Higher June 2017 Paper 1 Q14
14 White shapes and black shapes are used in a game.
Some of the shapes are circles.
All the other shapes are squares.
The ratio of the number of white shapes to the number of black shapes is 3 : 7
The ratio of the number of white circles to the number of white squares is 4 : 5
The ratio of the number of black circles to the number of black squares is 2 : 5
Work out what fraction of all the shapes are circles. (4)
| Answer | Mark | Notes |
|---|---|---|
| \(\dfrac{1}{3}\) | P1 | process to solve the problem e.g. \(\dfrac{3}{10} \times \dfrac{4}{9} \left(= \dfrac{12}{90} = \dfrac{2}{15}\right)\) OR finds the number of white circles for their chosen number OR for 9 : 21 (or a multiple of 9 : 21) |
| P1 | second step of the process e.g. \(\dfrac{7}{10} \times \dfrac{2}{7} \left(= \dfrac{14}{70} = \dfrac{2}{10} = \dfrac{1}{5}\right)\) OR finds the number of black circles for their chosen number OR for a multiple of 2 : 5 where the ratio parts sum to “21” | |
| P1 | for complete process e.g. \(\text{``}\tfrac{2}{15}\text{''} + \text{``}\tfrac{1}{5}\text{''} \left(= \dfrac{4}{30} + \dfrac{6}{30}\right)\) OR finds the total number of circles for their chosen number OR for 3 ratios that could be used to solve the problem eg 9 : 21 with 4 : 5 with 6 : 15 | |
| A1 | for \(\dfrac{1}{3}\) oe |