4MB1/02 — January 2023 (Edexcel IGCSE Maths): Past Paper

A car travels at an average speed of 60 km/h for 2 hours. It then travels at an average speed of x km/h for 3 hours. The car travels at an average speed of 64.2 km/h for the whole journey. Calculate the value of x

cm³ cm A E C Figure 1 Figure 1 shows triangle ABC The point D lies on AB and the point E lies on AC such that DE and BC are parallel. AD = 8 cm DE = 3cm AE : EC = 1 : 2 ∠DEA = ∠BCA = 90° Calculate the area, in cm² to 2 significant figures, of the region BCED shown shaded in the diagram. Area of trapezium = 2 a b h

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: B, D, A, E, C · Figure values: 8, 3.

B (3x + 5) m C Diagram NOT accurately drawn (3x + 17) m A D (3x + 2) m (3x + 2) m F E (3x + 21) m Figure 2 Figure 2 shows a hexagon ABCDEF in which BC = (3x + 5) metres AF = DE = (3x + 2) metres FE = (3x + 21) metres BC is parallel to FE and AB = DC The perpendicular distance between BC and FE is (3x + 17) metres. The perimeter of the hexagon ABCDEF is 172 metres. Calculate the value of x

Figure 3 Figure 3 shows a circle centre O and radius 3.8 cm The points A and B lie on the circle. The point C is such that AC and BC are tangents to the circle and ∠ACB = 70° The region inside the quadrilateral OACB but outside the circle is shown shaded in Figure 3 Calculate the area, in cm² to 3 significant figures, of the shaded region.

Figure not shown in this reconstruction — the printed paper includes a diagram (not drawn accurately). Labels in the original figure: B, O, A, C · Figure values: 3.8, 70°.

Solve the simultaneous equations x 5y x 2 3 xy Show clear algebraic working.

Diagram NOT accurately drawn D C B A 4a 5b O Figure 4 Figure 4 shows triangle OAB The point C lies on AB such that AC = AB → → Given that OA = 4a and OB = 5b →

find an expression for OC in terms of a and b Give your answer in its simplest form. The point D is such that OCD is a straight line. Given that BD is parallel to OA →

use a vector method to find an expression for OD in terms of a and b Give your answer in its simplest form.

7 ℰ = {odd numbers between 0 and 30} A = {multiples of 3} B = {prime numbers} C = {factors of 30}

Complete the Venn diagram for this information showing the position of each of the numbers in the universal set. ℰ A B C

n B C A A number is chosen at random from the universal set, ℰ

Write down the probability that the number is in the set C A Given that the number chosen from ℰ is a multiple of 3

find the probability that the number is also a factor of 30

Aanshi makes granola. She uses nuts, dried raspberries and oats in the ratios 2 : 3 : 7 by weight. Aanshi uses 80 grams of nuts.

Work out the weight, in grams, of oats she uses to make the granola. Nuts cost $26 for 500 grams.

Work out the cost of the nuts used to make 270 grams of the granola. Aanshi is going to buy 500 grams of dried raspberries from one of the following online supermarkets. US supermarket UK supermarket 125 g dried raspberries $30 50 g dried raspberries Special offer £3.70 plus Tax at 25% Buy 375 g get 125 g extra free Postage £20 Postage $5 Using an exchange rate of $1 = £0.71

compare the cost, including postage, of 500 g of dried raspberries bought from the US supermarket with the cost of 500 g of dried raspberries bought from the UK supermarket. State which supermarket is the cheaper when buying 500 g of dried raspberries. Show your working clearly.

J Diagram NOT G accurately drawn 13 cm 5 cm K I F 20 cm 12 cm H Figure 5 Figure 5 shows a solid right-angled triangular prism FGHIJK in which FG = 13 cm FH = 12 cm IJ = 5 cm HI = 20 cm The faces FHIK and GHIJ of the prism are rectangles.

Calculate the total surface area, in cm², of the prism FGHIJK

Calculate the size, in degrees to one decimal place, of ∠FJI A company makes door wedges the same size and shape as the triangular prism FGHIJK The company packs the door wedges into boxes that are in the shape of a cube of side 60 cm.

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

Calculate the maximum number of door wedges that can fit into the box.

A box contains 8 green counters and 2 white counters only. Peter takes at random 2 counters from the box.

Calculate the probability that Peter will take 1 green counter and 1 white counter. A bag contains 28 blue beads and n red beads only. Naasir selects a bead from the bag at random.

Explain why the probability of the bead being red cannot be 11 Naasir keeps the first bead and selects a second bead at random from the bag. The probability of both beads being different colours is Given that there are fewer blue beads than red beads …………… , ……………

calculate the probability that both beads are blue. Show clear algebraic working.

The equation of a curve C is y 1 where k is a constant. x x A minimum point on C occurs when x = –1.5

Show that the value of k is 12 12 9

Complete the table of values for $y = \frac{12}{x} + \frac{9}{x^2} + 1$ Give your values of $y$ to 2 decimal places.

On the grid opposite, plot the minimum point and the points from your completed table.

Join all the points to form a smooth curve.

By drawing a suitable straight line on the grid, find the range of values, to one decimal place, of x in −6 ≤ x ≤ − 0.8 , for which 12 9 1 2 1≤ x x x 2

The functions f and g are such that where x > 1

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

Find the value of k such that g(k) = 8

Find fg(−3)

Find the inverse of the function f in the form Simplify your answer. The function h is defined for all values of x as where a and b are constants. Given that h(2) = 4

find the value of a and the value of b Show clear algebraic working.