What to Do When You Don't Know How to Start a Maths Question

Some students freeze when they see a tricky algebra question. They don't know where to begin.

A simple trick is to start from the basics and list everything you know.

Example Question:

Prove that a shape with angles \(12x + 34\), \(7x - 6\), \(15x\), and \(8x - 4\) is a trapezium.

5 marks

Step 1: What Do We Know About Trapeziums?

• A trapezium has four angles.
• The sum of all four angles must be 360°.
• Exactly two of the sides are parallel.

So, we can add them all up, as we know they must equal to 360:

\[(12x + 34) + (7x - 6) + (15x) + (8x - 4) = 360\]

Step 2: Solve for \(x\)

First, collect like terms:

• All the \(x\) terms: \[12x + 7x + 15x + 8x = 42x\]
• All the numbers: \[34 - 6 - 4 = 24\]

So we get:

\[42x + 24 = 360\]

Now, subtract 24 from both sides:

\[42x = 336\]

Divide by 42:

\[x = 8\]

Step 3: Find the Angles

Now, we might as well know what each angle is.

So let's substitute \(x = 8\) back into each angle:

\[12(8) + 34 = 96 + 34 = 130\]

\[7(8) - 6 = 56 - 6 = 50\]

\[15(8) = 120\]

\[8(8) - 4 = 64 - 4 = 60\]

The four angles are: 130°, 50°, 120°, and 60°.

Step 4: Check for Parallel Sides

Now, at this point we have probably achieved 3 of the 5 marks.

To get the last two, what do we know about angles in parallel sides?

Maybe you can remember co-interior angles add to 180.

If opposite angles add to 180°, then the sides between them are parallel.

\[130° + 50° = 180°\]

\[120° + 60° = 180°\]

Since we have two pairs of co-interior angles (C-shape) adding to 180°, the shape must have one pair of parallel sides.

This proves the shape is a trapezium. ✅

Conclusion

If you're stuck, don't panic. Start with the basics:

• ✅ Write down what you know about the shape.
• ✅ Look for key properties (like angles adding to 360°).
• ✅ Solve step by step and check your answers.

Breaking problems down like this makes hard questions much easier. Try it next time! 💡

By Giuliano Grasso