WASSCE Integrated Science past questions and answers

In a circuit diagram, a resistor is drawn as a plain rectangular box — exactly like the component labelled R at the top of this circuit. A resistor opposes (limits) the flow of electric current and converts electrical energy into heat.

Why not the other options? A transformer is drawn as two coils side by side; a capacitor as two short parallel plates; a diode as a triangle pointing to a bar. None of these match a plain rectangular box, so the answer is D, resistor.

For reference, the circle marked A in the diagram is an ammeter (it measures the current), and the long-thin and short-thick parallel lines on the left are the cell that drives the current round the circuit.

Work done = Force × distance moved in the direction of the force.

W = 50 N × 3 m = 150 J (joules).

Work is measured in joules (J), not watts (W) — option B uses the wrong unit, since watts measure power (the rate of doing work).

Mechanical advantage (MA) = Load ÷ Effort = 200 N ÷ 50 N = 4. The lever multiplies the effort four times, so a 50 N effort can balance a 200 N load. This matches the lever’s geometry: the effort is applied 4 m from the fulcrum while the load is only 1 m from it, so effort arm ÷ load arm = 4 ÷ 1 = 4. (By the principle of moments, 50 N × 4 m = 200 N × 1 m, so the lever balances.)

Universal indicator changes colour with pH. In an acidic solution (low pH) it turns red or orange (answer B): red/orange at pH 1–3 (strong acid), through yellow for weaker acids. As the chart shows, green is neutral (pH 7) and blue/purple is alkaline (high pH).

Why the others are wrong: D (green) is the NEUTRAL colour; C (blue/purple) is the ALKALINE colour; A (colourless) is wrong because universal indicator always shows a colour — it never goes colourless.

When resistors are connected in parallel, the combined resistance is found from:

1/R = 1/R₁ + 1/R₂

For the two 6 Ω resistors: 1/R = 1/6 + 1/6 = 2/6 = 1/3, so R = 3 Ω.

Shortcut: for two EQUAL resistors in parallel, the combined value is simply half of one — 6/2 = 3 Ω. The parallel resistance (3 Ω) is smaller than either resistor on its own, because adding a second path gives the current an extra route to flow through.

Common errors: 6 + 6 = 12 Ω is the SERIES rule (B), and 6 × 6 = 36 (A) forgets to divide by the sum — neither applies to a parallel pair.

The triangle stores one relationship: the quantity on TOP equals the product of the two underneath.

So m = n × M.

Rearranging for the number of moles gives n = m / M, that is, mass divided by molar mass. The answer is B.

How to use the triangle: cover the quantity you want to find. Covering n leaves m above M, which means divide m by M.

Worked example: 36 g of water, whose molar mass is 18 g/mol.
n = 36 / 18 = 2 mol.

Why the other options are wrong. Check them with units, which is the fastest way to catch an inverted formula.

Molar mass ÷ mass turns the relationship upside down and gives units of mol/g, not mol.

Mass × molar mass gives g²/mol, which is not an amount of substance at all.

Mass + molar mass adds two quantities that measure different things. Adding a mass to a molar mass is never a valid operation.

Avogadro's number (Nₐ = 6.02 × 10²³) is the number of particles (atoms, molecules, or ions) in one mole of any substance. One mole of carbon-12 has a mass of exactly 12 g and contains 6.02 × 10²³ atoms.