Maths - Prelim

2022

Significant Figures

4309
1 = 4
2 = 3
3 = 0
4 = 9

0.03045
1. 3
2. 0
3. 4
4. 5

(Ignore first numbers if zero.)

----

Round 73271 to 3 significant figures.
73300

Cuboid (VOLUME)

length x breadth x height

Cylinder (VOLUME)

π x r² x height

Prism (VOLUME)

Area of face x length

Factorising - Trinomials

a² + 2a + 1

• find numbers which add together to make 2 and multiply to make 1
(1+1=2, 1x1=1)

• put in brackets with letter
(a+1)(a+1)

Factorising - Completing the square

x² - 8x + 2
• Half the value in front of x (8 -> 4)
(x-4)²
• Subtract the square of that value
(x-4)² - 16+2
• Tidy up
(x-4)² - 14

Factorising - Difference of 2 Squares

36a² + b²
• Square root and put in brackets - One with +, one with -
(6a-b)(6a+b)

Factorising - Highest common factor

14b + 42r
• Find the common factor
eg. 7( )
• Add in the other factors
eg. 7(2b+6r)
• Tidy up
eg. 7x2(b+3r)
14(b+3r)

Gradient

y2 - y1
m = -----------
x2 - x1

Area of a Sector

sector area angle
------------------ = ---------
circle area 360

eg AS angle
----- = --------
πr² 360

AS 85
----- = --------
πr² 360

AS = π x 7² x 85/360 = 36.3

Dividing Fractions

Keep, Change, Flip

5 11
- ÷ --
3 4

5 4
= - x --
3 11

20 4
= ---- = --
35 7

Multiplying Fractions

Multiply across the top + multiply across the bottom

eg. 5 11
- x ---
3 4

55
= ----
12

Adding Fractions

Must have the same denominator

1 1
- + -
3 4

4 3
-- + --
12 12

7
= --
12

Multiplying Indices

When multiplying we add the indices
e.g.

c² x c⁵
c²⁺⁵
= c⁷

Negative Indices

When the indice is negative you turn it into a fraction
e.g. a⁻³

1
= --
a³

Straight Line

y = mx+c

m = gradient
c = point where line cuts y axis

e.g.
y = 2x-7
&
2y = 4x+18
y = 2x+9
m=2 c=9

Triangle Trig

Cosine or Sin
No right angle

Finding the angle - Cosine Rule

b²+c²-a²
COS A = --------------
2bc

Finding the side - Cosine Rule

a² = b² + c² - 2bc cos A

Standard Deviation

∑x² = squared values added
(∑x)² = values added then squared
n = no. of values
substitute in formula

Powers of Indices

When taking powers of powers we multiply the indices
eg. (c²)⁵
= c²×⁵
= c¹⁰

Dividing Indices

Subtract
eg. 4a⁵ ÷ 2a⁴
= 2a⁵⁻⁴
= 2a¹
= 2a

Radius of arc (backwards)

Flip the fractions
eg.

28.4 65
------- = ----
πD 360

π*D 360
------- = ----
28.4 65

π*D = 360/65 × 28.4
D = 157.29 ÷ π = 50.06
R = 25.03

Arcs - Length

arc length angle
----------------------- = -------
circumference 360

eg.