Higher June 2023 Paper 1 Q20
20 K, L and M are weights.
Both of the scales balance exactly.
How many M weights are needed to balance one L weight? [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 – finds K in terms of L and substitutes | ||
| 3K = 4L or K = L + 2M | M1 | oe correct equation eg \(\text{K} = \dfrac{4\text{L}}{3}\) or \(\text{L} = \dfrac{3\text{K}}{4}\) may be implied by values on diagram |
| \(\dfrac{4\text{L}}{3} = \text{L} + 2\text{M}\) | M1dep | oe correct equation in L and M eg 4L = 3L + 6M |
| 6 | A1 | condone 6M (= L) |
| Alternative method 2 – finds two variables in terms of the other variable | ||
| Finds one variable in terms of one other eg L is \(\dfrac{3}{4}\) of K | M1 | oe fractions, decimals, percentages or ratio eg K : L \(= 1 : \dfrac{3}{4}\) may be implied by values on diagram |
| Finds two variables in terms of the other eg L is \(\dfrac{3}{4}\) of K and M is \(\dfrac{1}{8}\) of K | M1dep | oe fractions, decimals, percentages or ratio eg K : L : M \(= 1 : \dfrac{3}{4} : \dfrac{1}{8}\) may be implied by values on diagram |
| 6 | A1 | condone 6M (= L) |
| Alternative method 3 – assumes a mass for one unknown | ||
| Assumes a mass for one unknown and works out the mass of one other | M1 | eg K = 2 kg and L = 1.5 kg |
| Assumes a mass for one unknown and works out the masses of the other two | M1dep | eg K = 2 kg and L = 1.5 kg and M = 0.25 kg |
| 6 | A1 | condone 6M (= L) |
Additional guidance
Condone 1.33 or better for \(\dfrac{4}{3}\), but 0.125 for \(\dfrac{1}{8}\) must be correct
3K : 4L is not enough for M1
Ignore units