Introduction to a Level Maths at Mggs

Faculty of Mathematics

Introduction to Core Maths (OCR Level 3 Certificate in Quantitative Reasoning)

2017-2018

1 INTRODUCTION TO CORE MATHS AT THE HUCKNALL SIXTH FORM CENTRE

Thank you for considering studying Core Maths at the Hucknall Sixth Form Centre This is a one-year course and you will sit two exams at the end of year 12. The Mathematics Faculty is committed to ensuring that you make good progress throughout your course. In order that you make the best possible start to the course, we have prepared this booklet.

It is vitally important that you spend some time working through the questions in this booklet - you will need to have a good knowledge of these topics as you commence your course. You should have met most of the topics before at GCSE. Work through the examples making sure you understand them. You can also use mymaths to help you if you need further support on any of the topics. At the end of the booklet are some sample questions to test your understanding.

We will test you within 4 weeks of the course starting to check how well you know the topics. You will be expected to gain 70% of the marks, so it is important that you have looked at all the booklet before then. If you do not pass this test, you will be given one re-test, failure to pass a second time will mean removal from the course. The test will cover the topics in this booklet along with some problem solving questions

We hope that you will use this introduction to give you a good start to your Core Maths work and that it will help you enjoy and benefit from the course more.

Miss Boultby (Teacher of Mathematics with responsibility for Core Maths)

CONTENTS

Chapter 1 Working with percentages Page 3 Chapter 2 Working with averages Page 4 - 5 Chapter 3 Statistical diagrams Page 6 - 8 Chapter 4 Substitution Page 8 Chapter 5 Financial Problem Solving Page 9 Sample questions Page 10 - 14

2 Chapter 1: Working with Percentages Calculating a percentage of an amount To find a percentage of any amount, first change the percentage into a decimal then multiply the amount by the decimal. The decimal is known as a multiplier. Examples: Find 72% of £485 = 0.72 x 485 = £349.20

Find 6% of £760 = 0.06 x 760 = £45.60

Calculating a percentage increase or decrease First, add or subtract the percentage from 100, then convert this into a decimal and multiply as above Examples: Increase £72 by 8%: 100+8 = 108% = 1.08: 1.08 x 72 = £77.76

Decrease £420 by 26%: 100 – 26 = 74% = 0.74: 0.74 x 420 = £310.80

Writing a number as a percentage Divide the number by the amount it is out of and then multiply by 100

Example: Write 75 as a percentage of 450 = 75 ÷ 450 x 100 = 16.7%

Writing an increase or decrease as a percentage Divide the increase or decrease by the original quantity and then multiply by 100

Example:

The price of a coat is reduced from £75 to £65 in a sale. What is the percentage reduction? Reduction = £10 10 ÷ 75 x 100 = 13.3%

Finding the original amount (Reverse percentages) If we know the percentage change and the new amount we can work out the original amount by dividing by the multiplier

Example:

A coat costs £13 in a sale where everything has 35% off. What was the original price of the coat? 13 ÷ 0.65 = £20

Repeated percentage change Multiply the starting amount by the multiplier raised to a power, where the power is the number of times the change is repeated

Examples: How much money will you have if you invest £1000 at an annual rate of 3% for 5 years? 1000 x 1.035 = £1159.27 3 Chapter 2: Working with averages and other summary measures

Basic Averages If you are given a list of values the following can be calculated: Mode: The most common value Median: The middle value when the values are listed in order Mean: Add up all the values and divide by how many there are Range: The difference between the largest and smallest values

Examples: Find the mode, median, mean and range for this set of data: 6, 9, 2, 7, 7, 6, 5, 9, 6 Mode = 6 Median: 2, 5, 6, 6, 6, 7, 7, 9, 9. The middle number is 6. Mean = (6 + 9 + 2 + 7 + 7 + 6 + 5 + 9 + 6)/9 = 6.3 Range = 9 – 2 = 7

Averages from a frequency table Mode: The value with the highest frequency Median: The middle value Mean: Multiply each value by its frequency and add these together. Divide this total by the total frequency Range: The difference between the largest and smallest values

Example:

4 Averages from a grouped frequency table Modal group/class: The group with the highest frequency Median: You can identify the group containing the median (see example) Mean: Multiply each midpoint by the frequency and add these together. Divide this total by the total frequency. This gives an ESTIMATE for the mean as you do not know each individual value

Example:

Other summary measures Upper and lower quartiles: These are found ¼ and ¾ of the way through a data set. The difference between them is known as the Interquartile Range

Where n is the number of values

Example:

5 Chapter 3: Statistical diagrams

Scatter diagrams A scatter diagram shows two variables plotted against each other. Two variables are correlated if they are related to each other.

Example:

6 Histograms These are used to show continuous data The vertical axis is FREQUENCY DENSITY which is calculated using the formula:

Examples:

Cumulative Frequency and box plots Cumulative frequency is a running total of frequencies for a set of data. Once you have drawn a cumulative frequency diagram, you can use it find the median and quartiles. This information can them be used to construct a box plot (box and whisker diagram) which is a useful way of comparing two sets of data

Example:

7 Chapter 4: Substitution

Key things to remember:  Think about which order you should do a calculation (BODMAS)  Make sure you understand how to use your calculator correctly to input values into complex formulas (use brackets if necessary)

Example:

12 x 25 = 300 monthly mortgage payments

= £870.32 (Make sure you work through this question and get the same answer)

8 Chapter 5: Financial Problem Solving

Key things to remember: These are like the multi-step questions you will have seen at GCSE. You will need to identify what is required in order to answer the question – READ CAREFULLY!

Example:

There are 11 people going on the trip BUT they only need to pay for 10 10 x 635 = £6350 – total cost before discount £6350 x 0.88 = £5588 – total cost after discount £5588 ÷ 11 = £508 – how much each person pays

9 Sample Questions

Your test will ask similar questions to this one. You will be expected to achieve 70% on your actual test to proceed with Core Maths

11 5(b)

12 13 6

Solutions are available on the Holgate Academy Homework Hub in the year 11 section