Hint
Use the stated units and precision. Apply the length scale and convert centimetres to metres.
Worked solution
(a)
Apply the length scale and convert centimetres to metres.
Multiply 8 by 400 to get real centimetres, then divide by 100: \(32\) m.
Answer: \(32\)
(b)
Convert to common units and divide by the scale denominator.
Convert the real length to 4000 cm, then divide by 400 to obtain 10 cm.
Answer: \(10\)
(c)
The three lengths satisfy the triangle inequality. Each arc fixes a distance from one endpoint, so their intersection meets both remaining side requirements. Either reflected intersection gives a congruent triangle.
Answer: Draw the base 6 cm; intersect arcs of radii 4 cm and 5 cm from its respective endpoints; join the intersection to both endpoints.
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit complete valid alternative methods and consequential reasoning. An unexplained result does not earn a method mark.
(a) · 2 marks
- 1 mark: Apply the length scale and convert centimetres to metres.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
(b) · 2 marks
- 1 mark: Convert to common units and divide by the scale denominator.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Check the answer against the original conditions.
(c) · 3 marks
- 1 mark: Draw and label the stated base accurately.
- 1 mark: Use the two correct arc centres and radii, retain the arcs and join the third vertex.
- 1 mark: Give the complete requested result, using the required units, precision and boundary inclusion.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
Total: 7 marks.