4MB1/01 — November 2023 (Edexcel IGCSE Maths): Past Paper

A pattern is made with grey and white squares.

Write down the order of rotational symmetry for this pattern.

Shade, on the grid below, exactly 5 squares to make a pattern with 4 lines of symmetry.

−3 4 3 Write down a number from the above list that is

both a rational number and a natural number …………… , ……………

an irrational number.

The nth term of a sequence is given by 3n 2 − 20 Find the difference between the 4th term and the 5th term of this sequence.

Using ruler and compasses only and showing all your construction lines, construct the bisector of angle FGH H F G

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

Factorise fully 5mp 2 − 10 p

Harpreet has been given 22 × 3 × 55 × 7 red bricks 22 × 54 × 7 2 green bricks 24 × 32 × 53 × 7 blue bricks Harpreet is asked to arrange the bricks in rows according to the following rules. Each row must contain just one colour of brick. Each row must contain the same number of bricks. Calculate the maximum number of bricks there can be in a row.

Given that a = find the exact value of ½ a½

A car travels at an average speed of 80 km/h for 2.5 hours and then travels a further distance of 25 km in 0.5 hours. Calculate the average speed, in km/h, of the car for the whole journey km/h

In a survey, 32 students were asked whether they study either History (H) or Geography (G). Given that, of these students, 2 x − 5 study Geography and 5 x − 1 study History

complete the Venn diagram for this information, giving the missing value in terms of x E G H x

Calculate the value of x x =

Calculate the mean of the two numbers 4 × 10100 and 3.6 × 10101 Give your answer in standard form.

y 7 L O 1 2 3 4 x The diagram above shows the line L with equation y mx c, the line with equation y = 4 and the line with equation x = 3

Find the value of m and the value of c m = c =

On the grid, shade and label the region R defined by 0 ≤ y≤4 and 0 ≤ x≤3 and y ≤ mx + c

Simplify x 2 + 3x + 2

A bag contains red pens, blue pens, black pens, green pens and purple pens. A pen is selected at random from the bag. The table gives information about the probability of the colour of the pen that is selected.

Tisam draws a pie chart to show the information about the number of pens of each colour in the bag. The size of the angle of the sector representing green pens is 50.4°

Show that x = 0.14

Calculate the value of y y =

A bag contains red counters, blue counters and yellow counters such that number of red counters : number of blue counters = 5 : 2 number of blue counters : number of yellow counters = 3 : 4 The number of yellow counters in the bag is 56 Calculate the total number of counters in the bag.

Here is hexagon ABCDEF

AB = (2x+1) cm DE = 2x cm FE = 5x cm AF = (3x+4)

The perimeter of the hexagon is 40 cm. Find the area, in cm², of the hexagon.

…………… cm²

A = $\begin{pmatrix} 2 & -1 \\ 4 & 3 \end{pmatrix}$ B = $\begin{pmatrix} -3 & -1 \\ 2 & 7 \end{pmatrix}$

Calculate 3A − 2B

B = $\begin{pmatrix} -3 & -1 \\ 2 & 7 \end{pmatrix}$ C = $\begin{pmatrix} p & -3 \\ 4 & 1 \end{pmatrix}$ BC = $\begin{pmatrix} -10 & 8 \\ 32 & 1 \end{pmatrix}$

Calculate the value of p

p =

OABC is a sector of a circle, centre O, with ∠AOC = 75° The arc length ABC = 54 cm. Calculate the area, in cm² to 2 significant figures, of the sector cm²

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: A, B, O, C · Figure values: 75°.

The diagram shows two mathematically similar solids, A and B Diagram NOT accurately drawn A B The volume of solid B is 43% less than the volume of solid A The total surface area of solid A is 700 cm² Work out the total surface area, in cm² to 3 significant figures, of solid B cm²

A, B, C and D are four points on a circle. P is the midpoint of AB APBX is a straight line. DCX is a straight line. BX = 4 cm CX = 5 cm DC = 2 cm ∠PCX = 115° Calculate, in degrees to one decimal place, ∠BPC BPC °

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: X, B, P, C, A, D · Figure values: 4, 5, 2.

Express $3x^2 + 6x - 9$ in the form $p(x + q)^2 + r$ where p, q and r are integers to be found.

Hence, or otherwise, solve the equation $3x^2 + 6x - 9 = 0$ without using a calculator. Show your working clearly.

A particle is moving along a straight line. At time t seconds, the displacement, x metres, of the particle from a fixed point O on the line is given by x 2t 3 8t 2 15t At time t seconds, the velocity of the particle is v m/s

Find an expression for v in terms of t v =

Find the least speed, in m/s, of the particle m/s

In the diagram, A, B, and C are points on a circle, centre O DBE is the tangent to the circle at the point B EBC 54° AOB 102° Find, in degrees, the size of ∠OCA Give reasons for each stage of your working. OCA °

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: C, O, E, A, B, D · Figure values: 102°, 54°.

A box contains n buttons. The buttons are either red or blue such that number of red buttons : number of blue buttons = 3 : 5 A sample of 2 buttons is taken at random from the bag. Given that the probability of the 2 buttons being the same colour is $\frac{10}{19}$, find the value of n

n =

Make h the subject of p = h

The diagram shows triangle ABC

AB = (4x + 6) cm BC = 3x cm AC = (6x + 4) cm ∠ACB = 60°

Find the area, in cm² to 3 significant figures, of triangle ABC cm²

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: B, A, C · Figure values: 60°.

Write 8 in the form a b where a and b are prime numbers.

Without using your calculator and showing all your working 6 2 3 express in the form p + q where p and q are integers. 3 2

f(x) = 12x³ − 4x² − 25x + 14

(a) Use the factor theorem to show that (3x − 4) is not a factor of f(x)

g(x) = f(x) − 2

Factorise fully g(x) Show clear algebraic working.