4MB1/02 — June 2022 (Edexcel IGCSE Maths): Past Paper

The GDP per capita for a region is defined as follows

$\text{GDP per capita} = \frac{\text{total GDP}}{\text{population}}$

Complete the table below, giving each value to 2 significant figures.

E is the universal set and A, B and C are three sets. E = { p, q, r, s, t } A = { q, r, s } B = { p, q, t }

A ∩ B

A ∪ B

A¢ ∩ B Given that A ∩ C = {r}

write down all the possibilities for set C One of the possibilities for set C is selected at random.

Find the probability that this set C is such that B ∩ C = ∅

Given that 2 x × 4 y = 128

show that x + 2y = 7 8x Given that = 32 4y

show that 3x – 2y = 5

Hence, or otherwise, solve the simultaneous equations 2 x × 4 y = 128 8x = 32 4y

Sophie conducted a survey on the time spent on the internet per day. There were 90 people in her survey. The results are shown in the table below. Time (t minutes) Frequency 0 ≤ t < 10 5 10 ≤ t < 30 7 30 ≤ t < 60 15 60 ≤ t < 120 36 120 ≤ t < 240 19 240 ≤ t < 360 8

Write down the class interval that contains the median time spent on the internet per day.

Calculate an estimate for the mean time spent on the internet per day. Sophie drew a histogram for the information in the table. In her histogram, the bar for the class interval $30 \le t < 60$ is a square with sides of length 3 cm. Given that the bar for the class interval $10 \le t < 30$ is a rectangle of width $w$ cm and of height $h$ cm

find the value of w and the value of h

A closed box is in the shape of a hollow cuboid. The dimensions of the cuboid are 12 cm by 4.0 cm by 3.0 cm. Each length is given to 2 significant figures. A tin of paint contains enough paint to cover exactly 200 cm²

Determine if this tin of paint is definitely enough to cover the 6 outside faces of the closed box.

Calculate the length of the longest straight rod that can definitely fit inside the box. Give your answer to 3 significant figures. Show your working clearly.

A, P and B are three points on horizontal ground. A is 1 km due south of P PQ is a vertical tower. The angle of elevation of Q from A is 16.9°

Show that the height of the tower, in metres to 3 significant figures, is 304 m. B is 2 km due east of P BC is a vertical radio mast. The angle of elevation of Q from C, the top of the radio mast, is 8.2°

Calculate the size, in degrees to one decimal place, of the angle of elevation of C from A

B Diagram NOT C accurately drawn A E D Figure 1 → → Figure 1 shows quadrilateral ABCD such that AB = a and AD = b E is the point such that ADE and BCE are straight lines. → 1 Given that BC = b – a

show that AB is parallel to DC → Given also that λ is a scalar such that BE = λb – a

find the value of λ The area of triangle ABE is x square units. Given that the area of quadrilateral ABCD is P square units …………… , ……………

find an expression for P in terms of x

Diagram NOT accurately drawn 0.9 m 1.2 m 2.1 m Figure 2 Figure 2 shows the design for a garden feature. In the middle of the feature is a circular pond. The pond is surrounded by 6 identical flower beds. Each flower bed is in the shape of an isosceles trapezium.

Calculate the area, in m² to 3 significant figures, of one of the flower beds. Each flower bed needs to be filled with compost to a depth of 10 cm. The compost is sold in bags containing 50 litres of compost.

Show that 16 bags of compost will be needed to fill all six flower beds to a depth of 10 cm. Show your working clearly.

Find the area of the circular pond. Give your answer in m² to 3 significant figures. Area of trapezium = (a + b)h

9 [In this question the coordinates of the points are given in centimetres] The points with coordinates (1, 1), (2, 4), (4, 6) and (3, 3) are the vertices of quadrilateral A

On the grid opposite, draw and label quadrilateral A Quadrilateral A is transformed to quadrilateral B by a rotation of 90° anticlockwise about the origin, O

On the grid opposite, draw and label quadrilateral B Quadrilateral B is transformed to quadrilateral C under the transformation with matrix M where ⎛1 3⎞ M= 1 1

On the grid opposite, draw and label quadrilateral C

Calculate the determinant of M

Calculate the area of quadrilateral A.

[Determinant of matrix $\begin{pmatrix} a & b \\ c & d \end{pmatrix} = ad-bc$]

cm x cm Figure 3 Figure 4 Figure 3 shows a rectangle with dimensions 20 cm by 10 cm from which a square with sides of length x cm is removed from each of the corners. The shape in Figure 3 is then folded along the dotted lines to form a box, without a lid, in the shape of a cuboid, shown in Figure 4 The volume of the box is V cm³

Show that V = 4x 3 – 60x 2 + 200x dV

Find, to 3 significant figures, the value of x such that =0 dx 2a Question 10 parts (c), (d), (e) and (f) continue on page 26

Complete the following table of values for $V = 4x^3 - 60x^2 + 200x$

On the grid opposite, plot the points from your completed table and, using your answer to part (b), join them to form a smooth curve.

By drawing on the grid a tangent to the curve, find an estimate of the gradient of the curve at the point where x = 1.5 Starting with a square of side 15 cm and removing a square with sides of length x cm from each corner, a second box without a lid is formed by folding as in part (a). The volume of this box is B cm³ where B = 4x 3 – 60x 2 + 225x Given that B = 200

find, by drawing a suitable straight line on the grid, estimates, to one decimal place, of the possible values of x

The function f is defined as 3x + 1 f:x ↦ x −1

Find f(3)

State the value of x that must be excluded from any domain of the function f

Find the inverse of the function f Give your answer in its simplest form. The function g is such that x −1 fg( x) = 3x + 1

Find the value of a such that gf(a) = fg(a)