Esthermungai

Advice Read each question carefully before you start to answer it. • Check your answers if you have time at the end. • Good luck with your examination. Turn over A U B V C W D X E Y Figure 1 A Hamiltonian cycle for the graph in Figure 1 begins C, V, E, X, A, W, …. (a) Complete the Hamiltonian cycle. (b) Hence use the planarity algorithm to determine whether the graph shown in Figure 1 is planar. You must make your working clear and justif...

Candidates may use any calculator permitted by Pearson regulations. Calculators must not have the facility for symbolic algebra manipulation, differentiation and integration, or have retrievable mathematical formulae stored in them. Instructions • If pencil is used for diagrams/sketches/graphs it must be dark (HB or B). centre number and candidate number. Answer all questions and ensure that your answers to parts of questions are clearly labelled. Answer the questions in the spaces provid...

AQA Physics Paper 1 Higher Combined Science Predicted Paper 2022 Name ……………………………………………… Date ……………………………………………… 1 hour 15 minutes allowed Similar to your real exam, each question in this gets harder towards the end of each question, so if you find you can’t do the last part of a certain question, try the next question – they all start off easier then get harder. Grade boundaries These are VERY rough...

Given that z  3cos π   isin  π   1   3   3   z  2 cos π   isin  π   2   12  12  (a) write down the exact value of (i) | z1z2 | (ii) arg (z1z2) Given that w = z z and that arg (wn) = 0 , where n  + (b) determine (i) the smallest positive value of n (ii) the corresponding value of | wn | (2) (3) ...

1. The transformation P is an enlargement, centre the origin, with scale factor k, where k > 0 The transformation Q is a rotation through angle θ degrees anticlockwise about the origin. The transformation P followed by the transformation Q is represented by the matrix  4 4 3 (a) Determine (i) the value of k, (ii) the smallest value of θ M =  4 3  4  (4) A square S has vertices at the points with coordinates (0, 0), (a, –...

1. Kelly throws a tetrahedral die n times and records the number on which it lands for each throw. She calculates the expected frequency for each number to be 43 if the die was unbiased. The table below shows three of the frequencies Kelly records but the fourth one is missing. Number 1 2 3 4 Frequency 47 34 36 x (a) Show that x = 55 Kelly wishes to test, at the 5% level of significance, whether or not there is evidence that the tetrahedral die is unbiased. (b) Explain why there a...

1. Kelly throws a tetrahedral die n times and records the number on which it lands for each throw. She calculates the expected frequency for each number to be 43 if the die was unbiased. The table below shows three of the frequencies Kelly records but the fourth one is missing. Number 1 2 3 4 Frequency 47 34 36 x (a) Show that x = 55 Kelly wishes to test, at the 5% level of significance, whether or not there is evidence that the tetrahedral die is unbiased. (b) Explain why there a...

1. The transformation P is an enlargement, centre the origin, with scale factor k, where k > 0 The transformation Q is a rotation through angle θ degrees anticlockwise about the origin. The transformation P followed by the transformation Q is represented by the matrix  4 4 3 (a) Determine (i) the value of k, (ii) the smallest value of θ M =  4 3  4  (4) A square S has vertices at the points with coordinates (0, 0), (a, –...