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Formula, expression, identity, equation?

 algebra, equations, formula, GCSE, GCSE Higher, GCSE Maths, Hot Potato, Uncategorized  2 Responses »
Feb 022014
 

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


Use this exercise to make sure you understand the difference.

Equations of straight lines. y=mx+c

 GCSE, GCSE Higher, GCSE Maths, Graphs and Charts, Hot Potato, Uncategorized, y=mx+c  No Responses »
Jan 262014
 

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.

Try this jigsaw.

Can you match the following nth terms with their sequences?

 GCSE, GCSE Maths, Hot Potato, sequences, Uncategorized  No Responses »
Jan 152014
 

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.

Solve quadratic equations by factorisation

 equations, factorisation, GCSE, GCSE Higher, GCSE Maths, Hot Potato, quadratic equations, Uncategorized  No Responses »
Jan 122014
 

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.

Factorise Quadratics

 factorisation, GCSE Higher, GCSE Maths, quadratic equations, Uncategorized  1 Response »
Jan 122014
 

To solve simple quadratic equations you need to be able to factorise quadratic expressions, like x²+9x +20

To do this look for a pair of numbers that add up to 9 and muliply together to make 20.

If you can’t find the right pair, write down all the pairs of factors of 20.

1 x 20

2 x 10

4 x 5

Now we can see the correct pair is 4 and 5.

So x²+9x +20=(x+4)(x+5)

Check this by multiplying out the brackets.

Lets try one involving negative numbers.

x² -x -12

The pairs of factors of -12 are

-12 x 1

-6 x 2

-4 x 3

-3 x 4

-2 x 6

-1 x 12

The pair that add up to -1 (because there is -x in the expression) are -4 and 3

So x² -x -12=(x-4)(x+3)

Now you try

How old is your teacher?

 Addition, algebra, Entry 2, Entry 3, Functional Maths, Games, Level 1, Level 2, Multiplication, Subtraction, Time  No Responses »
Jan 212013
 

Ask your teacher (or somebody else) to

1.  Write down your house number.

2.  Double it.

3.  Add the number of days in a week.

4.  Multiply by 50.

5. Add your age.

6. Subtract the number of days in a year. (not a leap year)

7. Add 15

The answer is your teachers house number and their age!

Can you explain why this works?

Mystic Rose

 algebra, Art and Design, Circle, GCSE Maths, Level 2, Website  No Responses »
May 212012
 
This is a great investigation from N-Rich which combines geometry with simple algebra. Your task is to find a rule that will calculate how many lines there are in any mystic rose. To construct a Mystic Rose draw a circle then use your protractor to place equally spaced dots around the circle. You then join each dot to every other dot with a straight line.

Who wants to be a Mathionaire?

 Addition, Adult Numeracy, algebra, Angles, Division, Entry 2, Entry 3, Fractions, Functional Maths, Games, GCSE, GCSE Maths, Level 1, Level 2, Multiplication, Shape, Subtraction, Website  No Responses »
Jan 312012
 

This quiz starts with entry level questions but to win a million you need to be able to solve equations and be an expert at 3d shapes! Who wants to be a mathionaire?

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