Maths Skil s Check

Transcription

1 Maths Skills Check

2 2010 National Extension College. All rights reserved. Updated 2016 Test compiled by: Page layout: Graham Smithers Alison Kelt No part of this publication may be reproduced, stored in a mechanical retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without prior permission of the publisher. This publication is sold subject to the condition that it shall not by way of trade or otherwise, be lent, resold, hired out, or otherwise circulated without the publisher s prior consent in any form of binding or cover other than that in which it is published and without a similar condition being imposed on the subsequent purchaser. The National Extension College was set up to help people fit learning into their lives. Our mission is to widen learning opportunities by creating and promoting alternative modes of study. We provide home study courses for individual learners, training programmes for public and private sector businesses, and open learning resources for organisations delivering training. We have made every effort to trace and contact copyright holders. If notified, NEC will be pleased to rectify any errors or omissions at the earliest opportunity. For further details of NEC resources and supported courses, contact: National Extension College The Michael Young Centre School House Homerton Gaedens Cambridge CB2 8EB Tel Fax info@nec.ac.uk website:

3 Maths Skills Check Contents Introduction 3 The Level 2 maths courses offered by NEC 3 What is IGCSE? 3 Which tier is right for me? Frequently asked questions 5 So, should I enrol on the Foundation or Higher tier? 6 Practice questions 6 Sample questions from NEC courses 12 Sample questions 12 Answers 13 Answers to practice questions 13 Answers to sample questions 14

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5 Introduction NEC offers two mathematics courses of Level 2 standard (i.e. GCSE level). It is the aim of this skills check to help you decide which one is the one for you. When you are ready to enrol or you want to ask further questions, ring or our Course Advice team on info@nec.ac.uk Objectives When you have read and worked through the skills check, you should be able to: distinguish between the level 2 maths courses offered by NEC choose the course that is most suitable for you. The Level 2 maths courses offered by NEC Thecourses are: Foundation level IGCSE, which can lead to grades C to G. Higher level IGCSE, which can lead to grades A* to D. What is IGCSE? IGCSE stands for International General Certificate of Secondary Education. This exam is set internationally and is particularly useful for students studying outside the UK. However, many individual students in the UK also take this exam as do, increasingly, a number of UK schools. 3

6 The crucial differences between IGCSE and GCSE are: IGCSE has no non-calculator exam papers, just two calculator papers. IGCSE is a linear exam, i.e. you sit the two papers at the end of the course either in January or June. There are two tiers at IGCSE Foundation level and Higher level. Foundation level IGCSE can lead to grades C to G. It contains very little algebra but there is some basic set theory. Higher level IGCSE can lead to grades A* to D. It contains the usual algebra that you would expect in any maths exam quadratic equations, for example as well as more set theory, some differential calculus and the theory of functions. You will find sample questions for each of these exams in this booklet. In summary then, IGCSE has: two calculator papers no non-calculator paper a linear exam structure which is examined in either January or June very little algebra at Foundation level, but there is some set theory work on calculus and the theory of functions at Higher level, together with further work on set theory. Grade Foundation level Higher level A* A B C D E F G U Grades C-G Grades A* D (allowed E) 4

7 Which tier is right for me? Frequently asked questions 1 I need a C grade in order to enrol on a PGCE/paramedics/nursing course. Which course would you recommend? You need a C grade for your career move and the easiest way to achieve this is to take a Foundation course. 2 If I enrol on a Higher course, but then find that I cannot cope, what then? In that case you would be best advised to purchase a Foundation course. However, that means more expense and so it is important that your first choice is the right one. Working through the examples later on in this booklet will help you to make the right choice. 3 I cannot decide between Foundation and Higher level. What do you recommend? If a C grade is sufficient for your next career move, then go for Foundation level. Otherwise, go for Higher level. 4 I took O level years ago and need to brush up on my maths. What do you recommend? Go for Higher level. 5 I would eventually like to take Maths A level. Which course is best for that? Go for Higher IGCSE. As well as covering all the usual topics, this course also includes some calculus and function work both of which are valuable at A level. 6 I only need a C grade, but would like to get a higher grade than that, so I am going to purchase a Higher course. Do you agree? The crucial point is that you need a C grade. If you go for Higher level then there will be an opportunity for you to achieve a higher grade, but a lot more studying will be involved. Do you have the spare time to devote to this additional work? If you do, then it might be worth a try, (but see questions 2 and 3). If you are unlikely to have much spare time, then go for Foundation level. 5

8 So, should I enrol on the Foundation or Higher tier? In order to help you with this decision, you should: try the following questions 1 10, without a calculator then check your answers with the Answers section. Take as much time as you need. Practice questions 1 Work out Work out Work out Look at the triangle below: B 100 Not drawn accurately A C Write down the size of angle BCA t. 5 How many 41p stamps can I buy with a 5 note? For the remaining five questions, choose the answer that you think is correct. 6 The prices in a café were: tea 30p coffee 35p ham sandwich 90p bun 25p 6

9 Mary s bill came to What did she buy? a) a tea, a ham sandwich and a bun b) a tea, a coffee and a ham sandwich c) a tea, a coffee and two ham sandwiches d) two teas, a ham sandwich and a bun. 7 A B A and B are two rectangles. A is 10 cm wide and 1 cm deep. B is 5 cm wide and 2 cm deep. The area of A is: a) twice as big as the area of B b) the same as the area of B c) half the area of B d) less than half the area of B. 8 Here are eight sums: a) 41 2 b) c) d) 28 3 e) f) g) 82 2 h) 80 1 Work them out and put the answers in increasing order, from the smallest to the largest. Which order did you get? a) GFHCABDE b) GDEHCABF c) GEHCABDF d) none of these. 7

10 9 X In the diagram, the arrow X is pointing nearest to: a) 652 b) 659 c) 660 d) In the diagram, the total number of blocks in the stack is: a) 18 b) 20 c) 24 d) 26. Now go to p. 16 to check your answers. If you found these questions difficult, or didn t quite understand the meaning of some of them, then Foundation level is probably the tier you should choose. On the other hand, if you did rather well on these questions say eight or more correct then try the following ten questions. This time you may use a calculator. Take as much time as you need. 11 Work out The sides of a square are 7.6 cm long. What is the area of the square? A square has area 72 4 m. What is the length of one of its sides? 8

11 For the remaining seven questions, choose the answer that you think is correct. 14 The cost of running a disco is 170. Two hundred and forty-nine people come, paying 1.25 each. What is the profit? a) b) c) d) A car driver estimates she will average 42mph on a journey of 145 miles. The best estimate of the time her journey will take is: a) 2.89 hrs b) 3 hrs 7 min c) hr d) 3 hrs 45 min. 16 You have to add 3.61 to 4.58 and then multiply the result by 7. What is the answer? a) b) c) d) A brand of washing powder is sold in three sizes: S, M and L. The price and weight of each size is shown on the box. S 600 g 61p M 900 g 83p L 3000 g 2.89 The best and worst value sizes are: a) L best, S worst b) S best, M worst c) M best, L worst d) M best, S worst. 9

12 18 In a survey, 648 people were asked about television viewing; 267 people said they watched more than 12 hours a week. The percentage of the total who watched 12 hours or less was about: a) 32% b) 41% c) 59% d) 70%. 19 The diagram below shows an oil fuel tank in the shape of a cuboid m 1.35 m 1.8 m 1.25 m Its volume is about: a) 5.73m 3 b) 4.4m 3 c) 3.6m 3 d) 3.0m Starting with 18, you buy the following items: 2 loaves of bread at 72p each 3 packets of butter at 60p each 1 shoulder of lamb at large bottle of beer at tins of luncheon meat at 62p each 3 packets of biscuits at 45p each. The cash still available to spend is: a) 3.25 b) 4.98 c) 6.01 d) Now go to p. 16 to check your answers. 10

13 If you found these questions difficult, or didn t quite understand the meaning of some of them, then Foundation level is still probably the tier you should choose. On the other hand, if you did rather well on the questions say eight or more correct then try this final set of ten questions. You may use a calculator. Take as much time as you need. 21 I gave Peter and Julie the same number. Peter trebled it and then subtracted 5. Julie just added 6. They both got the same answer. What number did I give them? 22 Car hire from Axial charges 20 registration fee and 50p a mile. Car hire from Bonnet charges 60p a mile. I need to hire a car for a 200 mile journey. Which car hire firm should I choose? 23 In a sale, all prices have been reduced by 20%. The sale price of a jacket is 72. What was the price of the jacket before the sale? 24 The sizes of angles in a triangle are in the ratio 1:2:3. What is the largest angle called? 25 I needed to cycle a distance of 9 miles. I left home at 14:50 and arrived at my destination at 15:35. What was my average speed in mph? 26 Look at the pattern below: 2, 6, 12, 20, 30, 42, What is the 99th number in this pattern? 27 Work out 5x 2 7x 1.4 when x Eight apples and four pears cost me 5. Apples were twice as expensive as pears. How much would I have saved by buying just eight apples? 29 Last year the exchange rate was 13 Australian dollars = 3 Hong Kong dollars. How many Australian dollars would I have got for 42 Hong Kong dollars? 30 Work out # Now go to p. 16 to check your answers. If you found these questions difficult, then Higher level is probably not for you. On the other hand, if you didn t find these too bad and got more than half correct, then you might consider tackling the Higher tier. 11

14 Sample questions from the NEC courses Below are some representative questions for each of the NEC IGCSE courses. You may attempt these questions if you wish answers can be found at the end of this booklet but they are really intended just to give you a flavour of the courses and to help you confirm which course is right for you. Sample questions IGCSE, Foundation level 1 Express 360 as a product of powers of prime factors. 2 Find the interest earned after one year on $4000 invested at 3% per annum. 3 A = {3 sided shapes} B {shapes with two equal sides} What is the mathematical name for members of A «B? 4 Solve the equation 6x 5 2x A cuboid has volume 105 cm 3, length 3 cm and width 5 cm. What is the height of the cuboid? IGCSE, Higher level 1 A curve has equation y 2x 2 5x 4. Find the coordinates of the point on the curve where gradient equals 9. 2 Functions f(x) and g(x) are defined by f() x = x Calculate f 1 g(2). 3 E {integers less than 24} A {x : 3 x 9} B {Multiples of 4} and g(x) x 2 2, where x 0. Find the value of n (A» B). x 12x Simplify fully. x The base radius of a cone is 3 cm and its height is 4 cm. Calculate: a) the slant height of the cone b) the total surface area of the cone, leaving your answer as a multiple of. 12

15 Answers Answers to practice questions d 7 b 8 c 9 d 10 c or cm cm 14 c 15 c 16 b 17 d 18 c 19 d 20 c or 5 22 Either. Both cost , a right-angle 25 12mph

16 Answers to sample questions IGCSE, Foundation level $120 3 isosceles triangle 4 x = 9 5 7cm IGCSE Higher level 1 ( 1, 11) x 6 x a) 5cm b) 24 cm 3 14