Question 1 of 3
Mathematics · Algebraic equations
Solve 3x + 5 = 20.
Undo the addition first, then undo the multiplication.
- Subtract 5 from both sides: 3x = 15.
- Divide both sides by 3: x = 5.
- Check: 3 × 5 + 5 = 20.
Physical Sciences · Motion in one dimension
A car changes velocity from 0 m·s⁻¹ to 20 m·s⁻¹ in 5 s. Calculate its acceleration.
Acceleration is the change in velocity divided by the time taken.
- Use a = (v − u) / Δt.
- Substitute: a = (20 − 0) / 5.
- Acceleration = 4 m·s⁻².
Mathematics · Algebraic expressions
Factorise x² − 5x + 6.
Find two numbers whose product is 6 and whose sum is −5.
- The numbers are −2 and −3: (−2)(−3) = 6, and −2 − 3 = −5.
- Write the factors: (x − 2)(x − 3).
- Expand to check: x² − 3x − 2x + 6 = x² − 5x + 6.