80 80 < l ≤ 100 20 Frequency density 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Length (l cm)

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.

…………… %

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.

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 + x>0 x

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) = ...

B Diagram NOT accurately drawn 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

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

…………… cm²

Solve the simultaneous equations x 2 = 10 – y 2 x + 2y = 5 Show clear algebraic working.

A curve has equation y = x 3 – 4x 2 + 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