Foundation Mathematics. 9 March Examination Paper. Time: 2 hours

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Foundation Mathematics 9 March 06 Examination Paper Answer ALL questions. Clearly cross out surplus answers. Time: hours The maximum mark for this paper is 00.

1 Foundation Mathematics 9 March 06 Examination Paper Answer ALL questions. Clearly cross out surplus answers. Time: hours The maximum mark for this paper is 00. Any reference material brought into the examination room must be handed to the invigilator before the start of the examination. Candidates are allowed to use a scientific calculator during this examination. Graph paper will be provided by the centre. You must show your workings. are awarded for these.

2 Answer ALL questions Question a) Simplify the following. i) xy y 4 x y m m m 4 i (r 5 s 4 ) b) Simplify the following. i) 8x y 5 6xy 5 a(a + 5b) + 6a(a b) i uv u v c) Factorise the following. i) x y xy a + a 0 d) Simplify the following. i) m 6m 7 8a a e) Transpose the following formula to make t the subject. r = 4 + 5s t f) Solve the following equation and find the value of p. p + = 5 g) Solve the following quadratic equation by factorising. x + x + 8 = 0 Total 0 Page of 7 Foundation Mathematics NCC Education Limited 06

3 Question a) Solve the following quadratic equation by using the quadratic formula. x + 6x + = 0 You may leave your answer in surd form. b) Solve graphically the following simultaneous equations. y = 4x and y = x + for x Use the graph paper provided. 7 c) Calculate the gradient of the following curves at the point where x =. i) y = x + 0.5x y = x x d) A particle moves s metres in t seconds so that s = t + 5t 7t i) Find the velocity, v, after seconds. Find the acceleration, a, after t seconds. Total 0 Page of 7 Foundation Mathematics NCC Education Limited 06

4 Question a) i) Using differentiation, find the coordinates of the turning point on the curve y = x + x 5 4 Identify the turning point found in part (i) as either a maximum or minimum turning point. b) Integrate the following expression. 0x 4 7 c) The gradient of the curve which passes through the point (, 5) is given by 8x + x Find the equation of the curve. d) Evaluate the following definite integrals. i) (x 5 6x + ) dx (x + x) dx e) The part of the curve y = x + between the ordinates x = and x = is rotated about the x-axis. Calculate the volume of the solid generated. Leave your answer as a multiple of π. Total 0 Page 4 of 7 Foundation Mathematics NCC Education Limited 06

5 Question 4 a) The acceleration of a moving body at the end of t seconds from the commencement of motion is t + 0 m/s. Find the velocity at the end of seconds if the initial velocity is 0 m/s b) A packet contains 4 flower seeds. Of the 4 flower seeds, 8 will produce yellow flowers and 6 will produce red flowers. Two seeds are selected at random from the packet (without replacement) and planted. i) Draw a probability tree diagram to show all the possible outcomes. 8 Use your tree diagram to work out the probability that both seeds selected will be the same colour flower seeds. i Use your tree diagram to work out the probability that one yellow flower seed and one red flower seed are selected in any order. iv) Use your tree diagram to work out the probability that at least one of the flower seeds is yellow. c) The probability that it will rain on Tuesday is 5 What is the probability that it will not rain? d) How many different teams of can we make from a group of 5 people? Total 0 Page 5 of 7 Foundation Mathematics NCC Education Limited 06

6 Question 5 a) A manager records the number of different types of sandwiches sold in a café. The results are shown in the table below. Number of different types of sandwich sold in a café. Sandwich Frequency Cheese and onion 7 Egg and cress 8 Chicken salad 0 Cheese salad Chilli chicken i) Is this data primary or secondary data? Is this data continuous or discrete? i Draw a bar chart to illustrate this data. 4 iv) The café manager decides to present the data as a pie chart. Calculate the relative frequency and the angle of the sector on the pie chart for the egg and cress sandwich and the chicken salad sandwich. 4 Question 5 continues on next page Page 6 of 7 Foundation Mathematics NCC Education Limited 06

7 Question 5 (continued) b) A train station records the delay times (in minutes) of all the trains leaving from the station during one week as follows. Time (minutes) Frequency 0 < < 0 0 < < 0 0 < < 0 6 i) Copy and complete the following table which calculates the cumulative frequency. Time (minutes) Frequency Cumulative frequency 0 < < 0 0 < < 0 0 < < 0 6 State which class interval the lower quartile (Q) value will lie within and then calculate the value using the formula for the lower quartile. i State which class interval the upper quartile (Q) value will lie within and then calculate the value using the formula for the upper quartile. c) The following data set is recorded i) Calculate the range of the data. Calculate the mean of the data. Total 0 End of paper Page 7 of 7 Foundation Mathematics NCC Education Limited 06

Foundation Mathematics. Sample. Examination Paper. Time: 2 hours

Foundation Mathematics. Sample. Examination Paper. Time: 2 hours Foundation Mathematics Sample Examination Paper Answer ALL questions. Clearly cross out surplus answers. Time: hours The maximum mark for this paper is 100. Any reference material brought into the examination