Cheatography

# Quadratic Expressions & Trigonometry Cheat Sheet by NiffyYT

Cheat Sheet for Math

### Factor­ising using a common multiple

 5x²+10x LCM is 5x = 5x(x+2)

### Factor­ising & Expanding Two Squares

 Rewrite as a difference of two squares x²-16 = x²-4² = (x+4)(x-4) Rewrite as a difference of two squares 16x²-9y² = (4x)²-­(3y)² = (4x+3y­)(4­x-3y) Difference of squares in the form ab²x²-­ac²y² 18x²y⁴­-98x2z2 = 2x2(9y­⁴-49z2) = 2x²[(3­y²)­²-(­7z)²] = 2x²(3y­+7z­)(3­y-7z)

### Factor­ising Monic Trinomials

 Factorise x² +4x+3 Find factors of 3, summing to 4 1 & 3 = (x+1)(x+3) Factorise x²-12x+32 Find factors of 32, summing to -12 -4 & -8 = (x-4)(x-8)

### Perfect Squares

 Is 16x²-8²+1 a perfect square? a=4, b=1 -2x4x1=8 Yes, (4x-1)²

### Algebraic Fractions

 5x+10/5 5(x+2/5 = (x+2) Factorise where possible x²-5x+­6/x­²-7x+12 = (x-3)(­x-2­)/(­x-3­)(x-4) = (x-2)(x-4) Multiply & Dividing 2x²/x²+x ÷ 4x²/6x+6 = 2x²/x(x+1) ÷ 4x²/6(x+1) = 2x²/x(x+1) X 6(x+1)/4x² =6/2x = 3/x Adding & Subtra­cting 5/xy + 6/xy - m/xy 5+6-m/xy = 11-m/xy b. when the denomi­nators are different 1/x - 2/y LCD = xy 1 X y/xy - 2 X x/xy 1/x - 2/y = y/xy - 2x/xy = y-2x/xy

### Trigon­ometry

 c² = a² + b² SOH CAH TOA DMS button on calculator XX*XX'XX'' Find the missing side. x tan77* = x/5.9 x = 5.9tan77* = 26 b. x in denomi­nator tan29*­16'­=23.1/x x = 23.1/t­an2­9*16' = 41.22 Find a missing angle use sin⁻¹ tan⁻¹ or cos⁻¹ with existing sides

### Simult­aneous Equations

 Substi­tution Method y = 3x-7 (1) 2x-3y=12 (2) Sub (1) into (2) 2x+3(3x+7) = 12 2x+9x-­21=12 11x = 33 x = 3 Elimin­ation Method 3x-2y =14 (1) 5x+2y = 18 (2) + ------­---­---­---­---­---­---­----- 8x = 32 x = 4 sub into (2) 20+2y=18 2y = -2 -20 both sides y = -1