Higher June 2019 Paper 3 Q8
8 \(ABC\) is a right-angled triangle.
Here is Sarah’s method to find the length of \(BC\).
\(\begin{aligned} BC^2 &= AB^2 + AC^2 \\ &= 6^2 + 8^2 \\ &= 100 \\ BC &= 10 \end{aligned}\)
(a) What mistake has Sarah made in her method? (1)
Roy is going to enlarge triangle \(PQR\) with centre \(C\) and scale factor \(1\frac{1}{2}\)
He draws triangle \(XYZ\).
(b) Explain why Roy’s diagram is not correct. (1)
| Answer | Mark | Mark scheme |
|---|---|---|
| Mistake described | C1 | for statement describing a mistake Acceptable eg should be \(AC^2 - AB^2\) she should do \(8^2 - 6^2\) she should be subtracting not adding the numbers she thought that \(BC\) was the hypoteneuse when it was actually \(AC\) should be \(BC^2 + AB^2 = AC^2\) should be \(8^2 = 6^2 + BC^2\) Not acceptable eg she has not used Pythagoras correctly \(6^2 + 8^2\) is 120 the answer should be \(\sqrt{28}\) or 5 or 5.3 or 5.2915 \(BC + AB = AC\) |
| Answer | Mark | Mark scheme |
|---|---|---|
| Explanation | C1 | for explanation Acceptable examples the scale factor used is 2.5 \(5 \div 2\) is not 1.5 \(10 \div 4\) is more than 1.5 the scale factor is not 1.5 he has not used the correct scale factor has enlarged it by too much \(ZY\) should be 6 Not acceptable examples the grid is not large enough he has used the wrong centre |
Additional guidance
Note that a diagram alone is insufficient.