Flashcards in Mathematical Skills Deck (16)
What are the basic rules of indices?
a^(n) = a * a * a *... (n times)
a^(-n) = 1/a^(n)
a^(1/n) = nth root of a
a^(x) * a^(y) = a^(x+y)
a^(x) / a^(y) = a^(x-y)
(a^(x))^(y) = a^(xy)
How are indices presented in units?
e.g. velocity units = m/s -> ms^(-1), acceleration units = m/s^(2) -> ms^(-2)
What is standard form?
Standard form is a way of presenting a number with many digits easily. It is usually written as a digit from 1-10 x10^(n). e.g. 300000000 ms^(-1) = 3.00 x10^(8) ms^(-1), 0.000015 A = 1.5 x10^(-5) A
What is a fraction? What is a percentage?
a/b is a fraction, it means a divided by b.
Fractions can be written as percentages by multiplying them by 100. e.g. a/b * 100
What are radians?
Radians are another way of measuring angles instead of degrees. Radians use the symbol c (suspended) instead of ° or can be written in terms of pi.
360° = 2π
180° = π
What symbols represent less then and greater than; much less than and much more than; less than or equal to and more than or equal to?
x less than y. x y
x much less than y. x > y
x less than or equal to y. x ≤ y
x more than or equal to y. x ≥ y
What is direct and inverse proportion?
Direct proportion -
y ∝ x -> y = kx
(As one increases, the other increases proportionally)
Inverse proportion -
y ∝ 1/x -> y = k/x
(As one increases, the other decreases proportionally)
k is a constant.
Which symbol represents 'change in'?
Delta Δ. e.g. Δv means a change in velocity.
Which symbol is commonly used to represent an angle?
Which symbol means 'approximately equal to'?
x is approximately equal to y. x ≈ y
What is the quadratic formula?
For... ax^(2) + bx + c = 0 where a, b, and c are constants.
x = [-b ± (b^(2) -4ac)^(1/2)] / 2a
How do you find the areas and volumes of different geometrical figures?
rectangle - A = bh
cuboid - V = bhl
parallelogram - A = b * (perpendicular h)
circle - A = πr^(2) or πD^(2) / 4
circle - V = πD or 2πr
triangle - A = bh or 1/2ab * sinC
trapezium - A = 1/2(a+b)h
sphere - A = 4πr^(2)
sphere - V = 4/3πr^(3)
What is SOHCAHTOA?
Sin x = Opposite/Hypotenuse
Cos x = Adjacent/Hypotenuse
Tan x = Opposite/Adjacent
What is Pythagoras' theorem?
a^(2) + b^(2) = c^(2)
As long a c is the hypotenuse of a right-angled triangle.
What is the sum of angles in a triangle?
180° or π rad