Higher November 2021 Paper 3 Q9
9 Rectangle \(ABCD\) is split into four smaller rectangles.
Two of the smaller rectangles are shaded.
Not drawn accurately
\(4 : x = 1 : 2\)
For rectangle \(ABCD\), work out the ratio \(\quad\) shaded area : unshaded area
Give your answer in its simplest form. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| \((x =)\ 4 \times 2\) or \((x =)\ 8\) or area of top right rectangle is \(12 \times 2\) or \(12 \div 4 \times\) their 8 or 24 or area of bottom left rectangle is \(56 \div 2\) or \(4 \times 56 \div\) their 8 or 28 | M1 | may be on diagram implied by length of bottom left or bottom right vertical section is 7 |
| Area of top right rectangle is \(12 \times 2\) or \(12 \div 4 \times\) their 8 or 24 and area of bottom left rectangle is \(56 \div 2\) or \(4 \times 56 \div\) their 8 or 28 or Total area is \((4 +\) their \(8) \times (12 \div 4 + 56 \div\) their \(8)\) or \(12 \times 10\) or 120 | M1dep | may be on diagram |
| (Total shaded area is) 52 | A1 | implied by 52 : 68 |
| 13 : 17 or 1 : \(\dfrac{17}{13}\) or \(\dfrac{13}{17}\) : 1 | B1ft | ft simplification of their ratio or conversion into the form 1 : \(n\) or \(n\) : 1 with M2A0 or M1M0A0 scored |
Additional guidance
| If their ratio cannot be simplified by dividing by a common factor they can only score B1ft by converting into the form 1 : \(n\) or \(n\) : 1 | |
| \(\dfrac{52}{120}\) : \(\dfrac{68}{120}\) | M1M1A1B0 |
| 68 : 52 simplified to 17 : 13 | M1M1A0B1ft |
| 13 cm2 : 17 cm2 | M1M1A1B0 |
| For B1, accept values as decimals rounded or truncated to 2 dp or better eg 1 : 1.31 or 0.76 : 1 | B1 |