Higher June 2017 Paper 2 Q17
17 P is a rectangle with length 50 cm and width \(x\) cm
Q is a rectangle with width \(y\) cm
Not drawn accurately
The length of Q is 20% more than the length of P.
The area of Q is 10% less than the area of P.
Work out the ratio \(\quad x : y\)
Give your answer in its simplest form. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(50 \times 1.2\) or 60 | M1 | oe length of Q May be on the diagram |
| \(50 \times x \times 0.9\) or \(45 \times x\) | M1 | oe area of P reduced by 10% May be on the diagram |
| their \(60 \times y =\) their \(45 \times x\) or \(\dfrac{y}{x} = \dfrac{\text{their } 45}{\text{their } 60}\) or \(y : x =\) their 45 : their 60 or equivalent ratio to 4 : 3 not in simplest form or equivalent fraction to \(\dfrac{4}{3}\) not in simplest form | M1dep | oe dep on M2 M3 \(\dfrac{1.2}{0.9}\) |
| 4 : 3 or \(1 : \dfrac{3}{4}\) or 1 : 0.75 or \(\dfrac{4}{3} : 1\) | A1 | |
| Alternative method 2 | ||
| \(50 \times 1.2\) or 60 | M1 | oe length of Q May be on the diagram |
| Chooses a value for \(x\) and reduces area of P by 10% | M1 | oe eg \((x = 8)\ \; 50 \times 8 \times 0.9\) |
| their \(60 \times y =\) their area of P reduced by 10% or equivalent ratio to 4 : 3 not in simplest form or equivalent fraction to \(\dfrac{4}{3}\) not in simplest form | M1dep | oe eg \(60y = 50 \times 8 \times 0.9\) or \(60y = 360\) or \((y =)\ 360 \div 60\) or 6 dep on M2 M3 \(\dfrac{1.2}{0.9}\) |
| 4 : 3 or \(1 : \dfrac{3}{4}\) or 1 : 0.75 or \(\dfrac{4}{3} : 1\) | A1 | |
Additional guidance
| Allow 1.33(…) for \(\dfrac{4}{3}\) | |
| 4 : 3 in working with 3 : 4 on answer line | M3A0 |
| \(1 : \dfrac{45}{60}\) | M3A0 |
| (Alt 1) \(\;50x = 60y \times 0.9\) | M1M0M0A0 |
| (Alt 1) \(\;50x = 60y \times 1.1\) | M1M0M0A0 |
| (Alt 1) \(\;45x : 60y\) Answer 3 : 4 | M1M1 M0A0 |
| (Alt 1) \(\;y : x = 3 : 4\) Answer 3 : 4 | M3A0 |
| Alt 2 example \(50 \times 10 = 500\) (working not seen for reduction by 10% but completed correctly in next line) \(450 \div 60 = 7.5\) (60 here gains first M1) \(10 : 7.5 = 20 : 15\) | M1M1 M1A0 |
| Do not allow misreads eg increases length of P by 10% (instead of 20%) | |
| Alt 2 Allow choice of \(x\) to be 50 |