Chapter 1- Algebra (Pure Maths)

Question 1

how do you represent even numbers?

Answer 1

even numbers are represented as 2a, where a is an integer

Question 2

how do you represent odd numbers?

Answer 2

Odd numbers are represented as 2a+1 , where a is an integer

Question 3

What is Proof by deduction?

Answer 3

A proof by deduction is when you use known facts to build an argument to prove the statement is true.

Question 4

what is proof by exhaustion?

Answer 4

proof by exhaustion is when you break it down into two or more situations. Making sure to cover all possible situations, then prove separately they must be true.

Question 5

what’s disproof by counter-example?

Answer 5

disproof by counter-example is when you find a case where a statement doesn’t hold.

Question 6

what is the difference of two squares?

Answer 6

The difference of two squares a² - b² = (a-b)(a+b)

The ‘ab’ terms cancel

Question 7

how to add simple fractions ?

Answer 7

a/x + b/x + c/ x = (a+b+c)/x

Question 8

aⁿ+aᵐ= ?

Answer 8

aⁿ+aᵐ= aⁿ⁺ᵐ

Question 9

aᵐ / aⁿ = ?

Answer 9

aᵐ / aⁿ = aᵐ⁻ⁿ

Question 10

(aᵐ)ⁿ = ?

Answer 10

(aᵐ)ⁿ = aᵐⁿ

Question 11

a¹ = ?

Answer 11

a¹ = a

Question 12

a ¹/ m = ?

Answer 12

a ¹/ m = m√a

Question 13

a -ᵐ = ?

Answer 13

a -ᵐ = 1/ aᵐ

Question 14

aᵐ/ⁿ = ?

Answer 14

aᵐ/ⁿ = ⁿ√aᵐ = (ⁿ√a)ᵐ

Question 15

a⁰ = ?

Answer 15

a⁰ = 1

Question 16

√ab = ?

Answer 16

√ab = √a√b

Question 17

√a/b = ?

Answer 17

√a/b = √a/√b

Question 18

a=?

Answer 18

a = (√a)² = √a√a

Question 19

(√a + √b)( √a - √b ) = ?

Answer 19

(√a + √b)( √a - √b ) = a - b

Question 20

how to rationalise the denominator?

Answer 20

times by√3 /√3 or something equaling one

e.g ( 9 /√3 ) X (√3/√3)= 3√3