4MB1/02R — June 2024 (Edexcel IGCSE Maths): Past Paper

Gary buys furniture and sells it in a shop. In the shop on Monday, Gary has tables and chairs such that number of tables : number of chairs = 2 : 7 Gary has 42 chairs in the shop on Monday.

Calculate the number of tables Gary has in the shop on Monday. Gary buys a table for $240 and sells it for $276

Calculate the percentage profit from the sale of the table. Gary buys some chairs and sells them for $513 Gary’s percentage profit from the sale of the chairs is 35%

Calculate the price at which Gary bought the chairs. The cost of a table that Gary buys is $732 An identical table costs 684 euros in France. Using the exchange rate $1 = 0.95 euros

find the difference in the costs of the tables. State whether your answer is in euros or $.

C B D 125° 125° 125° 125° E Diagram NOT A F accurately drawn L y° G K H J I Figure 1 Figure 1 shows a hexagon ABCDEL and a regular octagon EFGHIJKL BAL ABC CDE DEL 125 ° BCD ALE ALK y °

Calculate the value of y A different regular polygon has T sides and is such that an interior angle (10 x 25)° an exterior angle (7 x 83)°

Calculate the value of T [Sum of interior angles of polygon = (2n − 4) right angles]

Triangle A and triangle B are drawn on the grid opposite.

Describe fully the single transformation that maps triangle A onto triangle B Triangle A is transformed to triangle C by a reflection in the line with equation y

On the grid, draw and label triangle C Triangle A is transformed to triangle D by an enlargement with centre (0, 3) and scale factor 2

On the grid, draw and label triangle D Triangle A is transformed to triangle E under the transformation with matrix M where 2 1 M

On the grid, draw and label triangle E

Solve the inequality 4 x + 3 ≤ 31

Solve the inequality 1 2 x 3 21

Hence represent on the number line opposite, the set of values of x for which 4 x + 3 ≤ 31 and 1 2 x 3 21 −2 −1 0 1 2 3 4 5 6 7 8 9 10 x

Complete the table of values for y 2 x³ 5x x −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 y 3.75 6 5.25 3 0.75 2.25

On the grid opposite, plot the points from your completed table and join them to form a smooth curve.

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

By drawing a suitable straight line on your grid, find estimates to one decimal place, for the solutions of the equation 2 x 3 5 x 2 in the range −2 x 2 y −2 −1 O 1 2 x −2 −4

6 80 gardeners were asked if they grow potatoes (P), carrots (C) or lettuce (L) Of these gardeners 9 grow potatoes, carrots and lettuce 17 grow potatoes and carrots 23 grow carrots and lettuce 19 grow potatoes and lettuce 48 grow carrots 49 grow lettuce 2 grow none of these three crops

Using this information, complete the Venn diagram below to show the number of gardeners in each subset. E P C L

Find n(C ∩ Lʹ ) One of the gardeners is chosen at random. Given that this gardener grows carrots …………… , ……………

find the probability that this gardener also grows lettuce.

A B C 8 5

Find 4 A + 2B

Find AC 1 0

Find the matrix D such that A 1 D 2I where I = 0 1 a b 1 d b The inverse of matrix is c d ad bc c a

Aalia delivers letters and parcels.

Last week Aalia worked for 5 days and wrote down 5 integers that represent the distance, in miles, she drove each day. For these integers the mode is 15 the median is 16 the largest − the smallest = 7 Find 5 integers that Aalia could have written down.

Aalia has 8 letters to deliver to Tom. The mean weight of the 8 letters is 104 grams. 5 of the letters are each of weight 89 grams. The mean weight of the remaining letters is A grams. Work out the value of A The histogram shows information about the weights of all the parcels Aalia has in her delivery van on Friday. 75 of the parcels in the van each have a weight between 2 kg and 6 kg. Aalia takes 2 parcels at random from the van.

Find an estimate for the probability that both parcels weigh more than 4 kg.

Q Diagram NOT accurately drawn P 160° R 37° O T Figure 2 Figure 2 shows the points P, Q, R and T on a circle centre O POR 160 ORT

Work out the size, in degrees, of ∠PTR

Give a reason for your answer.

Work out the size, in degrees, of ∠TPO The sector, OPQR, is cut out from the circle in Figure 2 A hollow right circular cone is formed by joining OP and OR together as shown in Figure 3 O Q Diagram NOT accurately drawn P 160° R P R Q O Figure 3 196 The curved surface area of the cone is π cm²

Calculate the volume, in cm³ to 3 significant figures, of the cone. 1 2 Volume of cone 3 r h Curved surface area of cone rl

f and g are two functions such that f : x ↦ x² + 2x where x > −1 g:x ↦ x+2

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

Find f(3)

Find the value of x for which g(x) = 5

Find fg(24)

Find the value of x for which gf(x) = 4 Show your working clearly. The function h is such that h : x ↦ 5 x 2 − 10 x − 4 where x ≥ 1

Find the inverse of h(x) in the form h −1 : x ↦ ... b b 2 4ac The solutions of ax 2 bx c 0 where a 0 are given by x 2a

Solve the simultaneous equations x y 2 x y 2 xy 2 2 Show clear algebraic working. b b 2 4ac The solutions of ax 2 bx c 0 where a 0 are given by x 2a

for Question 12 6 ( 2 a 3) 12 35 25 5w 7 252 a 1 Find an expression for w in terms of a Give your answer in the form na + m where n and m are integers.