Work out \(\dfrac{\text{length of shortest side}}{\text{length of longest side}}\)
Give your answer as a fraction in its simplest form. [2 marks]
(b) Here is a different triangle.
Not drawn accurately
\(x = 3y\)
Work out the size of angle \(y\). [3 marks]
Mark scheme (a)
Answer
Mark
Comments
\(\dfrac{1}{3}\)
B2
B1 (may be seen in diagram) 120 or 100 or 0.4(0) may be seen in a fraction eg \(\dfrac{120}{40}\) or \(\dfrac{0.4}{1.2}\) or correct, but unsimplified fraction eg \(\dfrac{20}{60}\) or their fraction written in simplest form
SC1 1 : 3
Additional guidance
Ignore units on answer line
Do not ignore further work after \(\dfrac{1}{3}\) seen
If converting to mm both values must be correct
\(\dfrac{1}{3}\) given as a decimal or percentage must be correct to 2sf or better
B1
B1 for simplifying their fraction can only be awarded from the use of digits 1, 12 and 4, eg \(\dfrac{40}{1200}\), answer \(\dfrac{1}{30}\) \(\dfrac{1200}{40}\), answer 30 \(\dfrac{40}{1200}\), answer \(\dfrac{1}{3}\) \(\dfrac{2}{4}\), answer \(\dfrac{1}{2}\)
B1 B1 B0 B0
\(\dfrac{0.04}{1.2}\), answer \(\dfrac{1}{30}\)
B1
\(\dfrac{1}{40}\) or \(\dfrac{40}{1} = 40\)
B0
Mark scheme (b)
Answer
Mark
Comments
\(180 - 112\) or 68 or \(3y + y + 112 = 180\)
M1
oe
their 68 \(\div (3 + 1)\) or their 68 \(\div\) 4 or \(y = \dfrac{\text{their } 68}{4}\) or 51 or \(x = 17\)
M1
oe their 68 must be \(\lt 180\) but not 112 51 or \(x = 17\) imply M1M1
17
A1
Additional guidance
Check diagram for workings and answer
17 seen in diagram or working and 51 on answer line
