CD_ONLY_Review_Exercise.pdf - Whole Course Review Exercise...

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1 1 The equation of a straight line l is given by where m is a parameter. The point P lies on l where a Find the angle between OP and l , where O is the origin. b Find the equation of a line perpendicular to l , and passing through the point in Cartesian form. c The point R has coordinates Find an equation of a plane passing through P , Q and R in scalar product form. d Is the line l contained in, parallel to, or does it intersect the plane? If it intersects, determine the coordinates of the point of intersection. e The points S and T are on l and are given by and respectively. Show that there is no value of for which OS and OT are perpendicular. 2 In a yearly school soccer tournament, records are kept of the number of goals scored by each team. The tournament has been running for 20 years. The results for the last year are summarised in the table below. a State the modal value. b Calculate the median. c Calculate the mean. d Calculate the standard deviation. e Calculate an unbiased estimate for the standard deviation of the number of goals in the last 20 years. f Two of the teams are chosen at random. What is the probability that the sum of their scores is 17? g Given that the sum of the scores for the two teams is 17, what is the probability that the difference of their scores is 3? h These scores are used to model the predicted scores for the following year. Write down the probability distribution for X where X is the number of goals scored. i Find E( X ) and Var( X ). 3 a Prove, using the method of mathematical induction, that b Hence evaluate c Let If z is a root of a quadratic equation, calculate the second root. d Calculate in the form and draw these roots on an Argand diagram. r e i 4 1 z z 3 i 1 2 i . ¢ 3 i 1 2 i 16 . ¢ 3 i 1 2 i 4 n 1 4 2 n , n H . m m 3 m m m p 1 3, 1, 3 2 . Q ˛ 1 0, 4, 3 2 m 2. r £ 1 2 4 m £ 2 1 3 Number of 6 7 8 9 10 11 goals Frequency 3 5 6 7 4 3 Whole Course Review Exercise
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c For this value of c , find the general solution to these equations.
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