Mathematics SL. Mock Exam 2014 PAPER 2. Instructions: The use of graphing calculator is allowed.

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Mock Exam 2014 Mathematics SL PAPER 2 Instructions: The use of graphing calculator is allowed Show working when possible (even when using a graphing

1 Mock Exam 2014 Mathematics SL PAPER 2 Instructions: The use of graphing calculator is allowed Show working when possible (even when using a graphing calculator) Give your answers in exact form or round to 3 significant figures Write your name on the line below NAME: Mathematics SL Mock Exam

2 1 (a) Consider the geometric sequence 3, 6, 12, 24, Write down the common ratio Find the 15 th term Consider the sequence x 3, x +1, 2x + 8, When x = 5, the sequence is geometric Write down the first three terms Find the common ratio (c) (d) Find the other value of x for which the sequence is geometric For this value of x, find (4) the common ratio; the sum of the infinite sequence (Total 12 marks) Mathematics SL Mock Exam

3 2 Let f(x) = log 3 2 x + log3 16 log 3 4, for x > 0 (a) Show that f(x) = log 3 2x Find the value of f(05) and of f(45) The function f can also be written in the form f(x) = ln ax ln b (c) Write down the value of a and of b (iii) Hence on graph paper, sketch the graph of f, for 5 x 5, 5 y 5, using a scale of 1 cm to 1 unit on each axis Write down the equation of the asymptote (d) Write down the value of f 1 (0) (1) The point A lies on the graph of f At A, x = 45 (e) On your diagram, sketch the graph of f 1, noting clearly the image of point A (4) (Total 16 marks) Mathematics SL Mock Exam

4 3 The diagram below shows a quadrilateral ABCD with obtuse angles A Bˆ C and A Dˆ C diagram not to scale AB = 5 cm, BC = 4 cm, CD = 4 cm, AD = 4 cm, B ÂC = 30, A Bˆ C = x, A Dˆ C = y (a) Use the cosine rule to show that AC = cos x (1) Use the sine rule in triangle ABC to find another expression for AC (c) Hence, find x, giving your answer to two decimal places Find AC (d) Find y Hence, or otherwise, find the area of triangle ACD (5) (Total 14 marks) Mathematics SL Mock Exam

5 4 A farmer owns a triangular field ABC One side of the triangle, [AC], is 104 m, a second side, [AB], is 65 m and the angle between these two sides is 60 (a) Use the cosine rule to calculate the length of the third side of the field Given that sin 60 = 3, find the area of the field in the form 3p 3 where p is an integer 2 Let D be a point on [BC] such that [AD] bisects the 60 angle The farmer divides the field into two parts A 1 and A 2 by constructing a straight fence [AD] of length x metres, as shown on the diagram below (c) Show that the area of A 1 is given by 65x 4 Find a similar expression for the area of A 2 (iii) Hence, find the value of x in the form q 3, where q is an integer (7) (d) Explain why sina Dˆ C = sinadˆ B Use the result of part and the sine rule to show that BD 5 = DC 8 (5) (Total 18 marks) Mathematics SL Mock Exam

6 5 In this question, distance is in kilometres, time is in hours A balloon is moving at a constant height with a speed of 18 km h 1, in the direction of the vector At time t = 0, the balloon is at point B with coordinates (0, 0, 5) (a) Show that the position vector b of the balloon at time t is given by b = x y = 0 + t 144 z 5 0 At time t = 0, a helicopter goes to deliver a message to the balloon The position vector h of the helicopter at time t is given by h = x y = 32 + t 24 z 0 6 Write down the coordinates of the starting position of the helicopter Find the speed of the helicopter (4) (c) The helicopter reaches the balloon at point R Find the time the helicopter takes to reach the balloon Find the coordinates of R (5) (Total 15 marks) Mathematics SL Mock Exam

7 6 A fisherman catches 200 fish to sell He measures the lengths, l cm of these fish, and the results are shown in the frequency table below Length l cm 0 l < l < l < l < l < l < l < 100 Frequency (a) Calculate an estimate for the standard deviation of the lengths of the fish A cumulative frequency diagram is given below for the lengths of the fish Use the graph to answer the following Estimate the interquartile range Given that 40 % of the fish have a length more than k cm, find the value of k In order to sell the fish, the fisherman classifies them as small, medium or large Small fish have a length less than 20 cm Medium fish have a length greater than or equal to 20 cm but less than 60 cm Large fish have a length greater than or equal to 60 cm (c) Write down the probability that a fish is small The cost of a small fish is $4, a medium fish $10, and a large fish $12 (d) Copy and complete the following table, which gives a probability distribution for the cost $X Cost $X P(X = x) 0565 (e) Find E(X) (Total 15 marks) Mathematics SL Mock Exam

Express g(x) in the form f(x) + ln a, where a (4)

Express g(x) in the form f(x) + ln a, where a (4) SL 2 SUMMER PACKET PRINT OUT ENTIRE PACKET, SHOW YOUR WORK FOR ALL EXERCISES ON SEPARATE PAPER. MAKE SURE THAT YOUR WORK IS NEAT AND ORGANIZED. WORK SHOULD BE COMPLETE AND READY TO TURN IN THE FIRST DAY