This exercise involves reading and analysing data from charts, calculating averages and percentages and estimating length. It will also help you with the Driving Theory Test and hopefully help you to stay safe when you are driving.
There is an interactive version here and a worksheet version here. Here’s a quiz which involves rounding, addition and subtraction for Motor Vehicle students. Each time you do it you will get a different selection of questions. Many thanks to Auto Trader for the adverts. Here are the highlights of the 2015 Mens Final.

Can you use your skills to answer the questions? They range from easy Entry Level to GCSE questions involving data handling,  time, distance, speed and Pythagoras. There is a Scale Drawing task that is very good practice for Level 1 students.  In this exercise you will need to read the information from an Amey press release about the massive Streets Ahead contract. You will then use your skills to answer the questions. You can download a worksheet or use the interactive version here.

There are two extra questions on the worksheet which are also below.

This table shows the number of fatal injuries by industry in 2014/15. • Draw a suitable chart to display this data.
• Write two interesting facts that the graph shows.

In May 2015 the United Kingdom went to the polls. A Conservative Government was elected. The UK uses the “first past the post” electoral system. The country is divided into 650 constituencies. The candidate with the most votes from each constituency is elected. Most other countries in Europe use various forms of proportional representation. This means that the number of MP’s for each party would be proportional to the number of votes that were cast for them. (There are many different forms of PR, but in this exercise, to keep it simple we are going to work out the number of MPs by dividing the vote for each party by the total vote and then multiplying by 650, which is the total number of MP’s in the House of Commons. )

First fill in the missing numbers in this table. You will need a calculator. Remember that to round to two decimal places you need to look at the 3rd decimal place. If this is 5 or more round the 2nd decimal place up. If it is less than 5 then ignore it. eg 34.349239=34.35 to 2dp. 2.983432909=2.98 to 2 dp.

If you got the first exercise correct I want you to illustrate your results with two pie charts. Use this table to work out the degrees for each party. You can draw them in excel or with a protractor and pencil.

If you would rather do this exercise using a worksheet download here.

This is one in a large series of short videos from NCETM showing how people use maths at work. See the others here.

When you have watched the video see if you can convert time into decimals and work out how much employees should be paid.

Interactive Worksheet Pdf worksheet

If you have not yet tried Squares and Cubes do this first.

A square root is the opposite of squaring a number. The symbol for square root is  √.

So if 3²=9 then  √9=3

A cube root is the opposite of cubing a number. The symbol for cube root is ³ √.

So if 3³=27 then ³ √27=3

TrySquares, Square Roots, Cubes and Cube Roots to help you become familiar with the important examples of this. To square a number you multiply it by itself. For example 3² =3×3=9

To cube a number you multiply it by itself three times. So 3³=3x3x3=27

If you are studying GCSE it is very helpful to learn the common squares and cubes to save you time in the non calculator exam. This exercise will help you do that-don’t be tempted to use a calculator! For Functional Skills students you can use a calculator. Look for the x² and x³ buttons on your scientific calculator and use these.

Each time you do this exercise you will get a different selection of questions. To do it again click the refresh icon on your browser. Surds are numbers left in square root or cube root format. We leave them as surds because in decimal form they go on forever, so it uses up lots of ink to write them and accuracy is quickly lost. There are lots of tricks to simplify surds and these two videos from maths520 show them clearly. This topic is important for Higher GCSE students. Have you got it? Try these questions on BBC Bitesize. then continue to these. Also try the jigsaw.

Do you understand the difference between a formula, expression, identity and equation?

A formula is a rule written using symbols that describe a relationship between different quantities. Typical maths formulae include

A = πr² (area of a circle)

C=πd (circumference of a circle)

An expression is a group of mathematical symbols representing a number or quantity. Expressions never have equality or inequality signs like =, >, <, ≠ ,≥ ,≤. Some examples

3a

3xy + 4x

t² + t³

An identity is an equation that is always true, no matter what values are chosen.

Examples

3a + 2a =  5a

x²+x² = 2x²

5 x 10 = 10 x 5

An equation is a mathematical statement that shows that two expressions are equal. It always includes an equals sign.

Examples

x² =100

3x(x+5)= 42

(x+3)(x-2)=0

GCSE students need to be able to work out the equation of a graph from what it looks like.
If it’s a straight line graph you just need to look for two things.
1. The Intercept. This is where the line crosses the y axis.
2. The gradient. This is the steepness of the line. If the line goes up from left to right it will be positive. If the line goes down from left to right it will be negative. The larger the number the steeper the line. This example shows the line y=2x-4. The line goes up two units for each unit it goes across. The gradient is 2÷1=2. It crosses the y axis at -4, so the intercept is -4.

Mathematicians use y=mx+c as the general formula for any straight line. The gradient is m and the intercept is c.

Try this exercise to see if you can match the graphs with their equations.

Try this exercise to see if you can match the equations with the correct gradient and intercept.

Each number in a sequence is called a “term”. In the sequence 3, 6, 9, 12, 15 the first term is 3 and the 5th term is 15.

You could call this sequence “the three times table”. In algebra we describe it as 3n.In other words the first term is 3×1, the second term is 3×2 etc.

3n+ 4 describes the sequence 7, 10, 13, 16, 19… because the first term is 3×1+4=7, the second term is 3×2+4=10 and the third term is 3×3+4=13. Notice that because n is multiplied by 3 the sequence goes up in 3’s.

Have a go at matching these nth terms with the right sequence. In the last exercise you learnt how to factorise quadratic expressions. We will now use this in order to solve simple quadratic equations.

Suppose x²+9x +20 = 0

If we factorise we get (x+4) (x+5) = 0

In other words, two numbers multiply together to make 0. This means one of those numbers must be 0!

So we know EITHER x+4 = 0 OR x+5 = 0

If x +4 = 0 x = -4

If x+5 =0 then x=-5

So the solution is x = -4 or -5

Remember quadratic equations will nearly always have 2 solutions.

Try this- you will probably need pencil and paper to factorise the equations first. Substitution in maths means swopping the letters for the right numbers so you can work out the value of an expression. Don’t forget that ab means a multiplied by b and c/d means c divided by d. Have a go at this interactive worksheet to get the idea. http://www.mathswithgraham.org.uk/potatoes/numeracy/substitution.htm