Algebra

Question 1

Adding / Subtracting Algebraic Expressions:

Answer 1

We can only add / subtract ‘like terms’.
‘Like terms’ = terms with the same letter/same variables
e.g. 5d + -2d= ‘like terms’ but 5d + 5d² are NOT
‘like terms’

Question 2

Multiplying expressions

Answer 2

BOMDAS

Question 3

Dividing expressions

Answer 3

Factorise
[2𝑥 + 6] [2(𝑥 + 3)]
[𝑥2 − 9] = [(𝑥 + 3)(𝑥 − 3)]
=[ 2 ]

[𝑥 − 3]

Question 4

Adding/subtracting fractions

Answer 4

Find common denominator + multiply top + bottom to get the same denominator for both

Question 5

Dividing fractions

Answer 5

Long devision + simplify

Question 6

Factorising

Answer 6

Take out highest common factor
Grouping
Quadratic trinomial
Difference of 2 squares

Question 7

Manipulating formula

Answer 7

1) Get rid of brackets/ fractions/square roots.
2) Bring all terms with the letter you want to 1side and move the rest to the other.
3) Factorise out the letter you want (if necessary).
4) Divide both sides to leave the letter you want one 1 side

Question 8

Solving linear equations

Answer 8

1)Remove brackets+fractions
2. Bring all’x’ terms to one side + numbers to the
other side
3. Add/subtract ‘like terms’.
4. Solve the simple equation remaining.

Question 9

Minus b formula

Answer 9

x = (-b ± √ (b² - 4ac)
2a

Question 10

If there is a fraction

Answer 10

MULTIPLY IT OUT

Question 11

Forming quadratic equations from the roots

Answer 11

1)Let x = both of the roots.
2)Create two factors that = 0.
3)Multiply the two factors
Example: roots -1 and 3.
x=−1 𝑜𝑟 𝑥=3
x+1=0 𝑜𝑟 𝑥−3=0
(𝑥+1)(𝑥−3)=0
x(𝑥−3)+1(𝑥−3)=0
x²−3𝑥+𝑥−3=0
x²-2x-3=0

Question 12

Simultaneous equations

Answer 12

Choose a variable to get rid of (y)
Multiply the no. infront of y to make them equal, but different signs
Solve for x, then sub back in to get y