2.1.3. Algebra Basic
Substitution:
Substitution refers to the process of replacing letters in a formula with their values to find one more value in the formula.
To substitute numbers in the formula
Write down the formula
Replace variables with their values
Rearrange the formula if necessary
Simplify
Use your calculator (if allowed) for calculation
Common formulae
There are some common formulae to be aware of.
Equation of a straight line
\( y=mx+c \)
Three equations of motions
\( v=u+at \)
\( v^2=u^2+2as \)
\( s=ut+ \frac{1}{2} at^2 \)
Where
\( v \) stands for final speed
\( u \) stands for initial speed
\( a \) stands for acceleration
\( t \) stands for time
\( s \) stands for distance
You do not need to memorize these formulas, but you should be able to enter numbers into them.
Worked example:
\( y=mx+c \)
Find the value of \( y \) when \( m=-2, x=-7 \) and \( c=-3\) .
Substitute the values in the formula
\( y=(-2)(-7)+(-3) \)
Simplify
\( y=14-3 \)
\( y=11 \)
\( y=11 \), when \( m=-2, x=-7 \) and \( c=-3 \)
Collecting like terms
Similar terms are grouped together to simplify algebraic expressions. It is also referred to as collecting like terms.
To do this
Identify the like terms
Add/Subtract coefficients of like terms
Worked example:
Simplify
\( 3a-5b-a+2b \)
Collect like terms
\( 3a-a-5b+2b=2a-3b \)
As \( 2a \) and \( -3b \) are unlike terms, so we can not simply it further
\( 2a-3b \)
Test yourself
Question 1:
\( y=x^4-4x^3 \)
Find the value of \( y \) when \( x=-1 \).
[2]
Question 2:
\( s=ut+ \frac{1}{2} at^2 \)
Find \( s \) when \( t=26.5, u=104.3, a=-2.2 \).
Give your answer in standard form, correct to \( 4 \) significant figures.
[4]
Question 3:
One solution of the equation \( ax^2+a=150 \) is \( x=7 \).
Find the value of \( a \).
[2]
Question 4:
Simplify
\( 2p-q-3q-5p \)
[2]
Question 5:
Simplify
\( 3a+7b-4a+b \)
[2]