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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...

In this question you must show detailed reasoning. Use Fermat’s Little Theorem to determine the least positive residue of 2180 (mod 23) 2 (4) ■■■■ DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS ARE

4 The eleven numbers listed above are to be packed into bins of size n where n is a positive integer. When the first-fit bin packing algorithm is applied to the eleven numbers, the bins are packed as shown below. Bin 1: 17 8 12 Bin 2: 16 24 Bin 3: 19 11 4 Bin 4: 23 13 Bin 5: 20 (a) Explain why this packing means that the value of n must be 40 The original list of eleven numbers is to be sorted into descending order. (b) Use a quick sort to obtain the fully sorted list. You must make...

[In this question, i and j are horizontal perpendicular unit vectors.] A particle A has mass 3 kg and a particle B has mass 2 kg. The particles are moving on a smooth horizontal plane when they collide directly. Immediately before the collision, the velocity of A is (3i – j)ms–1 and the velocity of B is (–6i + 2j)ms–1 Immediately after the collision the velocity of A is  −2i + 2 j m s–1     (a) Find the total kinetic energy of the two particles before the co...

The discrete random variable X has the following probability distribution x – 1 0 1 3 5 P(X = x) 0.2 0.1 0.2 0.25 0.25 (a) Find Var(X ) (b) Find Var(X 2) 2 (3) (3) ■■■■ DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREAQuestion 1 continued ■■■■ (Total for Question 1 is 6 marks) 3 Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA

1. (a) Given that y = ln(3 + x2) complete the table with the value of y corresponding to x = 3, giving your answer to 4 significant figures. x 2 2.5 3 3.5 4 4.5 5 y 1.946 2.225 2.725 2.944 3.146 3.332 (1) In part (b) you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (b) Use Simpson’s rule with all the values of y in the completed table to estimate, to 3 significant figures, the value of  ln(3 + x2)dx 2 (3) (c) ...

1. (a) Using the definition of sinhx in terms of exponentials, prove that 4sinh3 x + 3sinh x  sinh 3x (2) (b) Hence solve the equation sinh 3x = 19sinh x giving your answers as simplified natural logarithms where appropriate. 2 (5) ■■■■ DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS ARE

Pearson Edexcel A Level GCE In Mathematics (9MA0) Paper 01,2,31 and 32 Pure Mathematics,Mathematics Pure,Statistics and Mechanics QP & MS JUNE 2024

1. f(z) = z4 − 6z3 + az2 + bz + 145 where a and b are real constants. Given that 2 + 5i is a root of the equation f(z) = 0 (a) determine the other roots of the equation f(z) = 0 (b) Show all the roots of f(z) = 0 on a single Argand diagram. 2 (7) (2) ■■■■ DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS

P (0.5kg) Figure 1 Figure 1 shows a particle P of mass 0.5kg at rest on a rough horizontal plane. (a) Find the magnitude of the normal reaction of the plane on P. 2 (1) The coefficient of friction between P and the plane is 7 A horizontal force of magnitude X newtons is applied to P. Given that P is now in limiting equilibrium, (b) find the value of X. 2 (2) ■■■■ DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE I

Xian rolls a fair die 10 times. The random variable X represents the number of times the die lands on a six. (a) Using a suitable distribution for X, find (i) P(X = 3) (ii) P(X< 3) Xian repeats this experiment each day for 60 days and records the number of days when X = 3 (b) Find the probability that there were at least 12 days when X = 3 (c) Find an estimate for the total number of sixes that Xian will roll during these 60 days. (d) Use a normal approximation to estimate the probab...

y = 4x3 − 7x2 + 5x − 10 (a) Find in simplest form (i) dy dx d2 y (ii) dx2 d2 y (3) (b) Hence find the exact value of x when 2 dx2 = 0 (2) ■■■■ DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREAQuestion 1 continued ■■■■ (Total for Question 1 is 5 marks) 3 Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT W

g(x) = 3x3 − 20x2 + (k + 17) x + k where k is a constant. Given that (x – 3) is a factor of g(x), find the value of k. 2 (3) ■■■■ DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREAQuestion 1 continued ■■■■ (Total for Question 1 is 3 marks) 3 Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT

Pearson Edexcel As level GCE In Geography (8GE0) Paper 1 , 2 :Dynamic Landscapes and Dynamic Places QP & MS JUNE 2024

Pearson Edexcel A level GCE In Geography (9GE0) Paper 1,2 and 3 Question paper & mark scheme june 2024

SECTION A Globalisation Answer ALL questions. Write your answers in the spaces provided. You must use the Resource Booklet provided. 1 (a) State one social challenge created by the rapid urban growth of megacities. (1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

Answer Section A and EITHER Section B OR Section C. SECTION A Tectonic Processes and Hazards Answer ALL questions. Write your answers in the spaces provided. You must use the Resource Booklet provided. 1 (a) Complete the missing part of the hazard risk equation. Event × Vulnerability Risk of disaster = . .. . . .. . . .. . . .. . . .. . . . .. . . .. . . .. . . .. . . .. . . . .. . . .. . . .. . . .. . . .. . . . (b) Study Figure 1 in the Resource Booklet. (i) Compare the distribution...

Answer ALL questions. You must use the Resource Booklet provided and your own knowledge and understanding from across your course of study to answer the questions in this paper. 1 Explain why transnational corporations (TNCs) benefit from globalisation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

SECTION A Globalisation / Superpowers Answer ALL questions in this section. 1 (a) Explain one way in which globalisation has increased flows between countries. (4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

SECTION A Tectonic Processes and Hazards Answer ALL questions in this section. This is part of an investigation showing the total number of deaths caused by earthquake events for 11 years from 2011 to 2021. Year Total deaths from earthquake events 2011 21,942 2012 689 2013 1,572 2014 756 2015 9,624 2016 1,297 2017 1,012 2018 4,535 2019 244 2020 180 2021 2,476 Figure 1 Deaths from earthquake events, 2011–2021 2 ■■■■ DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AR...