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

James bought a car on 1st March 2016 On 1st March 2017, the value of the car was 20% less than the amount that James paid for the car on 1st March 2016 On 1st March 2018, the value of the car was 10% less than the value of the car on 1st March 2017 On 1st March 2018, the value of the car was £20 340

Calculate the amount, in £, that James paid for the car on 1st March 2016 On 1st March 2019, the value of the car was £19 323

Calculate the percentage decrease in the value of the car from 1st March 2018 to 1st March 2019

A mixture for concrete is made up of 105 kg of cement, 252 kg of sand and 273 kg of gravel. Given that the mass of cement : the mass of sand : the mass of gravel = 1 : (2x + y) : (x + 2y)

write down two different equations in x and y. Simplify your equations.

Hence solve these two equations for the value of x and for the value of y. Give each value as a simplified fraction.

Find the inverse of the matrix 5 4

Use your answer to part (a) to find the value of x and the values of y that satisfy ⎛ 2 2⎞ ⎛ y 2 − 9 x⎞ ⎛ 0 ⎞ = 5 4 x −2 a b⎞ 1 ⎛ d − b⎞ ⎤ ⎢Inverse of matrix: ⎜ = ⎥ ⎣ ⎝ c d ad − bc −c a

Bag B1 and bag B2 each contain soil. The weight of soil in B1 is 7.5 kg to the nearest 100 g. The weight of soil in B2 is 5 kg to the nearest 10 g.

the lower bound for the total weight of soil in the two bags …………… , ……………

the upper bound for the difference in the weights of soil in the two bags …………… , ……………

the lower bound, to the nearest 50 g, for the difference in the weights of soil in the two bags. A large jar is to be filled with sweets. The jar will be filled using bags of sweets. The weight of the sweets in each bag of sweets is 220 g to the nearest 5 g. When the jar is full of sweets, the weight of sweets in the jar is 10 kg to the nearest 0.2 kg. Bertie has 45 bags of sweets.

Giving your reasons, determine whether Bertie has a sufficient number of bags of sweets to be sure that he can fill the jar with sweets.

Solve = 54 Show clear algebraic working. (4)

Solve = 54 Show clear algebraic working.

The functions f, g and h are defined as f : x ↦ x + 3 g : x ↦ x² – 2x + 3 h : x ↦ x ≠ 0 x ⎛ 1⎞

Find (i) g(–3) (ii) f h ⎜ − 4⎠

Express the inverse of the composite function hf in the form (hf)–1 : x ↦ ... and simplify your answer.

State the value of x that must be excluded from any domain of (hf )–1

Find the two values of x for which hgf(x) = 2

Write down all the multiples of 3 lying between 1 and 20 Ahmed and Hani play a game with 20 numbered balls. The 20 balls are numbered from 1 to 20 1 2 3 20 The balls are put in a bag. Ahmed takes at random a ball from the bag, makes a note of its number and puts the ball back into the bag. If the number of the ball is a multiple of 5, Ahmed wins the game. If Ahmed does not win the game, Hani takes at random a ball from the bag, makes a note of its number and puts the ball back into the bag. If the number of the ball is a multiple of 3, Hani wins the game. If Hani does not win the game, Ahmed takes at random a ball from the bag, makes a note of its number and puts the ball back into the bag. If the number of the ball is a multiple of 6, Ahmed wins the game. If Ahmed does not win the game, Hani takes at random a ball from the bag, makes a note of its number and puts the ball back into the bag. If the number of the ball is a multiple of 4, Hani wins the game. If Hani does not win the game, the game stops and the result is a draw. The incomplete probability tree diagram for the game is shown below.

Complete the probability tree diagram for Ahmed and Hani’s game.

Determine which player, Ahmed or Hani, is more likely to win the game. Give a reason for your answer. Ahmed wins Hani wins Ahmed does not Ahmed win wins Hani Hani does not wins win Ahmed does not win Hani does not win

Diagram NOT A accurately drawn 100 cm E D 30 cm 70° B M C Figure 1 Figure 1 shows triangle ABC in which AB = 100 cm, AC = 30 cm and ∠ACB = 70° Calculate, to 3 significant figures …………… , …………… the size, in degrees, of ∠ABC …………… , ……………

the length, in cm, of BC. As shown in Figure 1, the point E lies on AB and the point D lies on AC such that ED and BC are parallel and AD : DC = 1 : 2

Write down the length, in cm, of DC. The midpoint of BC is the point M.

Calculate the area, in cm² to 3 significant figures, of triangle DCM. area Δ ABC Given that = k, area ΔDCM

find the value of k without working out the area of triangle ABC. ⎡ Sine rule a = b = c ⎤ ⎢ sin A sin B sin C ⎥ ⎢ ⎥ ⎢Cosine rule $a^2$ = $b^2$ + $c^2$ − 2bc cos A ⎥ ⎢ ⎥ ⎢ 1 ⎥ ⎢⎣ Area of triangle = ab sin C ⎥⎦

The triangle A has vertices with coordinates (–5, 2), (–11, 0) and (–7, 6).

On the grid, draw and label triangle A. Triangle B is the image of triangle A under the enlargement with centre (1, 4) and scale factor −

On the grid, draw and label triangle B. Triangle C is the image of triangle B under a rotation of 180° about the point (3, 1).

On the grid, draw and label triangle C.

Describe fully the single transformation that maps triangle C onto triangle A.

a C 2 B Diagram NOT accurately drawn M N D O A a Figure 2 Figure 2 shows trapezium ABCD in which the point O is the midpoint of AD and the point M is the midpoint of CD. → → 1 → Given that OA = a, CB = a and OB = b …………… , …………… AB (ii) AC (iii) CD (iv) AM → → → → The lines OB and AM intersect at N so that AN = λ AM and ON = μOB , where λ and μ are positive constants. →

Find and simplify an expression in terms of a, b and λ for ON

Hence find the value of λ and the value of μ The area of triangle OAB is 14 square units.

Find the area of triangle BNA.

Part of the curve with equation $y = x^2 - 5x + 3$ is drawn on the grid. The equation of another curve is $y = -\frac{x^3}{6} + \frac{6x^2}{5} - \frac{3x}{2}$

Complete the table of values for $y = -\frac{x^3}{6} + \frac{6x^2}{5} - \frac{3x}{2}$ Give your values of $y$ to 2 decimal places.

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

Use the two curves on the grid to find an estimate, to 2 decimal places, of the range x³ x 2 7 x of positive values of x for which − − +3<0 6 5 2 Show your working clearly. For positive values of x, the two curves on the grid intersect at the points P and Q.

Find an estimate, to 1 decimal place, of the gradient of the straight line through P and Q. The equation of the straight line through P and Q has the form y = ax + b

Find, to 1 decimal place, the value of b.