Higher June 2023 Paper 2 Q12
12 Show that these two rectangles are similar. [2 marks]
Not drawn accurately
| Answer | Mark | Comments |
|---|---|---|
| \(8 \div 5\) or \(19.2 \div 12\) or \(\dfrac{8}{5}\) or \(\dfrac{19.2}{12}\) or 1.6 or \(12 \div 5\) or \(19.2 \div 8\) or \(\dfrac{12}{5}\) or \(\dfrac{19.2}{8}\) or 2.4 | M1 | oe use of a valid pair of sides to make an appropriate calculation or value eg \(5 \div 8\) or 0.625 or \(5 \div 12\) or [0.416, 0.417] |
| \(8 \div 5 = 19.2 \div 12\) or \(\dfrac{8}{5} = \dfrac{19.2}{12}\) or \(12 \div 5 = 19.2 \div 8\) or \(\dfrac{12}{5} = \dfrac{19.2}{8}\) | A1 | oe showing sides are in proportion eg \(5 \div 8 = 12 \div 19.2\) or \(\dfrac{5}{12} = \dfrac{8}{19.2}\) |
Additional guidance
| For A1 equating may be implied by two calculations or two fractions with correct evaluation eg \(8 \div 5 = 19.2 \div 12\) is implied by \(8 = 5 \times 1.6\) and \(19.2 = 12 \times 1.6\) | M1A1 |
| For A1 equating may be implied by calculations eg1 \(8 \div 5 = 19.2 \div 12\) is implied by \(8 \div 5 = 1.6\) and \(12 \times 1.6 = 19.2\) eg2 \(8 \div 5 = 19.2 \div 12\) is implied by \(\dfrac{8}{5} \times 12 = 19.2\) | M1A1 M1A1 |
| \(5 \times 19.2 = 8 \times 12\) | M1A1 |
| \(5 \times 19.2 = 96\) and \(8 \times 12 = 96\) | M1A1 |
| Non-contradictory working can be ignored eg correct response along with area calculations | M1A1 |
| Ignore words eg references to scale factors, enlargement, angles | |
| Working on diagrams may be seen eg1 Arrows or lines from 5 to 8 and 12 to 19.2 with \(\times 1.6\) on them eg2 Arrows or lines from 5 to 8 and 12 to 19.2 with 1.6 on them Arrows or lines must unambiguously link relevant numbers | M1A1 M1A0 |
| For \(8 \div 5\) or \(\dfrac{8}{5}\) allow 8 : 5 etc |