WAEC Mathematics theory practice with worked answers

When you practise WAEC Mathematics theory, write each step so someone else can follow it. Define any unknowns, show the formula or equation you use, and give the final answer in the requested units. Try these two original practice questions before reading the solutions.

Practice 1. Simultaneous equations

Two exercise books and three pens cost ₦1,650. Three exercise books and two pens cost ₦1,850. Find the cost of one exercise book and one pen. Assume each exercise book costs the same and each pen costs the same.

1. Let b be the price of one exercise book in naira and p be the price of one pen in naira. The equations are 2b + 3p = 1650 and 3b + 2p = 1850.
2. Multiply the first equation by 2 to get 4b + 6p = 3300. Multiply the second by 3 to get 9b + 6p = 5550.
3. Subtract the first new equation from the second. The p terms cancel and 5b = 2250, so b = 450.
4. Substitute b = 450 into the first original equation. This gives 900 + 3p = 1650, so 3p = 750 and p = 250.

An exercise book costs ₦450 and a pen costs ₦250. Check both totals. Two books and three pens cost ₦900 + ₦750 = ₦1,650. Three books and two pens cost ₦1,350 + ₦500 = ₦1,850.

When you multiply an equation, multiply its right-hand side too. When you subtract, keep the same order on both sides. For example, subtracting 4b from 9b goes with subtracting 3300 from 5550.

Practice 2. Area and fencing for a triangular garden

A school plans a right-angled triangular garden. The two sides meeting at the right angle are 9 metres and 12 metres. Find the area of the garden, then find how much fencing will go around all three sides if there is a 1-metre opening for a gate.

1. Sketch the triangle. Mark the right angle between the 9 m and 12 m sides, so either of those sides can act as the base and the other as the perpendicular height.
2. Use the area formula. Half of 9 × 12 gives 54 m².
3. Find the side opposite the right angle using Pythagoras’ theorem. Its length squared is 9² + 12² = 81 + 144 = 225. The positive square root is 15 m.
4. Add the three sides to get a perimeter of 9 + 12 + 15 = 36 m. Subtract 1 m for the gate opening. The school needs 35 m of fencing.

The area uses square metres and the fencing uses metres. Check that the hypotenuse is longer than each of the other two sides. Keep the two requested answers on separate lines, so the perimeter calculation does not get mistaken for the length of fencing.

Try a fresh question and check the units

A right-angled triangle has perpendicular sides of 5 cm and 12 cm. Find its area and perimeter. Give yourself time to draw and label the triangle before comparing your answer.

Check your work. Half of 5 × 12 is 30 cm². The third side is the square root of 25 + 144, which is 13 cm. The perimeter is 5 + 12 + 13 = 30 cm. The answers have the same number here, so the unit is what tells the reader which measurement you mean.

• Did I copy the given values correctly and state what my variables mean?
• Did I show the operation that connects each step to the next?
• Did I answer every part, include the right unit, and follow any requested rounding?

Compare your method with the explanations in WAEC’s General Mathematics e-Learning resources. Put any step you still cannot explain on your weekly revision plan.