Foundation November 2021 Paper 3 Q24
24 Here are two rectangles.
Not drawn accurately
Show that the rectangles are similar. [1 mark]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(\dfrac{28}{35} = 0.8\) and \(\dfrac{40}{50} = 0.8\) or \(\dfrac{35}{28} = 1.25\) and \(\dfrac{50}{40} = 1.25\) or \(\dfrac{28}{40} = 0.7\) and \(\dfrac{35}{50} = 0.7\) or \(\dfrac{40}{28} = 1.42857\ldots\) and \(\dfrac{50}{35} = 1.42857\ldots\) | B1 | oe decimal values must be the same, but may be correctly rounded or truncated |
| Alternative method 2 | ||
| \(35 \times \dfrac{40}{50} = 28\) or \(35 \div \dfrac{50}{40} = 28\) or \(28 \times \dfrac{50}{40} = 35\) or \(28 \div \dfrac{40}{50} = 35\) or \(50 \times \dfrac{28}{35} = 40\) or \(50 \div \dfrac{35}{28} = 40\) or \(40 \times \dfrac{35}{28} = 50\) or \(40 \div \dfrac{28}{35} = 50\) | B1 | oe calculation including all four values eg \(\dfrac{35 \times 40}{50} = 28\) |
Additional guidance
| Calculations must be shown | |
| Accept decimal truncation but truncated values must be the same eg \(\dfrac{40}{28} = 1.42\) and \(\dfrac{50}{35} = 1.42\) | B1 |
| \(\dfrac{28}{35} = \dfrac{40}{50}\) and \(28 \times 50 = 35 \times 40\) and \(1400 = 1400\) or \(\dfrac{28}{35} = \dfrac{40}{50}\) and \(28 \times 50 = 1400\) and \(35 \times 40 = 1400\) | B1 |
| \(28 \times 1.25 = 35\) and \(40 \times 1.25 = 50\) (oe ALT1) | B1 |
| \(28 \times 1.25 = 35\) and \(\dfrac{50}{40} = 1.25\) | B1 |
| \(28 \times 1.25 = 35\) | B0 |
| Answers as fractions without a common denominator eg \(\dfrac{28}{35} = \dfrac{40}{50}\) | B0 |
| \(\dfrac{28}{40} = 1.4\) and \(\dfrac{50}{35} = 1.4\) | B0 |
| \(\dfrac{28}{7} = \dfrac{40}{10} = 4\) and \(\dfrac{35}{7} = \dfrac{50}{10} = 5\) | B0 |