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ALGEBRA

Exam Cog
①LIKE TERMS
  1. Same letter & power only
  2. 5a + 3a = 8a
  3. x2 = x·x
②MULTIPLYING OUT

Every term × every term.

⚠ Like signs +, unlike signs −
③PERFECT SQUARES

(a + b)2 = (a + b)(a + b) — write it twice, then expand.

④FACTORISING
  1. Take out the common factor
  2. Four terms → group in pairs
  3. a2 − b2 = (a − b)(a + b)
⑤ALGEBRAIC FRACTIONS
  1. Common denominator
  2. Multiply each top
  3. Expand & tidy
⚠ −(x − 7) = −x + 7
⑥LETTERS ON BOTTOM

Denominator = the brackets multiplied.

Leave as (x + 1)(2x + 3).

Cancel if top & bottom factorise.

⑦SOLVING EQUATIONS
  1. Multiply out brackets
  2. Gather the letter one side
  3. Divide
⑧INEQUALITIES

Solve like an equation.

⚠ FLIP the sign when × or ÷ by a negative

List only values in ℕ or ℤ.

⑨NUMBER LINE & SETS

● filled = included (≤, ≥)

○ open = not included (<, >)

ℕ ℤ ℚ ℝ

⑩LONG DIVISION

Divide → multiply → subtract → bring down.

⚠ Put in 0x2 for a missing term
⑪PATTERNS

Equal gaps → linear.

Equal 2nd gaps → quadratic.

× a constant → exponential.

⑫QUADRATIC TRINOMIALS

Factorise ax2+bx+c:

  1. Guide number = a×c
  2. Two numbers: × to it, + to b
  3. Split the middle, group
⑬SOLVING QUADRATICS
  1. Get = 0, factorise, brackets = 0
  2. Else −b formula
★ x = (−b ± √(b2−4ac)) / 2a
⑭CHANGE OF SUBJECT
  1. Multiply out / cross-multiply
  2. Gather the wanted letter
  3. Factor it out, divide
⚠ Square both sides to kill a √
⑮SIMULTANEOUS EQ.
  1. Match a letter’s number
  2. Add / subtract to eliminate
  3. Clear fractions first

Words → two equations.