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

Write down all the letters of the above word that have

exactly one line of symmetry …………… , ……………

rotational symmetry of order 2

Show that 1 2 1 1 2 3 5 5 Show your working clearly.

The nth term of a sequence is 3n2 + 2 Calculate the sum of the 4th term and the 5th term of the sequence.

Using ruler and compasses only and showing all your construction lines, construct the bisector of angle PQR. P Q R

Find the Highest Common Factor (HCF) of 216 and 540 You must show all your working.

Given that y = 3x6 − x³ dy find dx dy = ……………dx

Given that y = 3x6 − x³ dy find dx dy = dx

The diagram shows △ABC. DBCE and ACF are straight lines such that ∠ABD = 107° and ∠ECF = 58° Calculate the size, in degrees, of ∠BAC. ∠BAC = °

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: A, D, E, B, C, F · Figure values: 107°, 58°.

p, q, 17 and r are four integers such that p < q < 17 < r and r = p + 18 The median of p, q, 17 and r is 13 The mean of p, q, 17 and r is 15 Find the value of p, the value of q and the value of r. p = q = r =

The straight line L is drawn on the grid. y L −3 −2 −1 O 1 2 3 x −1 −2 −3 −4 −5 −6 Find an equation for L.

Write 1.2 × 10−4 as an ordinary number. 6 10144 5 10142

Calculate 5 105 Give your answer in standard form.

A triangle has sides of length 8 cm, 10 cm and 15 cm. Calculate the size, in degrees to one decimal place, of the smallest angle of the triangle.

…………… °

x cm A 7.5 cm C E 8 cm 6 cm D A, B, C and D are points on a circle. EAB and EDC are straight lines. ED = 6 cm DC = 8 cm EA = 7.5 cm AB = x cm Calculate the value of x. x =

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: B, A, C, E, D · Figure values: 7.5, 8, 6.

Without using a calculator, and showing all your working, express 75 + 243 in the form a where a is a positive integer. Show your working clearly.

For all values of x, 15 − 28x − 7x 2 = a + b(x + c)² where a, b and c are integers. Find the value of a, the value of b and the value of c. a = b = c =

Solve the inequality 6x2 + 5x – 25 > 0 Show clear algebraic working.

Simplify fully 6x4 y

Simplify fully (2a⁵b³)⁴

C Diagram NOT B accurately drawn 8.5 cm 12.6 cm A 8.0 cm E 3.2 cm D In the diagram, ACD is a triangle with point B on AC and point E on AD such that EB is parallel to DC. AB = 8.5 cm AE = 8.0 cm ED = 3.2 cm DC = 12.6 cm

Calculate the length of EB cm

Calculate the length of AC cm

A B p 2 2q 3 17 4 Given that 3A 2B 7 0 find the value of p and the value of q. p = q =

Solve the simultaneous equations 3x + 2y = −1 4x − 3y = −5.3 Show clear algebraic working. x = y =

The diagram shows the right angled triangle ABC where ∠ABC is 90° and AC = 9 cm. The point D lies on AB such that BD = 3 cm and ∠BCD = 23° Calculate the size, in degrees to one decimal place, of ∠ACD. °

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: A, D, B, C · Figure values: 9, 3, 23°.

Given that a = −5 2 2a

find the value of 2a 2 c

Write 2 in the form c x where x is a rational number. c

Solid $A$ and solid $B$ are similar. The table gives information about the surface areas and the volumes of $A$ and $B$.

Calculate the value of $x$.

Ameer drove from his home to a business meeting. The distance that Ameer drove was 210 km, to the nearest 10 km. The time that he took was 3 hours 25 minutes, to the nearest 5 minutes. Calculate the upper bound, in km / h to one decimal place, of Ameer’s average speed as he drove from his home to the business meeting km / h

Express 2 as a single fraction in its simplest form. 2 x 4 x 2 6 x 4 x 16 Show clear algebraic working.

Garcia makes bags from fabric. Garcia buys a length of fabric that is 40 metres long. The cost of the fabric is $5 per metre and he uses all the fabric to make bags. Each bag that he makes uses a length of 80 cm of the fabric. Garcia sells of the bags he made for $14 each bag. He then reduces the selling price of each bag by 15% and sells the rest of the bags he made. Calculate the percentage profit that Garcia makes by selling all the bags he made

…………… %

Neeta is going to play one game of chess and one game of snooker. The probability that she will win the game of chess is 0.35 The probability that she will win the game of snooker is 0.48 The two events are independent.

Complete the probability tree diagram. chess snooker win win 0.35 not win win not win not win

Find the probability that Neeta will win only one of the games.

The diagram shows a shaded region, S, formed by removing a regular hexagon from a circle. The centre of the circle is the point O. The hexagon has centre O and sides of length 8 cm. Given that area of the hexagon = area of S calculate the radius, in cm to one decimal place, of the circle cm

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: S, O · Figure values: 8.

A bag contains n beads. There are 4 orange beads in the bag. The rest of the beads are purple. Donald is going to take at random 2 beads from the bag. The probability that both beads will be the same colour is Find the value of n. Show clear algebraic working. n =

A curve has equation y = x³ − 4x2 + 5x + 3 P and Q are two points on the curve. P is the point with coordinates (2, 5) The gradient of the tangent to the curve at P is equal to the gradient of the tangent to the curve at Q. Find the exact coordinates of Q. ( …………… , …………… )