Basic Algebra & Equations
Dr. Davinder Bhachu & Nick Featherstone
Teachers
Contents
Introduction - Linear Equations & Substitution
Linear Equations:
Equations like appear frequently. You’ll need to:
Isolate by undoing addition/subtraction and then multiplication/division.
Sometimes expand brackets or deal with fractions e.g.
Substitution in Formulas:
Formulas express relationships. You’ll:
Plug in given values.
Rearrange if solving for an unknown e.g. cost = unit price × quantity
Common UCAT Formulas:
Area:
Speed:
Volume:
Cost:
Example
Cost of syringes: Total
Dosage adjustments:
Explainer Video
This topic is supported by a video walkthrough from the UCAT Maths team. It covers solving equations, rearranging formulas, and common pitfalls.
Practice Set - Substitution & Rearranging
Set A – Medical Supply Calculations
Context: You are managing orders for a medical supply firm. The cost formula is: , where quantity of kits.
Question 1 - Easy
If , what is the total cost?
Answer
Question 2 - Medium
If total cost is , how many kits were bought?
Answer
Question 3 - Medium
What would the cost be if the fixed fee was removed?
Answer
New cost
Question 4 - Hard
Rearrange in terms of the (quantity) as the subject.
Answer
Subtract
Rearranged formula:
Worked Examples
Question 1 - Easy (Linear Equation)
A clinic spends on syringes. Find .
Answer
syringes
Worked solution
Subtract
Divide by
Question 2 - Medium (Fractional Equation)
Solve: for .
Answer
Worked solution
Subtract
Multiply both sides by
Question 3 - Medium (Formula Substitution)
A rectangle has and .
Use to find the area.
Answer
Worked solution
Worked Examples Video