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Notation

You will be expected to use computer notation to answer some questions on this site, as you need to be very familiar with this notation when taking Massey Mathematics papers.  For each operation shown below we give the mathematical notation used in schools and most text books and typical computer notation used in many software packages.

Operation

Mathematical
Notation

Computer
Notation

Mathematical
Notation Examples

Computer
Notation Examples

Addition

a number + a number

a number + a number

3 + 2
a + b

3+2
a+b

Subtraction

a number - a number

a number - a number

3 - 2
a - b

3-2
a-b

Multiplication

a number × a number or (a number)(a number)

a number*a number

3 × 2 or (3)(2)
a × b or (a)(b) or ab

3*2
a*b

Division

a number ÷ a number or one number divided by another

a number/a number

3 ÷ 2  or   3/2
a ÷ b  or   a/b

3/2
a/b

Powers

a number raised to a number

a number^a number

32
ax

3^2
a^x

Exponential function

e raised to a number

exp(a number)

e2, e
ex

exp(2), exp(1)
exp(x)

Logarithm (base 10)

log a number

log(a number)
see below

log 2
log x

log(2)
log(x)

Natural logarithm

ln a number

ln(a number)
see below

ln 2
ln x

ln(2)
ln(x)

Square root (positive)

square root of a number

sqrt(a number) or a number^0.5

square root of 32
square root of x

sqrt(32) or 32^0.5
sqrt(x) or x^0.5

Reciprocal

1 divided by a number

1/ a number or a number^(-1)

1/32
1/x

1/ 32 or 32^(-1)
1/x or x^(-1)

Sine

sin a number

sin(a number)

sin p
sin x

sin(pi)
sin(x)

Cosine

cos a number

cos(a number)

cos p
cos x

cos(pi)
cos(x)

Tangent

tan a number

tan(a number)

tan p
tan x

tan(pi)
tan(x)

When you have complex expressions, you may need to use brackets to obtain the desired order of operations.  While textbooks may use round, square and curly brackets in an expression, in computer expressions we use only curved brackets, for example, ( expression ).

Examples of expressions in computer notation using brackets:

5^x+2 represents 5x + 2 whereas 5^(x+2) represents 5x + 2.
(x + 1)/(x + 2) represents x+1 divided by x+2 whereas x + 1/x + 2 represents x + 1 divided by x + 2.
To enter e raised to a times e raised to the x, use exp(a*exp(b)).     y raised to x squared is entered as y^(x^2).

Logarithms

Computer notation for logarithms varies from programme to programme. Matlab uses log10(a number) for logarithms to base 10 and log(a number) for natural logarithms whereas Excel uses both log(a number) and log10(a number) for logarithms to base 10 and ln(a number) for natural logarithms.

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