1. A map has scale 1:25,000. The distance between two points is 8.4 cm on the map. What is the actual distance in kilometres?
The actual distance is 8.4 × 25,000 = 210,000 cm. Since 100,000 cm = 1 km, this is 2.1 km.
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The actual distance is 8.4 × 25,000 = 210,000 cm. Since 100,000 cm = 1 km, this is 2.1 km.
The gradient is (19 - 7) / (6 - 2) = 3. Using (2, 7), 7 = 3 × 2 + b, so b = 1. The rule is y = 3x + 1.
Use Pythagoras: rise² = 5.2² - 4.8² = 27.04 - 23.04 = 4. The rise is 2.0 m.
The added water must be 220 - 40 = 180 L. At 18 L per minute, the time is 180 / 18 = 10 minutes.
Add the late branches: 0.35 × 0.60 + 0.65 × 0.15 = 0.21 + 0.0975 = 0.3075.
The area difference is (3x)² - x² = 9x² - x² = 8x². So 8x² = 128, x² = 16, and x = 4 because a side length is positive.
Year 8 maths practice should make proportional reasoning, linear rules, Pythagoras, rates, probability, and algebra feel structured rather than guessable. These examples preview that style before the no-login Year 8 Maths demo.
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