4MB1/01 — January 2021 (Edexcel IGCSE Maths): Past Paper

Without using a calculator and showing all your working, work out 5 3 5 −3 8 4 Give your answer as a mixed number in its simplest form.

Some students at a school are asked the following question “Did you walk to school today?” 52% of the students asked are in Year 7 and the rest of the students asked are in Year 8. 20% of the students asked are Year 8 students who walked to school. 42% of the students asked did not walk to school. Find as a percentage of all students asked, those who are in Year 7 and did not walk to school

…………… %

Each interior angle of a regular polygon is 176º Calculate the number of sides of the polygon.

Q = 10 − At Work out the value of Q when A = −2 and t = 3 Q =

Given that ⎛ −4 x⎞ ⎛ 3 1⎞ ⎛ x 4 y 1 + x 0 −1 = y −1 find the value of x. x =

Here are four numbers written in order of size. 1.5 2 p 19.5 The mean of the four numbers is three times the median of the four numbers. Find the value of p. p =

Here is hexagon ABCDEF. A 8 cm B Diagram NOT accurately drawn 9 cm 14 cm C 12 cm D F E All the corners of ABCDEF are right angles. AB = 8 cm AF = 14 cm BC = 9 cm CD = 12 cm Calculate the area, in cm², of ABCDEF cm²

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

Paul is carrying out an investigation into people’s wages in the United Kingdom. Paul asks two of his friends, Abdul and Sue, about the pay rise each received in the last year. Abdul says that he has had a 5% pay rise in the last year. Sue says that she has had a 7% pay rise in the last year. Paul says that, in the last year, Sue’s wages have risen by more than Abdul’s wages.

Explain why Paul might not be correct. Paul has also read an article about the National Minimum Wage in the United Kingdom. The article says that, from April 2017 to April 2018, the national minimum hourly wage increased by 4.4% to £7.83

Find the value of the National Minimum Wage before this increase. £

The diagram shows triangle ABC. The point D lies on AB such that ∠ADC = 90° AC = 4 cm AD = 3 cm BD = 5 cm Calculate the size, in degrees to one decimal place, of ∠ABC. °

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: C, A, D, B · Figure values: 4, 3, 5.

The nth term of a sequence is an where an = 2n + 2 By simplifying the expression for an or otherwise, explain why no term in the sequence is an integer. Show algebraic working and clearly explain your reasoning.

Factorise x² − 1 p and q are integers greater than 260 000 and p < q

Find the value of p and the value of q such that pq = 236 − 1 p = q =

The density, d grams/cm³, of an object of mass m grams and volume V cm³ is given by the formula m d = V m = 2800 to the nearest 10 V = 1600 to 3 significant figures. Calculate the lower bound, to 3 significant figures, of d. Show your working clearly.

Without using your calculator and showing all your working, express 13 + 11 13 − 11 in the form a + b where a and b are integers.

Jill travels to work either by car or by train. Each day that Jill travels to work, the probability that she travels to work by train is 0.1 On a day that Jill travels to work by train, the probability that she will be late for work is 0.05 On a day that Jill travels to work by car, the probability that she will be late for work is 0.01 On a randomly chosen day that Jill travels to work, she is late for work. Find the probability that Jill travelled to work by train on that day.

Simplify 4x − 3y + x + 5y

Simplify 2a3 × 4a3

Factorise fully 10ab − 24a2

Factorise p2 + 10p − 24

Given that a = 2.1 × 1056 and b = 8 × 1054

calculate ab Give your answer in standard form. n Given that a + b = k × 10 where k and n are integers …………… , ……………

find the smallest value of k and the corresponding value of n k = n =

Solve the simultaneous equations 5x + 3y = 2 3x − 8y = 4 Show clear algebraic working. x = y =

f (x) = x³ + ax − 3 where a is an integer. (x − 3) is a factor of f (x)

Use the factor theorem to show that a = −8 Given that f (x) = (x − 3)Q(x) where Q(x) is a quadratic expression in x

find Q(x) Q(x) =

A C B The diagram shows triangle ABC. Showing all your construction lines, construct

the perpendicular bisector of AB …………… , ……………

the bisector of ∠ACB. The region R consists of all the points inside the triangle that are closer to A than to B and closer to BC than to AC.

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

The diagram shows the circle ABCDE with centre O. AC is the diameter of the circle. AB is parallel to ED. ∠ACD = 80° ∠CDE = 120° Giving your reasons, find the size, in degrees, of ∠ACB. ° ∠ACB =

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: B, C, D, O, A, E · Figure values: 80°, 120°.

Diagram NOT accurately drawn 20 cm S 20 cm The diagram above shows a right circular solid cone S with base diameter 20 cm and height 20 cm.

Calculate the volume, in cm³ to 3 significant figures, of S cm³ Diagram NOT accurately drawn A B 10 cm 20 cm The shape B is formed from cone S by cutting S parallel to its base and removing cone A, as shown in the diagram above. The height of B is 10 cm.

Calculate the volume, in cm³ to 3 significant figures, of B

…………… cm³

The incomplete histogram and the incomplete table give information about the daily mean temperature for 184 days measured at Heathrow. None of the daily mean temperatures were less than 5°C and all the daily mean temperatures were less than 25°C.

Complete the histogram and the table.

The functions f and g are defined as f:xα x−3 g : x ↦ x² − 2

Find fg(6) The function h is defined as h(x) = gf (x)

Show that h(x) = x² − 6x + 7 The domain of h is {x : x ≥ n} The inverse of h is h−1

State the least value of n for which h−1 is a function. n =

For this value of n, find h−1(x) h−1(x) =

E Diagram NOT accurately drawn 32.3 m M D C N 34 m A B The diagram shows a solid right pyramid ABCDE with a square base ABCD on a horizontal plane. The vertex E of the pyramid is vertically above the centre of the base. BC = 34 m EA = EB = EC = ED = 32.3 m The point M is the midpoint of CE and the point N is the midpoint of BE. Given that AN + NM = x metres

calculate the value, to 2 significant figures, of x. x =

Calculate the size, to the nearest degree, of angle BAN.

…………… °

A particle P is moving along a straight line. At time t seconds, the displacement, s metres, of P from a fixed point O on the line is given by s = 5t 2 − t 3 0 ≤ t ≤ 5 At time T seconds, where T > 0 , P comes to instantaneous rest.

Find the exact value of T. T =

Find the total distance travelled by the particle between t = 0 and t = 5 m