Show Menu
Cheatography

Quadratic Expressions & Trigonometry Cheat Sheet by

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
 

Comments

No comments yet. Add yours below!

Add a Comment

Your Comment

Please enter your name.

    Please enter your email address

      Please enter your Comment.

          Related Cheat Sheets

          Discrete Math Cheat Sheet
          Linear Algebra - MATH 232 Cheat Sheet