Bridging task for 2016 entry AS Level Use of Mathematics Why do I need to complete a bridging task? Welcome to AS Use of Maths! By now you are probably enjoying a well-earned rest after your GCSE exams, but we d also like you to give some thought to your start at College in August. Experience tells us that students who know what to expect and who do some preparation during the holidays find adjusting to A Level study more straightforward. This work comprises an element of the assessment used during induction. When should I hand it in? You should have this booklet completed to the best of your ability so that you can hand it in to your teacher during your first AS Use of Maths lesson in September. The completed booklet will form a significant part of your assessment during your first few weeks with us. Information As the name suggests, this course is about how Maths is used in a variety of commercial, industrial and scientific contexts. You will study three modules: Algebra Here we study the techniques necessary for any advanced study of the subject. We concentrate on four particular areas: linear modelling, using quadratics, exponential growth and decay, modelling using trigonometric functions. Data Analysis This builds upon the statistics you have covered at GCSE level. Topics include: descriptive statistics, graphical representation of data, correlation and regression, the normal distribution. Decision Maths This is a fairly modern branch of mathematics concerned with solving practical problems. We will study Critical Path Analysis which is used to ensure that complex projects (such as the building of Huddersfield s new sports centre) run on time. We will also discover how a Sat-Nav device finds the shortest route for a motorist. Each module is examined by a one hour exam. 1
Graphical Calculators You are expected to use one of these throughout the course and in the exam. We are able to supply them at a competitive rate (about 60). We will provide more details at the start of the year about the particular model we need you to buy. What follows is some work to help you prepare for the start of your course. This should ensure that you keep your skills fresh and the questions we have set you should lead nicely into the new work that we start in September. 2
Section A. Data Analysis 1. The number of goals scored in 15 hockey matches is shown in the table. Number of goals Number of matches 1 2 3 1 5 5 6 3 9 4 Calculate the mean number of goals scored............................................................. 2. The table shows the results of a survey of children s weights. Weight, w, (kg) Number of children 20 < w < 30 5 30 < w < 40 9 40 < w < 50 13 50 < w < 60 8 60 < w < 70 7 70 < w < 80 8 Answer... goals (Total 3 marks) Calculate an estimate of the mean weight of the children.......... Answer... kg (Total 4 marks) 3
3. (a) The box plot shows the heights of a group of boys in a school. 130 140 150 160 170 180 190 Height (cm) (i) Write down the media height of these boys. Answer cm (ii) Find the interquartile range of the heights of these boys.... Answer cm (b) 15 girls in the school are chosen at random. Their heights, in centimetres, are shown below. 142, 147, 152, 156, 156, 159, 164, 166, 166, 166, 167, 170, 171, 171, 175 There are a total of 450 girls in the school. Use this sample to estimate how many girls in the school are less than 148 cm tall. Answer... (Total 5 marks) 4
4. (a) Adam and Betty take a mental arithmetic test each week for seven weeks. Adam s test scores are (i) What is the mode of Adam s scores? Answer... (ii) What is the median of Adam s scores? Answer... (b) Betty s test scores are 3 6 7 8 8 4 6 Complete this table. Range Mean Adam 3 8 Betty 5 (3) (c) Use the range and mean to compare their test scores. (Total 8 marks) 5
5. The weights of 80 bags of rice are measured. The table summarises the results. Minimum Lower quartile Median Upper quartile Maximum 480 g 500 g 540 g 620 g 720 g (a) Draw a box plot to show this information. 500 550 600 650 700 Weight (g) (3) (b) Write down the interquartile range for these data. Answer... g (c) How many bags weigh (i) less than 480 g Answer... (ii) less than 500 g? Answer... 6
(d) Draw a cumulative frequency diagram to show the information. 80 60 Cumulative frequency 40 20 0 500 550 600 650 700 Weight (g) (3) (Total 6 marks) 7
6. The table shows the number of petrol pumps and the number of cars queuing at midday at six garages. Number of petrol pumps 3 4 6 4 3 5 Number of cars queuing 6 5 3 4 5 4 (a) Plot a scatter graph of these data on the axes below. 6 5 Number of cars queuing 4 3 2 1 0 0 1 2 3 4 5 6 7 8 9 Number of petrol pumps b) Draw a line of best fit on your scatter graph. (c) Use your line to estimate the number of cars queuing at a garage with 8 petrol pumps. Answer... (d) Explain why your answer in part (c) may be unreliable.. (Total 5 marks) 8
Section B. Algebra. 7. Solve the following equations. (a) 2x + 5 = 3 Answer x =... 2) (b) 4(y 3) = 18 Answer y =... (3) (Total 5 marks) 8. A company uses this formula to find the cost, in pounds, to hire out a car. a) Calculate the cost of hiring a car for Cost = 25 number of days hired + 20 (i) two days, Answer... (ii) one week. Answer... (b) Linda hires a car for her holiday. She pays the company 270. For how many days does she hire the car? Answer... days (Total 6 marks) 9
9. (a) Complete this table of values for y = 2x 1 x 1 0 1 2 3 y 3 1 5... (b) On the grid draw the graph of y = 2x 1 for values of x from 1 to +3. y 5 4 3 2 1 1 O 1 2 3 1 x 2 3 (c) Find the coordinates of the point where the line y = 2x 1 crosses the line y = 2.... Answer (...,...) (Total 5 marks) 10
10. The line l on the graph passes through the points A (0, 3) and B ( 4, 11). y l 15 B 10 5 A 10 5 O 5 x (a) Calculate the gradient of the line l.. Answer... (b) Write down the equation of the line l.. Answer... (c) Write down the equation of the line which also passes through the point (0, 3) but is perpendicular to line l... Answer... (Total 5 marks) 11
11. (a) On the grid below draw and label the lines y = 4 and y = 2x + 1............... y 7 6 5 4 3 2 1 4 3 2 1 O 1 2 3 4 1 x 2 3 4 5 6 7 (4) (b) Write down the coordinates of the point where the lines y = 4 and y = 2x + 1 cross. Answer (...,...) (Total 5 marks) 12
12. (a) Complete the table of values for y = 2x 2 4x 1 x 2 1 0 1 2 3 y 15 1 1 5... (b) On the grid, draw the graph of y = 2x 2 4x 1 for values of x from 2 to +3. y 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 2 1 O 1 2 3 x 1 2 3 13
(c) An approximate solution of the equation 2x 2 4x 1 = 0 is x = 2.2 (i) Explain how you can find this from the graph.... (ii) Use your graph to write down another solution of this equation. Answer x =... (Total 6 marks) 14