Problem-solving practice 1 Revision Notes for AQA GCSE Maths

Problem-solving practice 1

Introduction to problem-solving

Problem-solving questions make up about half of your Foundation GCSE exam. These questions test your ability to reason, interpret, and communicate mathematically. When you encounter tricky or unfamiliar questions, having a clear strategy helps you tackle them confidently.

infoNote

Problem-solving skills are essential for GCSE success. Unlike routine calculations, these questions require you to think creatively and apply multiple mathematical concepts together. The key is developing a systematic approach that you can rely on under exam pressure.

Essential problem-solving strategies

When facing challenging questions in your exam, follow these five key strategies:

1. Sketch a diagram to see what is going on

Drawing a visual representation helps you understand the problem better
Even a rough sketch can reveal important relationships between elements
This strategy is particularly useful for geometry problems

2. Try the problem with smaller or easier numbers

If the numbers look complicated, substitute them with simpler ones first
This helps you understand the method before applying it to the actual values
Once you know the process, return to the original numbers

3. Plan your strategy before you start

Take time to think about your approach rather than rushing in
Identify what information you have and what you need to find
Consider which mathematical concepts or formulas might be relevant

4. Write down any formulae you might be able to use

List relevant formulas at the start of your solution
This prevents you from forgetting important relationships mid-calculation
Common formulas for geometry include area, perimeter, and angle relationships

5. Use x or n to represent an unknown value

Algebra is often the key to solving complex problems
Assign variables to unknown quantities and set up equations
This approach is especially powerful for problems involving multiple unknowns

chatImportant

These five strategies form your problem-solving toolkit. Practice using them regularly so they become automatic during your exam. Remember: even if you can't complete a problem, showing these strategies will earn you valuable method marks.

Practice problem 1: Quadrilateral angles

This problem demonstrates how to use algebra to find unknown angles in a quadrilateral.

lightbulbExample

Worked Example: Finding Unknown Angles in a Quadrilateral

Problem: A quadrilateral has angles of $3y$ , $5y$ , and $2y$ . Work out the value of $y$ .

Step 1: Recall the key angle fact The angles in any quadrilateral add up to $360°$ .

Step 2: Set up the equation We have three known angles: $3y$ , $5y$ , $2y$ , and one unknown angle. Let the fourth angle be represented as the remaining part.

Step 3: Create the equation $3y + 5y + 2y + \text{fourth angle} = 360°$

Since we need all angles to sum to $360°$ : $10y + \text{fourth angle} = 360°$

If the fourth angle is also expressed in terms of $y$ , or if we assume the quadrilateral has these three angles and we need to find $y$ , we can solve accordingly.

chatImportant

Common Mistake to Avoid: Don't forget that triangles have angles summing to $180°$ , while quadrilaterals sum to $360°$ . Always check which type of polygon you're working with before setting up your equation.

Top tip for angle problems: If you know what unknown angles should add up to, you can write an equation and solve it to find the value of the unknown. This method works for triangles ( $180°$ ), quadrilaterals ( $360°$ ), and angles around a point ( $360°$ ).

Practice problem 2: Bearings and distance

This problem combines bearings knowledge with scale drawings to find distances.

lightbulbExample

Worked Example: Using Scale Drawings for Bearings

Problem: A buoy is $6$ km from a ship on a bearing of $290°$ . A lighthouse is $8$ km east of the ship. Work out the distance between the buoy and the lighthouse.

Step 1: Choose an appropriate scale A suitable scale would be 1 cm = 2 km, which keeps your diagram manageable while maintaining accuracy.

Step 2: Draw the scale diagram

Start with a clear north line from the ship's position
Measure $290°$ clockwise from north to locate the buoy ( $6$ km = $3$ cm on your scale)
Draw the lighthouse $8$ km east of the ship ( $8$ km = $4$ cm on your scale)

Step 3: Measure the distance Use a ruler to measure the distance between the buoy and lighthouse on your diagram, then convert back using your scale.

When drawing scale diagrams:

Always use a ruler and sharp pencil
Draw lines clearly and don't rub out construction lines
Show your working clearly for full marks

infoNote

Key facts about bearings:

Bearings less than 180° are to the right of north
Bearings between 180° and 360° are to the left of north
Bearings always have three figures (use leading zeros if necessary)

chatImportant

Top tip for bearings: Remember that bearings are measured clockwise from north. When drawing bearing diagrams, always start by drawing a clear north line, then measure your angle clockwise from this reference point.

Assessment objectives

infoNote

This topic particularly targets:

AO2: Reason, interpret and communicate mathematically
AO3: Solve problems within mathematics and other contexts

These assessment objectives reward your ability to think mathematically and apply your knowledge to unfamiliar situations.

Remember!

bookmarkSummary

Key Points to Remember:

Follow the five-step strategy when facing unfamiliar problems - sketch, simplify, plan, list formulas, use algebra
Angles in a quadrilateral always sum to 360° - use this fact to set up equations with unknown angles
Draw accurate scale diagrams for bearings problems using a ruler and sharp pencil
Bearings are measured clockwise from north and always written with three figures
Show your working clearly - problem-solving questions reward your method even if your final answer isn't perfect

Problem-solving practice 1 (AQA GCSE Maths): Revision Notes