Sheet № 16 · Foundation + Higher · AQA · Edexcel · OCR
Forming and Solving Equations –
Forming equations from word problems is the skill that bridges arithmetic and algebra. Exam boards love it because it tests whether you can translate English into mathematics — and then solve what you have built. This topic appears on both Foundation and Higher tiers for AQA, Edexcel, and OCR, often within geometry, perimeter, and angle q
§Key definitions
Question:
The three angles of a triangle are x°, (2x + 10)°, and (x + 30)°. Find the value of x and state the size of each angle.
Check:
35 + 80 + 65 = 180 ✓
Answer:
x = 35; the angles are 35°, 80°, and 65°.
Q1 (Foundation):
The angles of a quadrilateral are x°, (x + 20)°, (2x − 10)°, and (x + 50)°. Find x.
Q2 (Foundation/Higher):
A triangle has sides of length x cm, (x + 3) cm, and (2x − 1) cm. The perimeter is 30 cm. Find the length of each side.
§Formulas to memorise
Identify the unknown → define it with a letter → write an expression for each part → set up the equation → solve
Angles in a triangle add up to 180°; angles on a straight line add up to 180°; angles in a quadrilateral add up to 360°
Read the problem twice. — Underline key information and the quantity you need to find.
Choose a variable. — Let x represent the unknown quantity. If there are two unknowns, try to express the second in terms of x.
Write expressions — for each part of the problem using x.
Form the equation — by connecting the expressions with an equals sign, using the given relationship (e.g., perimeter = 34, angles sum to 180°).
Solve the equation — using the methods covered in Solving Linear Equations.
Answer the question. — The problem might ask for x, or it might ask for something calculated from x, such as the length of a side. Re-read the question to check what is required.
Check — your answer makes sense in context (e.g., a length cannot be negative).
Worked example
The three angles of a triangle are x°, (2x + 10)°, and (x + 30)°. Find the value of x and state the size of each angle.
Working:
⚠ Common mistakes
- ✗Not reading the question carefully enough. Students find x but forget the question asks for the length or the area. Always re-read what is being asked.
- ✗Setting up the wrong equation. Confusing perimeter with area, or using the wrong angle fact. Double-check which formula applies.
- ✗Forgetting brackets in expressions. If the width is (x + 5), make sure you keep the brackets when substituting into a formula, especially with multiplication.
- ✗Accepting impossible answers. If x comes out negative and represents a length, something has gone wrong. Go back and check your equation.
- ✗Using two variables when one is enough. In most GCSE questions, you can express everything in terms of a single unknown. This keeps the equation simple and solvable.
✦ Exam tips
- →Write "Let x = ..." at the start. This tells the examiner what your variable represents and often earns the first mark.
- →Show the equation clearly before solving. Examiners award a mark for the correct equation, separate from the solving marks. Write it on its own line.
- →Context questions often have a follow-up. After finding x, you may need to calculate an area, a missing angle, or a cost. Do not stop at x.
- →On geometry forming questions, sketch a diagram if one is not given. Labelling sides or angles with your expressions helps you see the equation more easily.