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A continuous random variable X has cumulative distribution function F(x) given by  F(x) =  5 0 (x + 1)2 1 −1 x < −1 x 0  1 −   (4 − x)2 20 1 0 < x 4 x > 4 (a) Find the probability density function, f(x) (b) (i) Sketch f(x) (ii) Hence describe the skewness of the distribution. (c) Find, to 3 significant figures, the value of c such that P(1 < X < c) = P(c < X < 2) 2 (2) (2) (1) (3) ■■■■ DO NOT WRITE IN ...

Sharma believes that each computer game he sells appeals equally to all age ranges. To investigate this, he takes a random sample of 100 people who play these games and asks them which of the games A, B or C they prefer. The results are summarised in the table below. Computer game A B C Age range < 20 8 15 6 20 – 30 21 12 9 > 30 6 10 13 (a) Write down hypotheses for a suitable test to assess Sharma’s belief. (b) For the test, calculate the expected frequency for (i) those pl...

The table below is a Cayley table for the group G with operation ° ° a b c d e f a d c b a f e b e f a b c d c f e d c b a d a b c d e f e b a f e d c f c d e f a b (a) State which element is the identity of the group. (b) Determine the inverse of the element (b°c) (c) Give a reason why the set {a, b, e, f } cannot be a subgroup of G. You must justify your answer. (d) Show that the set {b, d, f } is a subgroup of G. (ii) Given that H is a group with an element x of order 3 and an...

n this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Sketch the graph of the curve with equation (b) Solve, using algebra, the inequality 1 y = 2x (2) 3 − 2x2 > 1 x2 2 (5) ■■■■ DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS

The cubic equation 2x3 − 3x2 + 5x + 7 = 0 has roots α, β and γ. Without solving the equation, determine the exact value of (i) α2 + β2 + γ2 3 3 3 (3) (ii) α + β + γ (3) (iii) (5 – α)(5 – β)(5 – γ) 2 (3) ■■■■ DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN

Find 2 x − 3 dx x2 giving your answer in simplest form. (4) ∫3 ■■■■ Turn over Question 1 continued

Pearson Edexcel GCE In A Level Further Mathematics (9FM0) Paper 01, 2,3,3B,3C,3D,,4A,4C and 4D, Core Mathematics, Pure Mathematics,Further Statistics 1, Further Statistics and Further Mechanics 2 QP & MS June 2024

1. C 1 A x 13 12 12 B S 7 2 2 15 8 13 13 19 7 D 10 E 17 11 5 5 T 44 15 5 10 C y 12 4 11 8 C 1 16 16 F Figure 1 Figure 1 shows a capacitated, directed network of pipes. The numbers in circles represent an initial flow from S to T. The other number on each arc represents the capacity, in litres per second, of the corresponding pipe. (a) (i) State the value of x (ii) State the value of y (b) State the value of the initial flow. (c) State the capacity of cut C1 ...

In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. A particle P moves along a straight line. Initially P is at rest at the point O on the line. At time t seconds, where t 0 • the displacement of P from O is x metres • the velocity of P is vms–1 in the positive x direction 96 • the acceleration of P is (3t + 5) ms−2 in the positive x direction (a) Show that, at time t seconds, v = be determined. ...

Two students are experimenting with some water in a plastic bottle. The bottle is filled with water and a hole is put in the bottom of the bottle. The students record the time, t seconds, it takes for the water level to fall to each of 10 given values of the height, h cm, above the hole. Student A models the data with an equation of the form t = a + b h The data is coded using v = t – 40 and w = h and the following information is obtained. v = 626 v2 = 64678 w = 22.47 Sww = 4.5...