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

Write 0.000 315 in standard form.

The bearing of village A from village B is 124° Find the bearing of village B from village A.

…………… °

p° H E B G 135° A D ABC and DEF are parallel straight lines and GBEH is a straight line. ∠ABE = 135° and ∠FEH = p° Find the value of p. p =

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

Without using a calculator and showing all your working, work out 7 3 1 ×2 8 5 Give your answer as a mixed number in its simplest form.

E = {even numbers between 1 and 29} A = {prime numbers} B = {factors of 24} List the elements of the set

B¢

A ∩ B

Here are the twelve most recent batting scores of a cricketer. 23 45 3 56 23 18 78 56 6 87 11 26 Find the median of these twelve scores.

The nth term of a sequence is given by 2 − 5n Write down the 3rd, 4th and 5th terms of the sequence …………… , …………… , ……………

Express 42 minutes as a percentage of 5 hours……………%

Express 42 minutes as a percentage of 5 hours

…………… %

Here is a number line. −8 −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 x

Show on the number line the inequality −3 ≤ x < 4

Write down the integer values of x for which −3 ≤ x < 4

A = $\begin{pmatrix} 2 & -3 \ 4 & 1 \end{pmatrix}$ B = $\begin{pmatrix} 5 & 0 \ 4 & -2 \end{pmatrix}$

Calculate

(a) A + B

(b) 2A − 4B

Express as a single fraction in its simplest form 5 2 − 3 − 2 x 2 + 5x

Given that, for all values of x, 4x3 − 8x2 − 12x + 11 = (2x + k)Q(x) + 11 where Q(x) is a quadratic expression in x, find the positive value of k. k =

Simplify ( 3x 2 y 3 ) 9 xy 2

Solve the simultaneous equations 3x + 2y = 8 −4x + 9y = 22 Show clear algebraic working. x = y =

y accurately drawn y=5+x y = 6 − 2x R x O The diagram shows the shaded region R, which is bounded by three straight lines, one of which is parallel to the y-axis. One vertex of R lies on the x-axis. Find three inequalities that define R.

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

A model of a ship is made to a scale of 3 : 400 The surface area of the model is 7200 cm² Calculate, in m², the surface area of the ship

…………… m²

The diagram shows △ABD and △BCD such that AB = 6.5 cm, AD = 2.5 cm, BC = 4.2 cm, ∠CBD = 35° and ∠ADB = 90° Calculate the area, in cm² to 3 significant figures, of the quadrilateral ABCD cm²

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: 4.2, 35°, 6.5, 2.5.

p= q = 5 2 x − 1 The vectors p and q are such that ½ p½ = ½ q½ Given that x < 0 find the value of x. x =

BOC is a sector of a circle, centre O, with ∠BOC = 30° The sector AOD of the circle, centre O, such that ODC and OAB are straight lines, is removed from the sector BOC to form the region S, shown shaded in the diagram. Given that OA = AB and that the perimeter of S is 10 m, calculate, giving your answer in terms of π, the length, in m, of AB m

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: C, D, S, O, B, A · Figure values: 30°.

The temperature (T °C ) at midday in a city was recorded each day for 50 days. The table shows information about these temperatures.

Write down the modal class.

Calculate an estimate, to the nearest °C, of the mean temperature at midday in this city during these 50 days °C

The functions f and g are defined for all values of x by f (x) = 3x − 5 g(x) = 2x2 + 1

Write down the range of g

Solve the equation f (x) = gf (2) x =

x= c a = 8.45 correct to 2 decimal places. b = 1.93 correct to 2 decimal places. c = 3.415 correct to 3 decimal places. The upper bound of x and the lower bound of x are the same correct to n decimal places. Calculate the value of x correct to n decimal places, for the largest integer n. You must show all your working and give a reason for your final answer. x =

Factorise completely 10a − 25ab

Factorise x² − 3x − 10

Factorise completely 50x2 − 72y2

The equation of a curve C is y = ( 2 x − 3) ( kx + 5) , where k is a constant. x The point A on C is a stationary point. Given that the x coordinate of A is find the value of k. k =

Diagram NOT accurately drawn A B 116° O C 40° D In the diagram, A, B, C and D are points on a circle, centre O. ∠ABC = 116° and ∠ODC = 40°

Calculate, giving your reasons, the size in degrees of ∠OAD. ° ∠ OAD =

Calculate, giving your reasons, the size in degrees of ∠ACD. ° ∠ACD =

26 30 people travelled from London to Manchester for a conference. Of these people 15 travelled by train 9 travelled by plane some travelled by both train and plane 12 did not travel by either train or plane Three people are chosen at random from those who travelled by plane. Find the probability that exactly two of these people also travelled by train.

3a A Diagram NOT O accurately drawn 5b C B D The diagram shows △OAB and a point D which is outside the triangle. The point C lies on AB such that AC = 3CB → 7 15 → → The point D is such that BD = a+ b where OA = 3a and OB = 5b 4 4 Find the ratio OC : CD

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