IGCSE Maths 2020 0580/41 Oct/Nov

IGCSE 2020 0580/41 Oct/Nov Questions (pdf)

IGCSE 2020 0580/41 Oct/Nov Mark Scheme (pdf)

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1. (a) Draw the image of shape A after a translation by the vector
   (b) Draw the image of shape A after a reflection in the line y =-1.
   (c) Describe fully the single transformation that maps shape A onto shape B.
   (d) Describe fully the single transformation that maps shape A onto shape C.
2. (a) A plane has 14 First Class seats, 70 Premium seats and 168 Economy seats.
   Find the ratio First Class seats : Premium seats : Economy seats.
   Give your answer in its simplest form.
   (b) (i) For a morning flight, the costs of tickets are in the ratio
   First Class : Premium : Economy = 14 : 6 : 5.
   The cost of a Premium ticket is $114.
   Calculate the cost of a First Class ticket and the cost of an Economy ticket.
   (ii) For an afternoon flight, the cost of a Premium ticket is reduced from $114 to $96.90.
   Calculate the percentage reduction in the cost of a ticket.
   (c) When the local time in Athens is 09 00, the local time in Berlin is 0800.
   A plane leaves Athens at 1315.
   It arrives in Berlin at 1505 local time.
   (i) Find the flight time from Athens to Berlin.
   (ii) The distance the plane flies from Athens to Berlin is 1802km.
   Calculate the average speed of the plane.
   Give your answer in kilometres per hour.
3. The box-and-whisker plots show the times spent exercising in one week by a group of women and a group of men.
   Below are two statements comparing these times.
   For each one, write down whether you agree or disagree, giving a reason for your answer.

4. (a) A rectangle measures 8.5cm by 10.7cm, both correct to 1 decimal place.
   Calculate the upper bound of the perimeter of the rectangle.
   (b) ABDF is a parallelogram and BCDE is a straight line.
   AF = 12cm, AB = 9 cm, angle CFD = 40° and angle FDE = 80°.
   (i) Calculate the height, h, of the parallelogram.
   (ii) Explain why triangle CDF is isosceles.
   (iii) Calculate the area of the trapezium ABCF.
5. (a) The diagram shows the graph of y = f(x) for -3 ≤ x ≤ 3
   (i) Solve f(x) = 14.
   (ii) By drawing a suitable tangent, find an estimate of the gradient of the graph at the point (-2, 4).
   
6. The diagram shows a field, ABCD, on horizontal ground.
   BC = 192m, CD = 287.9m, BD = 168m and AD = 205.8m.
   (a) (i) Calculate angle CBD and show that it rounds to 106.0°, correct to 1 decimal place.
   (ii) The bearing of D from B is 038°.
   Find the bearing of C from B.
   (iii) A is due east of B.
   Calculate the bearing of D from A.
7. These are the first four diagrams of a sequence.
   The diagrams are made from white dots and black dots.
   (a) Complete the table for Diagram 5 and Diagram 6.
8. (a) Factorise completely.
9. (a) There are 32 students in a class.
   5 do not study any languages.
   15 study German (G).
   18 study Spanish (S).
   (i) Complete the Venn diagram to show this information.
   (ii) A student is chosen at random.
   Find the probability that the student studies Spanish but not German.
   (iii) A student who studies German is chosen at random.
   (b) A bag contains 54 red marbles and some blue marbles.
   36% of the marbles in the bag are red.
   Find the number of blue marbles in the bag.
   Find the probability that this student also studies Spanish.
   (c) Another bag contains 15 red beads and 10 yellow beads.
   Ariana picks a bead at random, records its colour and replaces it in the bag.
   She then picks another bead at random.
   (i) Find the probability that she picks two red beads.
   (ii) Find the probability that she does not pick two red beads.
   (d) A box contains 15 red pencils, 8 yellow pencils and 2 green pencils.
   Two pencils are picked at random without replacement.
   Find the probability that at least one pencil is red.
   
10. (a) The diagram shows a sketch of the curve y = x² + 3x - 4
    (i) Find the coordinates of the points A, B and C.

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