4MB1/01 — November 2020 (Edexcel IGCSE Maths): Past Paper

Solve the inequality 7x + 3 ≤ 4x – 15

Show that 2 5 4 ÷ = 18 7 21

The nth term of a sequence is given by 3n 2 + 11 Calculate the difference between the 6th term and the 9th term of the sequence.

A = 2³ × 3 × 5² B = 2² × 3² × 5 × 7

Find the Lowest Common Multiple (LCM) of A and B.

Find the Highest Common Factor (HCF) of A and B.

The price of each sandwich in a cafe was increased by 4% Chris bought a sandwich after the price increase for $3.64 Calculate the increase in the price of the sandwich Chris bought. $

Given that a : b = 3 : 5 and that a : c = 7 : 4 find a : b : c Give your answer in its simplest form. a : b : c =

Diagram NOT accurately drawn 8.5 cm 9 cm 6.8 cm 7.2 cm 7.6 cm 9.5 cm The diagram shows two triangles. Show that the triangles are similar.

Given that y = x 4 – x² dy find dx dy = ……………dx

Given that y = x 4 – x² dy find dx dy = dx

The table gives information about the number of brothers that each student in a class has.

Calculate the mean number of brothers.

Without using a calculator and showing your working clearly, find the value of the integer a so that 180 − 27 − 20 + 147 = a( 5 + 3 ) a =

Solve + =2 4 5 Show clear algebraic working. x = ……………Solve + =2 4 5 Show clear algebraic working. x =

The diagram shows a half cylinder. 5 cm Diagram NOT accurately drawn x cm The half cylinder has a length of x cm and a semicircular cross section of diameter 5 cm. The volume of the half cylinder is 35π cm³ Calculate the value of x. x =

Simplify m12 ÷ m³ 3 3

Simplify fully $(125p^9w^3)^{\frac{2}{3}}$

Given that 2 5 p= and n = 6n + 5 4m + 2 find an expression for p in terms of m. Give your answer in its simplest form. p =

Akash drove from his home to his friend’s house. The distance Akash drove was 190 km, to the nearest 5 km. His average speed for the journey was 62 km/h, to the nearest km/h. Calculate the upper bound for the time taken by Akash to drive from his home to his friend’s house. Give your answer in hours and minutes, to the nearest minute hours minutes

5m In the diagram, AB represents a vertical wall and CD represents a vertical building. The height of the wall is 1.4 m. The bottom of the wall, B, and the bottom of the building, D, are on horizontal ground, such that BD = 5 m. The angle of elevation of C from A is 75° Calculate the height, in m to one decimal place, of the building m

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: C, A, B, D · Figure values: 1.4.

The histogram below shows information about the age of each person on a plane. There were 7 people on the plane with an age of 5 years or under. Calculate the number of people on the plane with an age of over 20 years.

A varies directly as the square of c A = 950 when c = 5 Calculate the value of A when c = 7 A =

Solve the simultaneous equations 5x – 3y = 21 3x – 4y = 22.5 Show clear algebraic working. x = y =

⎛ 4 3⎞ ⎛ −7 −2⎞ A= ⎜ B= −2 1 1 3 Find

A – B

AB

ABCD is a quadrilateral such that the points A, B, C and D lie on a circle, centre O. EAF is the tangent to the circle at A. ∠DAF = 78° ∠BCD = 96° Calculate the size, in degrees, of ∠BDA. Give reasons for each stage of your working. ° ∠BDA =

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: C, D, O, B, E, A, F · Figure values: 96°, 78°.

Given that can be written in the form 5 y 4 × ( 125 ) 4 n + 2 find an expression for y in terms of n. y =

The function g is such that g(x) = 9 – 10x – 5x 2 for all values of x Find the range of g. Show clear algebraic working.

A B D C ABCD is a quadrilateral. Leaving in all of your construction lines, construct the locus of all points inside the quadrilateral that are

4 cm from B …………… , ……………

equidistant from B and C …………… , ……………

equidistant from the lines DA and DC. The region R consists of all the points inside the quadrilateral that are more than 4 cm from B, closer to B than to C and closer to DC than to AD …………… , ……………

show, by shading, the region R. Label the region R.

Make a the subject of the formula B = ac + de

Factorise fully 14x 2y 3 – 21x 5y 2

The diagram shows a circle of radius 2x cm. The lines AB and DC are parallel and AB = DC = 2x cm. The area of the region shown shaded in the diagram is kx 2 cm² Find the exact value of k. k =

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

Aarya has a biased 5-sided spinner.

When the spinner is spun once, it can land on blue or yellow or green or pink or orange. Aarya spins the spinner many times and records the colour that the spinner lands on each time. She uses these results to calculate the probability of the spinner landing on each colour.

The table below gives the probabilities that Aarya calculated for blue, yellow and green.

Aarya’s calculations showed that the probability of the spinner landing on orange is 3 times the probability of the spinner landing on pink.

Complete the table for pink and for orange. When Aarya spun the spinner, it landed on green 90 times.

Work out an estimate for the total number of times Aarya spun the spinner.

In the diagram, ABCDEFGH is a regular octagon. ( ) The area of triangle GEF is 4 2 cm² Calculate the perimeter, in cm to one decimal place, of triangle BEG cm

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

Use the factor theorem to show that (x – 5) is a factor of x 3 – 6x 2 – 7x + 60

Hence factorise completely x³ – 6x 2 – 7x + 60