4MB1/01R — January 2022 (Edexcel IGCSE Maths): Past Paper

Without using a calculator and showing all your working, evaluate 3 5 3 ÷ 4 8 Give your answer in its simplest form.

The nth term of a sequence is given by Determine whether 222 is a term of this sequence. Show your working clearly.

Express 450 millilitres as a fraction of 3 litres. Give your answer in its simplest form.

All the people at a meeting were asked where they had been for their last holiday. All the people gave one answer. Elton recorded the continent of each person’s answer. Elton drew an accurate pie chart for his results. Elton’s results showed that 40 people had been to Europe for their last holiday. The angle in the pie chart for Europe is 64° Calculate the number of people at the meeting.

The bearing of P from Q is 063° Calculate the bearing of Q from P

…………… °

The diagram shows triangle ABC and triangle ADE. The point D lies on AB and the point E lies on AC such that DE is parallel to BC. AD = 16 cm DB = 5 cm DE = 12 cm Calculate the length, in cm, of BC cm

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: B, D, A, E, C · Figure values: 5, 16, 12.

A=2 ×3 ×5 3 2 4 B=2 ×3 ×5 2 3 n Given that the Lowest Common Multiple (LCM) of A and B is 3 375 000 find the value of the integer n. Show your working clearly. n =

y = 4x 5 − x² dy Find dx dy = ……………dx

y = 4x 5 − x² dy Find dx dy = dx

A, B, C and D are four points on a circle. The chord AC intersects the chord BD at P AP = 10 cm BP = 9 cm PD = 7 cm Calculate the length, in cm, of PC cm

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: A, B, P, D, C · Figure values: 10, 9, 7.

M = − 0.5 −1.5 Given that the determinant of matrix M is 0.5 find the value of x. x =

In the diagram, AB, BD and DE are three sides of a regular polygon with n sides. The point C is such that ABC and EDC are straight lines and ∠ BCD = 150° Calculate the value of n. n =

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: C, B, D, A, E · Figure values: 150°.

At the end of a college course, Pierre has to take five examinations. Each examination is marked out of 100 Pierre has to get an overall mean mark of 80% or more for the five examinations in order to pass the course. After taking the first four examinations, Pierre’s mean mark for these four examinations is 78% Calculate the lowest mark Pierre can get in his fifth examination so that he passes the course.

Solve − = 7 5 5 Show clear algebraic working. x = ……………Solve − = 7 5 5 Show clear algebraic working. x =

In the diagram, A, B and C are points on a circle. DAE is the tangent to the circle at A. ∠ BAC = 52° and ∠ CAE = 63° Calculate the size, in degrees, of ∠ ACB. Give reasons for each stage of your working. °

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: C, B, D, A, E · Figure values: 52°, 63°.

Given that m and n are integers, write in the form m + n 5 5−2 Show each stage of your working clearly.

P=a− c a = 15 to the nearest 5 b = 8.5 to one decimal place c = 5 to one significant figure Calculate the lower bound of P Show your working clearly.

Given that, for all values of x, 8x 2 − 48x +10 = a(x + b) 2 + c where a, b and c are integers, find the value of a, the value of b and the value of c. Show your working clearly. a = b = c =

The volume of a solid right circular cylinder is 225 cm³ The height of the cylinder is 7 cm. Work out the total surface area, in cm² to 3 significant figures, of the cylinder

…………… cm²

The diagram shows a right-angled triangle ABC in which ∠ ABC = 90° D is the point on BC such that BD = 5 cm DC = 8 cm AD = 18 cm Calculate the size, in degrees to one decimal place, of ∠ CAD °

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: C, D, A, B · Figure values: 8, 18, 5.

Make x the subject of the formula y=5+ 7−x Give your answer in its simplest form.

The diagram shows triangle ABC and triangle EDC. AB is parallel to DE. AC = 16 cm and CE = 12 cm. Given that the area of triangle ABC is 31.5 cm² greater than the area of triangle EDC, work out the area of triangle EDC cm²

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: B, E, C, A, D · Figure values: 12, 16.

The table shows information about the lengths of time, in minutes, that 70 people waited for a train.

Write down the modal class.

Calculate an estimate, to one decimal place, of the mean number of minutes waited minutes

The students who go to Crown Academy either live in village A or in village B such that number of students from village A : number of students from village B = 5 : 7 15% of the students from village A travel by bus to Crown Academy. of the students from village B travel by bus to Crown Academy. Of the students from village A and village B who do not travel by bus to Crown Academy, walk to Crown Academy. Find what fraction of the students walk to Crown Academy.

Find the two values of x such that 123 x × 34 x −3 x × 3 = 27 242 x Show your working clearly.

25 ℰ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} A = {2, 3, 5, 6, 9, 10} B = {3, 4, 6, 9, 12} List the members of

A ∩ B

A ∪ B

Aʹ C = {5, 6, 7}

Write down all the subsets of C.

Solve the inequality 7d + 3 ≤ 5d

Expand and simplify 5a(2a − 3) − 4a(3a + 1) 30 x³ y 4

Simplify fully 5 xy 3

Factorise 15n 2 − 11n − 14

The diagram shows quadrilateral ABCD such that AB = 8.2 m BC = 5.2 m AD = 6.7 m ∠ CAD = 48° ∠ ACD = 59° Find the area, in m² to 3 significant figures, of quadrilateral ABCD m²

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: B, C, A, D · Figure values: 5.2, 8.2, 59°, 48°, 6.7.

The curve C has equation y = 2x 3 − x + 12x + 5 The points P and Q lie on C. P is the point with coordinates (1, 8.5) The gradient of the tangent to C at the point P is equal to the gradient of the tangent to C at the point Q. Calculate the gradient of the line PQ. Show your working clearly.

Given that (x − 5) is a factor of 3x 3 − 20x 2 + kx + 10 where k is a constant …………… , …………… use the factor theorem to show that k = 23

Solve the equation 3x 3 − 20x 2 + 23x + 10 = 0 Show clear algebraic working.