Higher June 2019 Paper 2 Q17
17 There are some small cubes and some large cubes in a bag.
The cubes are red or the cubes are yellow.
The ratio of the number of small cubes to the number of large cubes is 4 : 7
The ratio of the number of red cubes to the number of yellow cubes is 3 : 5
(a) Explain why the least possible number of cubes in the bag is 88 (1)
All the small cubes are yellow.
(b) Work out the least possible number of large yellow cubes in the bag. (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| Explanation | C1 | for stating the LCM of (4 + 7) and (5 + 3) is 88 or there is no smaller multiple of 8 and 11 (than 88) |
| Answer | Mark | Mark scheme |
|---|---|---|
| 23 | P1 | for using a scale factor appropriately eg \(4 \times 8\ (= 32)\) or \(3 \times 11\ (= 33)\) or \(7 \times 8\ (= 56)\) or \(5 \times 11\ (= 55)\) or for writing a pair of suitable fractions, eg \(\dfrac{7}{11}\) and \(\dfrac{3}{8}\), or \(\dfrac{4}{11}\) and \(\dfrac{5}{8}\), or \(\dfrac{3}{8}\) and \(\dfrac{4}{11}\) |
| P1 | for finding the number of large cubes and red cubes, or small and yellow, or small and red eg \(7 \times 8\ (= 56)\) and \(3 \times 11\ (= 33)\), or \(4 \times 8\ (= 32)\) and \(5 \times 11\ (= 55)\), or \(4 \times 8\ (= 32)\) and \(3 \times 11\ (= 33)\) OR for a suitable fractional equation, eg \(\dfrac{7}{11} - x = \dfrac{3}{8}\) or \(\dfrac{5}{8} - x = \dfrac{4}{11}\) or \(x = 1 - \dfrac{3}{8} - \dfrac{4}{11}\) OR for a suitable pair of probabilities with a common denominator, eg \(\dfrac{56}{88}\) and \(\dfrac{33}{88}\), or \(\dfrac{32}{88}\) and \(\dfrac{55}{88}\), or \(\dfrac{33}{88}\) and \(\dfrac{32}{88}\) | |
| A1 | cao |
Additional guidance
May be seen in a two-way table or probability tree (both P marks)
\(\dfrac{23}{88}\) scores P2A0