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

The nth term of a sequence is given by 4n – 12 Write down the first 2 terms of the sequence. 1st term 2nd term

Bronze is made from copper and tin in the ratio of 22 : 3 by weight. Calculate the weight of copper, in kg, needed to make 12.5 kg of bronze kg

A pattern on a white grid is made from 6 shaded squares. Shade exactly 2 more squares so that the 8 shaded squares will make a pattern with rotational symmetry of order 4

Make u the subject of 1 2 s = ut + at

Without using a calculator and showing all your working, evaluate 1 4 3 ×2 8 5 Give your answer as a mixed number in its simplest form.

Factorise completely 2mc 2 + 6p2c 4

Inzamam cycles 6.4 km from his home to school. He leaves home at 07 40 and arrives at school at 08 20 Calculate his average speed, in km/h, for the journey km/h

Rohan asked each of the students in his school what colour paper they would prefer him to use for their worksheets. There are 150 students in Rohan’s school. Using his results, Rohan drew the following accurate pie chart. red orange blue green yellow Find how many of the 150 students preferred blue paper.

Solve 2(x + 7) = 5x – 6 x = ……………Solve 2(x + 7) = 5x – 6 x =

E ℚ ℕ ℤ Above is a Venn diagram showing the sets ℕ, ℤ, ℚ and E ∞ is the set of natural numbers, is the set of integers, ℚ is the set of rational numbers E is the universal set. Place each of the following four numbers in the correct place in the above diagram. 4 22 − 169 17 11 7

The diagram shows a biased spinner with four colours blue, red, green and yellow. When the spinner is spun once • the probability it lands on blue is twice the probability it lands on red • the probability it lands on yellow is three times the probability it lands on blue • the probability it lands on green is 0.25 Find the probability the spinner lands on yellow. red green Diagram NOT accurately drawn blue yellow

Here is a list of four numbers. 1.1 × 1015 2.1 × 1013 3.2 × 1014 3.7 × 1016 Find the median of these four numbers. Give your answer in standard form.

Given that x ≠ –4 x² + 4 x simplify 2x + 8

Using the diagram above, prove that the sum of the angles of triangle ABC is the same as the sum of the angles on the straight line DCE Give a reason for each stage of your proof.

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

The numbers A, B, and C are given as products of their prime factors. A = 35 × 74 × 1039 B = 316 × 79 × 114 C = 38 × 74 × 2692

Find the Highest Common Factor (HCF) of A, B and C Exactly one of the three numbers is the square of an integer N

Calculate the value of N N =

A= −6 −1

Calculate A + 2B

Calculate AB

OABC is a sector of a circle, centre O, with ∠AOC = 100° The area of the sector is 27 cm² Calculate the perimeter, in cm to 3 significant figures, of the sector cm

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: A, O, B, C · Figure values: 100°.

Given that p = show that =p–1 p Show your working clearly.

There are 1000 cm³ of orange juice in a carton. The total surface area of this carton is 700 cm² For a special offer, a new carton is designed. The volume of orange juice in the new carton is 33.1% more than the volume of orange juice in the original carton. The new carton is mathematically similar to the original carton. Calculate the total surface area of the new carton

…………… cm²

Given that a = where ½ a½ = 5 ⎝ 2x ⎠ find the exact value of x x =

The diagram shows triangle ABC A C B The region R consists of all the points inside the triangle that are closer to C than to B and also closer to AB than to AC Using ruler and compasses only and showing all your construction lines, construct and show by shading the region R Label the region R

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

y y=x L 2 y=2 O 2 4 6 8 10 x The diagram above shows the line L, the line with equation y = 2 and the line with equation y = x drawn on a grid.

Find an equation of the line L

Write down the three inequalities that define the region shaded in the diagram.

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

ABCD is a kite so that the points A, B, C and D lie on a circle with radius 7.5 cm. The diagonals, AC and BD, of the kite intersect at point E, so that AE = 3 cm. The line AEC is a diameter of the circle. Find the area of the kite ABCD cm²

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

In a triangle ABC AC = 6.5 cm BC = 12 cm ∠ABC = 30° Calculate, in cm² to 3 significant figures, the smaller of the areas of the two possible triangles ABC

…………… cm²

There are 25 sweets in a bag. n of the sweets are orange. The rest of the sweets are yellow. Chana takes a sweet at random from the bag. She eats the sweet. Chana takes at random another sweet from the bag. She eats the sweet. The probability that Chana eats one orange sweet and one yellow sweet is

Write down the probability that both sweets taken by Chana are the same colour.

Find the possible values of n Show clear algebraic working.

f(x) = 2x 3 + 9x 2 – 14x – 9

Using the factor theorem, show that (2x – 1) is not a factor of f(x) f ( x)

Express in the form (x + a)² + b 2x + 1 where a and b are integers to be found.

Hence find the exact solutions of f(x) = 0

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 = t 3 – 18t 2 + 81t 0≤t≤9 At time T seconds, where T < 9, P is at the point A on the line. At A, particle P instantaneously reverses its direction of motion and moves back towards O

Find the value of T T = As P moves from A back towards O, the greatest speed of P is V m/s

Find the value of V V =