Maths A-level Curriculum

Year 12 to Year 13: Bridging the Gap

Work through the following material, answering all questions showing as much working as you can.

You are not expected to necessarily be able to do all of the questions yet and please note that much of this material will be covered as part of the course.

Extra help lessons will then be scheduled to fill in gaps in your knowledge to help you achieve the results you deserve in your A2 year.

 

1)      Calculus

Differentiate the following and attempt to locate the turning points of the last three.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

**challenge: Can you sketch any of the above curves**

Integrate the following

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2)      Factorising and simplifying

Read the following examples:

Examples of factorising:

1)      Look for comparable terms in each part of the expression

2)      Compare the powers of the comparable expressions

3)      Try to write the large power as “the lower power + something”

4)      Then try and factorise

When you have fractions, convert them so that they have the same denominator

Question

Reasoning

 

 

 

 

 

 

Comparable expressions

 

Firstly: . Write  

 

 

Secondly: .

Write

 

 

 

 

 

 

 

Comparable expressions:

 

Firstly:  Write

 

Secondly:

Write

 

Fractions:  write as

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Comparable expressions:

 

Firstly: . Write

 

Secondly:

 

Write

 

Now try and factorise the following yourself

 

Question:

Comparable expressions:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Consider which of the following are true.

If you think it is not true try to provide a counter-example

If you think it is true, can you provide a proof? If you cannot prove it, why not research either in your text-book or on the internet...

1)      The product of four consecutive integers, each greater than 1, is divisible by 24.

 

 

2)      Every positive even number can be expressed as the sum of two prime numbers

 

 

3)       is divisible by 6, for all values of x greater than 2 (Hint: Try to factorise it)

 

 

4)      The sum of four consecutive integers is divisible by 4

 

 

5)      If  then

 

 

Make x the subject in the following expressions