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PAPER 3A: Further Pure Mathematics 1

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The ellipse E has equation x + y2 = 1 36 20 Find (a) the coordinates of the foci of E, (3) (b) the equations of the directrices of E. (2) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ ______...

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PAPER 3A: Further Pure Mathematics 1

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The ellipse E has equation x + y2 = 1 36 20 Find (a) the coordinates of the foci of E, (3) (b) the equations of the directrices of E. (2) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ ______...

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A-level PSYCHOLOGY Paper 1 Introductory topics in psychology

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0 1 Describe how Zimbardo investigated conformity to social roles. [4 marks] Extra space outside the box *02* 0 2 Fewer and fewer people use single-use plastic items, such as water bottles and plastic straws. Using your knowledge of social influence processes in social change, explain...

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MEDICAL SURGICAL ASSIGNMENT EXAM

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1. A client is admitted to the hospital with a traumatic brain injury after his head violently struck a brick wall during a gang fight. Which finding ID: 42 is most important for the nurse to assess further? A. A scalp laceration oozing blood. B. Headache rated "10" on a 0-10 scale. C. • Serosanguineous nasal drainage. Correct D. Dizziness, nausea and transient confusion. Any nasal discharge following a head injury should be evaluated to determine the presence of cerebral spin...

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A-level PSYCHOLOGY

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Section A Approaches in psychology Answer all questions in this section. 0 1 Outline the way in which Pavlov studied classical conditioning. [4 marks] 0 2 Some critics have said that Pavlov’s studies may lack ecological validity. What is meant by the term ecological validity? [2 marks] *02* outside the box ...

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Further Mechanics 1

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A van of mass 900 kg is moving along a straight horizontal road. At the instant when the speed of the van is v m s−1, the resistance to the motion of the van is modelled as a force of magnitude (500 + 7v) N. When the engine of the van is working at a constant rate of 18 kW, the van is moving along the road at a constant speed V m s−1 (a) Find the value of V. (5) Later on, the van is moving up a straight road that is inclined to the horizontal at an 1 angle θ , where sin...

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PAPER 3B: Further Statistics 1

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. 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 (1) 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 ther...

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Core Pure Mathematics

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Given that z1 = 3cos   π3 + isin   π3  z = 2cos12π  − isin12π  (a) write down the exact value of (i) | z1z2 | (ii) arg (z1z2) (2) Given that w = z1z2 and that arg (wn) = 0 , where n  + (b) determine (i) the smallest positive value of n (ii) the corresponding value of | wn | (3) _________________________________________________________________________...

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PAPER 3B: Further Statistics 1

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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 (1) 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 ...

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PAPER 1: Core Pure Mathematics 1

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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 M =  4 3 −4  (a) Determine (i) the value of k, (ii) the smallest value of θ (4) A square S has vertices at the points with coordinates (0, 0), (a, –a), (2a, 0) and (a, a) where...

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