Maths

Question 1

Name the 5 most common Pythagorean Triples

Answer 1

(3, 4, 5)
(5, 12, 13)
(7, 24, 25)
(8, 15, 17)
(20, 21, 29)

Question 2

What type of angle is the largest angle in a triangle where this is true: h² > a² + b²

Answer 2

Obtuse (x > 90°)

Question 3

What type of angle is the largest angle in a triangle where this is true: h² = a² + b²

Answer 3

Right-Angle (x = 90°)

Question 4

What type of angle is the largest angle in a triangle where this is true: h² < a² + b²

Answer 4

Acute (x < 90°)

Question 5

Factorise ax² + bx + c (Magic Multiplying Method)

Answer 5

a*c = ac
Write pairs of factors of ac
(y, z)
(k, l)
Find pair of factors that sum to = b
Say y + z = b
and k +l ≠ b
Then divide these factors by 'a'
Simplify
Denominator of first fraction (y/a) so 'a' is first number while y is second number
(a + y)
Now for second bracket do same
So it would be (a + z)
So final equation is
(a + y)(a + z)

Question 6

3 Rules of Bearings

Answer 6

1. Always measured from North
2. Always measured clockwise
3. Always 3 digits (40° wrong) (040° right)

Question 7

Simple Interest

Answer 7

Let 
Original value = x
Frequency of payment = y
and Interest Rate = z
x + y(z*x)

Question 8

Compound Interest

Answer 8

Let 
Original value = x
Frequency of payment = y
and Interest Multiplier (e.g. if interest rate is 10% then interest multiplier is 1.1) = z
x * z^y

Question 9

Recurring Decimals Magic Method 1

Answer 9

0.63 recurring (dots are above 6 and 3) then take that number and put it over an equal set of 9s ( e.g. 63/99 or 547/999 etc.)

Question 10

Recurring Decimals Magic Method 2

Answer 10

0.16 recurring (dot is only on 6 not 1) First split number into 0.1 and 0.06 (6 is recurring)
Imagine recurring number as 0.6 (6 is recurring)
Use Magic Method one to convert this into a fraction
Add how many ever zeros you originally took away from recurring number and add it to the the denominator of the fraction.
Convert 0.1 into fraction.
Add both fractions together

Question 11

What should you always do when multiplying and dividing algebraic fractions

Answer 11

F.F.F. Factorise Fully First

Question 12

Sine Formula

Answer 12

opp = hyp * sinθ

Question 13

Cosine Formula

Answer 13

adj = hyp * cosθ

Question 14

Tangent Formula

Answer 14

adj * tanθ = opp

Question 15

Index Laws

Answer 15

x^a * x^b = x^(a+b)
x^a / x^b = x^(a-b)
(x^a)^b = x^(a*b)
(ab)^n = a^n * b^n
(a + b)^n ≠ a^n + b^n

Question 16

Negative Powers

Answer 16

Divide 1 by the original value by however many times it says in the power (e.g. 4^(-2) is 1/4/4 or 1/16 because it says ‘-2’ so you divide 1 by 4 two times.

Question 17

Fractional Powers

Answer 17

Take denominator of the fractional power and root the starting number by that denominator (e.g. if fractional power was 1/3 then cube root starting number) We will call this number x
Now do 1 * x^ numerator of fractional power

Question 18

Standard Form Rules

Answer 18

A * 10^n (1≤A<10) and (n has to be an integer)

Question 19

Adding and Subtracting in Standard Form

Answer 19

You must first get n to be the same in both parts that you are adding (e.g. (2.5 * 10^5) + (4.3 * 10^4) you must either get both parts to be 10^4 or 10^5 then you can add as normal)

Question 20

Parallel Lines

Answer 20

Have the same gradient

Question 21

Perpendicular Lines

Answer 21

Have a negative reciprocal gradient. (flip fraction and multiply by -1) Product of 2 gradients of perpendicular lines = -1

Question 22

3 Methods of Simultaneous Equations

Answer 22

Elimination, Substitution, Graph

Question 23

Centimetres (cm) to Millimetres (mm)

Answer 23

x10

Question 24

How to convert a powered value

Answer 24

Say you have m^2 to cm^2. Then take original conversion (x100) and square or cube or power or whatever (in this case we are doing ^2 so the conversion is 100^2 or x10,000)

Question 25

Hectares (ha) to Metres Squared (m^2)

Answer 25

x10,000

Question 26

Hectares (ha) to Acres (ac)

Answer 26

x2.471

Question 27

Litres (l) to Centimetres Cubed (cm^3)

Answer 27

x1,000

Question 28

Inches (in) to Centimetres (cm)

Answer 28

x2.54

Question 29

Pints (pt) to Litres (l)

Answer 29

x0.568

Question 30

Kilograms (kg) to Pounds (lb)

Answer 30

x2.205

Question 31

Miles (mi) to Kilometres (km)

Answer 31

x1.609

Question 32

Miles (mi) to Yards (yd)

Answer 32

x1760

Question 33

Gallons (gal) to Pints (pt)

Answer 33

x8

Question 34

Speed (m/s) =

Answer 34

Distance (m) / Time (s)

Question 35

Density (g/cm^3) =

Answer 35

Mass (g) / Volume (cm^3)

Question 36

Miles per Hour (mph) to Metres per Second (m/s)

Answer 36

x(4/9)

Question 37

Kilometres per Hour (km/h) to Metres per Second (m/s)

Answer 37

x(5/18)

Question 38

Kilograms per Metres Cubed (kg/m^3) to Grams per Centimetres Cubed (g/cm^3)

Answer 38

/1000

Question 39

Volume of a Cylinder

Answer 39

πr²h

Question 40

Surface Area of a Cylinder

Answer 40

2πrh + 2πr²

Question 41

Volume of a Sphere

Answer 41

(4/3)πr³

Question 42

Surface Area of a Sphere

Answer 42

4πr²

Question 43

Volume of a Cone

Answer 43

πr²(h/3)

Question 44

Surface Area of a Cone

Answer 44

πr (l + r) (l is Slant Height) (if l is unknown can be calculated using Pythagoras theorem by saying l is the hypotenuse and height is ‘a’ and radius of base is ‘b’)

Question 45

Volume of Pyramid

Answer 45

(Base Area * Vertical Height) / 3

Question 46

Area of Sector

Answer 46

(θ / 360) * πr²

Question 47

Arc Length of Sector

Answer 47

(θ / 360) * 2πr

Question 48

Perimeter of Sector

Answer 48

((θ / 360) * 2πr) + 2r