Foundation June 2019 Paper 3 Q25
25 Are these two triangles mathematically similar?
Show how you decide.
Not to scale
[3]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Two correct corresponding ratios evaluated correctly eg \(\dfrac{6}{10} = 0.6\) and \(\dfrac{11}{15} = 0.7[...]\) | M2 | M1 for one correct ratio evaluated | \(\dfrac{11}{6} = 1.8[...]\) and \(\dfrac{15}{10} = 1.5\) \(\dfrac{6}{11} = 0.5[...]\) and \(\dfrac{10}{15} =\) 0.6 to 0.7 \(\dfrac{10}{6} =\) 1.6 to 1.7 and \(\dfrac{15}{11} =\) 1.3 to 1.4 Note. Ratios between 6 and 10 and between 15 and 11 may be seen as tangents. These give angles in left triangle of 30.9 to 31.0 or 59.0 to 59.1 and angles in right triangle of 36.2 to 36.3 or 53.7 to 53.8 |
| or A side calculated correctly using one ratio or scale factor and the other side | \(\left(\dfrac{15}{10} \times 6\right.\) or \(\left.\dfrac{6}{10} \times 15\right) = 9\) \(\left(\dfrac{10}{15} \times 11\right.\) or \(\left.\dfrac{11}{15} \times 10\right) = 7.3[...]\) \(\dfrac{11}{6} \times 10 = 18.3[...]\) or \(\dfrac{6}{11} \times 15 =\) 8.1 to 8.2 | ||
| No + the [corresponding] ratios or sides are not the same oe or No + the 11 should be 9 oe | A1dep | Dep on M2 | A0 for “the sides are 5 cm longer” |