4MB1/02 — June 2020 (Edexcel IGCSE Maths): Past Paper

A Diagram NOT x° accurately drawn 9.3 cm 5 cm 10.8 cm 124° B C y° D Figure 1 Figure 1 shows a quadrilateral ABCD. AB = 9.3 cm AC = 5 cm AD = 10.8 cm ∠ACD = 124° ∠ACB = 90° ∠CAB = x° ∠ADC = y° Calculate to one decimal place …………… , …………… the value of x …………… , ……………

the value of y. ⎡ a b c ⎤ ⎢⎣Sine rule: sin A = sin B = sin C ⎥⎦

On the grid below, by drawing suitable straight lines and using shading, show the region R that satisfies the inequalities 2x + 3y ≥ 6 1≤x≤3 y≤4 Label the region R. y –2 –1 O 1 2 3 4 5 x –1 The point P with coordinates (x, y) lies in the region that satisfies the inequalities 2x + 3y > 6 1<x<3 y<4 Given that x and y are integers …………… , ……………

write down the coordinates of all possible points P.

Express (5x – 6) ÷ − as a single fraction in its simplest form. ⎝ x+3 ⎠ x+2 Show clear algebraic working.

A Diagram NOT accurately drawn 9 cm 9 cm B 10 cm C Figure 2 Figure 2 shows triangle ABC. AB = 9 cm AC = 9 cm BC = 10 cm

Calculate the area, in cm² to one decimal place, of triangle ABC. Figure 3 shows two solid right prisms, each of length 7 cm. One of the prisms has triangle ABC as a cross section of the prism. The other prism has trapezium DEFG as a cross section of the prism. Diagram NOT A accurately drawn F E 9 cm 9 cm 5.5 cm 4.5 cm 7 cm D G 7 cm B 10 cm C Figure 3 In trapezium DEFG, DE = 4.5 cm FG = 5.5 cm The perimeter of trapezium DEFG is equal to the perimeter of triangle ABC.

Calculate the difference, in cm³ to one decimal place, between the volumes of the two prisms. ⎡ 1 ⎤ ⎢⎣ Area of trapezium = 2 (a + b)h ⎥⎦

Tahina travels to work by bus. Her total bus fare last week was £12.50 This week her total bus fare has increased by 8%

Calculate her total bus fare for this week. Tahina works in a kiosk selling hot drinks. She sells coffee, tea and hot chocolate. On Monday, Tahina sold a total of 378 hot drinks. The numbers of cups of coffee, tea and hot chocolate she sold were in the ratios 5 : 3 : 1

Calculate the difference between the number of cups of coffee and the number of cups of hot chocolate that Tahina sold on Monday. On Monday, of the number of cups of coffee Tahina sold were sold without milk.

Calculate the number of cups of coffee that Tahina sold without milk. The cost of each cup of coffee that Tahina sells from the kiosk is £2.80 Tahina went on holiday to the USA and to Canada. She bought a cup of coffee in the USA for $3.20 Using an exchange rate of £1 = $1.24

compare the cost of each cup of coffee sold from Tahina’s kiosk with the cost of the cup of coffee that Tahina bought in the USA. In Canada, Tahina bought a sandwich for 5.28 Canadian dollars. Using exchange rates of £1 = $1.24 and 1 Canadian dollar = $0.75

convert 5.28 Canadian dollars to pounds (£) Give your answer to 2 decimal places.

Solve the simultaneous equations x 2 + y 2 = 26 2x + y = 9 Show clear algebraic working.

A 10b C 4a Diagram NOT accurately drawn O 6b B Figure 4 Figure 4 shows a trapezium OACB. → → → OA = 4a OB = 6b AC = 10b P is the point on AB such that OPC is a straight line. → Find an expression for PC in terms of a and b. Give your answer in its simplest form.

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

The diagram shows kite A. Kite B is the image of kite A under a reflection in the line with equation y = –1

On the grid opposite, draw and label kite B. Kite A is transformed to kite C by a reflection in the line with equation x = 4 followed by ⎛ −8⎞ the translation −6⎠ Kite C is the image of kite B under a rotation through 180° about the point P.

On the grid opposite, draw and label kite C.

Find the coordinates of P. ⎛ 0 −1⎞ ⎛ 0 −1⎞ M= −2 0 N= 1 0 Kite A is transformed to kite D under the combined transformation with matrix MN.

On the grid opposite, draw and label kite D. area of kite D Given that =k area of kite A

find the value of k.

9 90 students from a sixth form college were each asked the following question. “Do you study any of Biology (B), Chemistry (C) or Physics (P)?” Of these 90 students 7 study all three subjects 15 study Biology and Chemistry 20 study Chemistry and Physics 37 study Chemistry 14 study Biology only 15 study Physics only The number of these students who study Biology and Physics but not Chemistry is three times the number of these students who study none of these three subjects. Let x be the number of these students who study none of these three subjects.

Show all this information on the Venn diagram, giving the number of students in each appropriate subset, in terms of x where necessary. E B C P

Find the value of x.

n(B¢ ∩ C)

n(B ∪ C ∪ P)

n(B ∩ C ∩ P¢) One of the students is to be chosen at random. Given that this student studies Chemistry …………… , ……………

find the probability that this student also studies Physics.

The function g is such that g:x ↦ x−3

State the value of x that must be excluded from any domain of g. The function h is defined for all values of x by h : x ↦ x² + 4

Write down the range of h.

Find h(–9)

Find hg(5)

Express the inverse function g–1 in the form g–1 : x ↦ ... 4(45 − 6 x + x ) 2

Show that hg(x) can be written as ( x − 3) 2

Solve hg(x) = 5 Show clear algebraic working.

Complete the table of values for $y = 2x^3 - 3x + 4$

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

By drawing on the grid a suitable tangent to the curve, find an estimate, to the nearest whole number, of the gradient of the curve at the point where x = 2

Use your graph to find the range of values of x, in –2.5 ≤ x ≤ 2.5, for which 2x 3 – 3x + 4 > 5x

Harvey has two bags of counters, bag A and bag B. Bag A contains 8 red counters, 3 orange counters and 4 yellow counters only. Bag B contains 3 red counters, 2 orange counters and 5 green counters only. Harvey takes at random one counter from bag A and one counter from bag B.

Complete the probability tree diagram on the opposite page.

Calculate the probability that the two counters taken have different colours. Harvey replaces the counters into the bags from which he took the counters. Chen has a bag, bag C, that contains 10 red counters and x orange counters only. Chen takes at random one counter from bag A, one counter from bag B and one counter from bag C. The probability that all three counters that Chen takes have the same colour is

Find the value of x. Bag A Bag B red red orange 8 green red orange orange green red yellow orange green