2.) Algebra

Question 1

The general rules with multiplying powers

Answer 1

• When multiplying powers of the same number, you add the powers (e.g. 3² + 3⁴ = 3²⁺⁴ = 3⁶)
• When dividing powers of the same number, you subtract the powers (e.g. 4⁵ ÷ 4³ = 4^5-3 = 4²)
• When applying a power to another power, you multiply the combined powers (e.g. (2²)³ = 2^2*3 = 2⁶)
• Any number to the power of one is itself (X¹ = X)
• Any number to the power of zero is one (X¹ = 0)
• 1 to any power is 1 (1^x = 1), as 1*1*1*1… will always be 1

Question 2

Simply put, what do negative and fractional powers represent?

Answer 2

Question 3

DOTS or Difference Of Two Squares formula?

Answer 3

A² – B² = (A + B)*(A – B)

Question 4

General rules for manipulating surds

Answer 4

Question 5

Answer 5

Question 6

The Quadratic Formula?

Answer 6

Question 7

How do you find the expression of a quadratic sequence?

Answer 7

• Find the difference of the numbers as you would an arithmetic sequence
• Find the difference of the differences, then that number divided by 2 will be the coefficient of your n^<u>2</u> part
• To find the rest, find the difference of the standalone Xn² sequence to your terms, which will then give you a linear expression

Question 8

General rules of quadratic inequalities

Answer 8

• X^{<u>2 </u>}˂ A^<u>2</u> translates to -A^{<u> </u>}˂ X^{<u> </u>}˂ A
• X^{<u>2 </u>}˃ A^<u>2</u> translates to X ˃ A or X ˂ -A
• To help visualise this, think about the U-shape of an X² graph, and it’s about the bits either above or below the X-axis

Question 9

General rules to help with proofs

Answer 9

• Even numbers can be presented as 2n and odd numbers presented as 2n +1
• The sum, difference and product of integers will always be another integer (but not the dividend!)