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

The functions f and g are defined as f(x) = 3x g(x) = 2x − 3

Write down the value of x for which f(x) = 81

Write down the value of x that must be excluded from any domain of g

Find fg(4)

Find the set of values of x for which –2x – 4 < 3x + 6 ≤ 21 – 2x

Solve the inequality 4x2 – 8x < 21

Hence represent on the number line on the opposite page, the set of values of x for which –2x – 4 < 3x + 6 ≤ 21 – 2x and 4x2 – 8x < 21 x –5 –4 –3 –2 –1 0 1 2 3 4 5

Peter has two boxes of bricks, box A and box B. Each box contains only red bricks, green bricks and yellow bricks. In box A there are 15 bricks of which 5 are red, 7 are green, and 3 are yellow. In box B there are 20 bricks of which 8 are red, 9 are green, and 3 are yellow. Ami is going to take a brick at random from box A and a brick at random from box B. She is going to put these two bricks on a table.

Complete the probability tree diagram. box A box B red red green 15 yellow red green green yellow red yellow green yellow

Calculate the probability that the two bricks on the table are different colours. Peter has a third box of bricks, box C. This box also contains only red bricks, green bricks and yellow bricks. After taking a brick from box A and a brick from box B, Ami then takes at random a brick from box C. Ami then puts this brick with the other two bricks on the table. The probability that there are three yellow bricks on the table is 1000

Find the least number of bricks that were in box C before Ami took a brick from box C.

A= B= C = 7 2 7 5 10 5 4 1

Find D such that 2A – B = 3D

Find A2

Find B–1

Find CA a b 1 d b Inverse of matrix c d ad bc c a

The graph of the straight line with equation 3x + y = 11 is drawn on the grid opposite for 0 ≤ x ≤ 4

On the grid, draw the graph of the straight line with equation 4x = 3 + 2y for 0 ≤ x ≤ 4

Use your graphs to find estimates, to one decimal place, of the value of x and the value of y that satisfy the simultaneous equations 3x + y = 11 4x = 3 + 2y

Solve the simultaneous equations 4x + xy – x² = –10 3y + x = 7 Show clear algebraic working. y 1 3x + y = 11 x 1 2 3 4 –1 –2

Triangle A is drawn on the grid opposite. Triangle A is reflected in the line with equation x = –1 to give triangle B.

On the grid, draw and label triangle B. Triangle A is transformed to triangle C under a rotation of 90° clockwise about the point with coordinates (1, 0)

On the grid, draw and label triangle C. Triangle B is transformed to triangle D under the translation

On the grid, draw and label triangle D. Triangle A is transformed to triangle E under the transformation with matrix M where 1 0 M

On the grid, draw and label triangle E. Triangle E is the image of triangle C under a single transformation.

Describe fully this transformation.

There are 480 people in an airport departure lounge. 30% of these people are catching a plane to Dubai.

Show that 336 of these people are not catching a plane to Dubai. The people in the airport lounge who are not catching a plane to Dubai are catching a plane to Sweden or a plane to Greece or a plane to Brazil. Of these 336 people the number catching a plane to Sweden is s the number catching a plane to Greece is g the number catching a plane to Brazil is b where s:g:b=6:7:8

Calculate the value of s Pablo went by plane from Canada to Brazil in February 2020 and in February 2021 In February 2020, the cost of his ticket was $680 In February 2021, the cost of his ticket was $730

Calculate the percentage increase, to one decimal place, in the cost of the ticket from February 2020 to February 2021 Pablo bought a ticket to go by plane to Sweden in June 2021 The cost of his ticket was $468 The cost of this ticket was 4% greater than the cost of his ticket the last time he went by plane to Sweden, which was in December 2020

Calculate the cost of Pablo’s ticket to Sweden in December 2020 At the end of his trip, Pablo had 320 Swedish krona left. He changed the 320 Swedish krona into Canadian dollars. Using the following exchange rates, 1 Canadian dollar = 0.57 euros 1 Swedish krona = 0.094 euros

calculate the number, to 2 decimal places, of Canadian dollars that Pablo should have received.

The equation of a curve C is y x x The curve C has a minimum at the point A

Show that the coordinates of A are (0.75, –1.5625)

Complete the table of values for $y = x^2 - \frac{3x}{2} - 1$

The point $A$ has been plotted on the grid opposite.

On the grid opposite, draw the curve with equation $y = x^2 - \frac{3x}{2} - 1$ for values of x from –3 to 4

Using your curve, find an estimate, to one decimal place, for the range of values of x for which x − x − 1 ≤ 3 Show your working clearly.

By drawing a suitable straight line on the grid, find estimates, to one decimal place, 7 1 of the solutions of the equation x 2 x 2 2 Show your working clearly.

Figure 1 Figure 1 shows a trapezium OACB in which OA is parallel to BC and OA : BC = 2 : 1 The point P lies on AC such that AP : PC = 3 : 1 → ® The point D is such that OD = λ OP where λ > 1 and such that BCD is a straight line. → → Given that OA = 6a and that OB = 8b ® use a vector method to find and simplify an expression, in terms of a and b only, for AD Show your working clearly.

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

Q Diagram NOT accurately drawn 51° M x R P T Figure 2 In Figure 2, P, Q, R and T are points on a circle with centre M such that ∠ PQR = 51°

Find the size, in degrees, of the angle marked x in Figure 2

Find the size, in degrees, of the obtuse angle PTR. B Diagram NOT accurately drawn S O 118° A C Figure 3 In Figure 3, A, B and C are points on a circle with centre O such that ∠ AOC = 118° and BA = BC. The area of the region S, shown shaded in Figure 3, is 70 cm²

Calculate the total area, in cm² to 3 significant figures, of the unshaded region inside the circle. Area of triangle ab sin C

Diagram NOT accurately drawn 3r cm 10 cm r cm Figure 4 Figure 4 shows a solid right circular cone of radius r cm and height 3r cm and a sphere of radius 10 cm. The total surface area of the cone is equal to the surface area of the sphere.

Calculate the value, to one decimal place, of r Curved surface area of cone rl Surface area of sphere = 4 r 2 V Diagram NOT accurately drawn 15 cm B C A D F E Figure 5 Figure 5 shows a right pyramid. The base ABCDEF of the pyramid is a regular hexagon and the vertex V of the pyramid is such that AV = BV = CV = DV = EV = FV = 15 cm and ∠AVD = 40°

Calculate the volume, in cm³ to 3 significant figures, of the pyramid. Area of triangle ab sin C Volume of pyramid 1 base area height