1. A LEVEL MATHEMATICS

2. Why study A Level Mathematics? Pythagoras said
“All things are number”

3. And some thoughts

4. University opportunities
It’s enjoyable
Variety of jobs
Happier person
It’s logical
University opportunities
More Money
Salary is a number and numbers make us happy
It’s stimulating
Better wages
It’s rewarding

5. A Level Maths is made up of 4 modules:
2 Pure Modules (Algebra,Geometry,Calculus,etc)
2 Applied Module (Statistics and Mechanics)
You have no choice which applied module you do for Maths although there is some choice for Further Maths. Your options are:
2 Pure Modules
Choices from Pure Modules
Further Statistics
Further Mechanics
Decision Maths

6. Why study A Level Mathematics Pythagoras said
“All things are number”

8. Algebra
Inequalities

9. Inequalities < means “is less than”
What are Inequalities?
Inequalities are just another time-saving device invented by lazy mathematicians.
They are a way of representing massive groups of numbers with just a couple of numbers and a
fancy looking symbol.
< means “is less than”
 means “is less than or equal to”
> means “is greater than”
 means ”is greater than or equal to”

10. Representing Inequalities on a Number line
x < 3 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6
x > -4
and
x ≤ 0 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6

11. Solving Linear Inequalities
If you multiply or divide by a NEGATIVE, the inequality sign swaps around!
Why on earth does the sign swap around?

12. !

13. Solving Linear Inequalities Graphically

14. For questions like this, just deal with each inequality in turn, shading as you go!
Note: When you have got more than one inequality like this, it’s normally best to shade the region
you DON’T WANT, so you can leave the region you do want blank! √
Putting it all together leaves us the blank region in the middle that satisfies all the inequalities!

15. 5. Solving Quadratic Inequalities !
1. Do the same to both sides to make the quadratic inequality as simple as possible
2. Sketch the simplified quadratic inequality
3. Use the sketch to find the values which satisfy the inequality
Example or

16. Solve the inequality x2 + x – 6 > 0.
Example 1
Solve the inequality x2 + x – 6 > 0.
Example 2
Solve the inequality x(x + 2) ≤ 1.

17. (a) x2 + 3x – 10 < 0 -5 < x < 2
Solve these inequalities using whichever method you prefer.
(a) x2 + 3x – 10 < < x < 2
(b) x2 + 11x + 18 ≥ 0 x ≤ -9 or x ≥ -2
(c) x2 – 9x + 18 > 0 x < 3 or x > 6
(d) 2p2 + 5p – 3 ≤ ≤ p ≤ 1/2
(e) 3a2 – a < 0 0 < a < 1/3
(f) 6t2 + 5t – 6 ≥ 0 t ≤ -3/2 or t ≥ 2/3

18. Quadratic Inequalities: Problem Solving
Harry is digging a rectangular flower bed.
The perimeter of the bed is to be 60m and the area is to be at least 200m2.
Work out the range of possible values for the width of the flower bed.

19. Quadratic Inequalities: Problem Solving
Example 4
The diagrams show the first three pentagonal numbers, 1, 5,
The nth pentagonal number is
Work out the first pentagonal number that is greater than 100.
n (3n – 1) 2

20. Match up the question to the answer.!
Inequalities
Match up the question to the answer.! 1. 2. 3. 4. 5. 6. 7. 8.

21. answers
1g 2a 3e 4d 5c 6 7b 8f