Meaning of Words

Interest: Is the money you pay to the bank when borrowing money from them. It can also be the money the bank pays you for keeping your money. It is calculated by multiplying the rate by the balance.

Rate: A percentage (e.g. 4%, 9.6%, 11%) used to calculate interest.

Balance: The amount of money a person has in a bank account. It is usually called the "Principal".

Compound Interest: Interest calculations made during a given period when money earns interest on top of the original calculated balances during that period at given intervals. (e.g. look at the example below)

To calculate compound interest annually: The annual interest is divided by the given intervals, then the first interval and every successive interval is multiplied by that rate and added to the new balance at every interval. (See the example below)

Example...
A person borrows $320 at 13.5% p.a. compounded monthly for 1 year. What will be the balance after 12 months?

13.5% ÷ 12 months = 1.125%, which is the rate for 1 month.

Quick Way: 320 × (1 + 0.01125)¹¹ = $361.90

Principal = $320
Rate = 1.125% or 0.01125 (1.125/100) interest charged each month.
Number of months times the rate is to be squared: 11 times (12 months - 1), because the first month has already been calculated.

Formula: C = P × (1 + R)^{n - 1}

Multiply the length of one side by itself then multiply the result by six because there are six sides to a cube and all sides are equal.

Formula: ^S_A = L² × 6

^S_A = surface area.

L = length

Example...

A cube has a length measurement of 4 cm. Find the surface area.

4² × 6 = 96 cm², is the surface area

To Find the Volume of a Cube:

Find the area of one side of the cube, then multiply the result by itself three times.

Formula: V = L³

V = volume

L = length

Example...

A cube has a length measurement of 4 cm. Find the volume.

V = 4³ 

4 × 4 × 4 = 64 

V = 64 cm²

Example:

Find the next five terms of the following sequence...

43, 50, 57.....

Answer: 64, 71, 78, 85, 92

43 + 7 = 50, 50 + 7 = 57, 57 + 7 = 64 ...

Substitute: Is to replace a number by a variable or to replace a variable by a number.

Example... (answers are in red)

Meaning of words

An octagon is a polygon having eight sides.
A polygon is a closed plain figure bounded by three or more straight sides that meet in pairs in the same number of vertices and do not intersect other than at these vertices.
Vertices is the plural of vertex.
Vertex means the point opposite the base of a figure or the point of intersection of two sides of a plain figure or angle.

Different methods or formulas are used for calculating the area of polygons. The following method is used for calculating the area of an octagon.

Formula: 2 × r²× 1.4142135 (the last number is the square root of 2)

r = radius

The radius is a straight line from the centre to any point on the outside of the shape.

Find the radius of the octagon, then perform the formula.
e.g. if the radius of an octagon was 4 cm, then 2 × 4²× 1.4142135 = 45.25 cm², which is the area.

An integer is any number which does not have a decimal place. It can be a negative number (e.g. -5, -7, -3) or positive number (e.g. 5, 7, 3).

e.g. 1, 2, 3, 5, 7, 11, 13 are prime numbers.

Meaning of words.

Interest: Is a percentage of money paid to the bank when borrowing money from that bank it is calculated by multiplying the rate by the balance.

Rate: Is a percentage (e.g. 4%, 9.6%, 11%) used to calculate interest.

In this case the explanation of the balance is the following: the amount of money owed to the bank at any given time. It is usually called the "principal amount owed".

Example:

Stan borrowed $12 000 at 12.68% p.a. for 3 years. Find the total amount he owes on top of what he has already borrowed.

($12 000 × 12.68%) × 3 = $4 564.80, this is the total interest charged.

$12 000 + $4 564.80 = $16 564.80, this is the amount owed.

Amount owed: $16 564.80