Foundation November 2019 Paper 2 Q15
15 Which of these fractions is closer in value to 1?
\(\dfrac{3}{4}\) \(\dfrac{13}{10}\)
You must show your working. [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| 0.75 or 1.3 | M1 | decimal or percentage eg 75(%) or 130(%) |
| 0.75 and 1.3 and \(\dfrac{3}{4}\) oe | A1 | oe decimal or percentage eg 75(%) and 130(%) and \(\dfrac{3}{4}\) oe |
| Alternative method 2 | ||
| 0.25 or 0.3 | M1 | decimal or percentage eg 25(%) or 30(%) |
| 0.25 and 0.3 and \(\dfrac{3}{4}\) oe | A1 | decimal or percentage eg 25(%) and 30(%) and \(\dfrac{3}{4}\) oe |
| Alternative method 3 | ||
| Converts both fractions to valid common denominator with at least one numerator correct | M1 | eg \(\dfrac{15}{20}, \dfrac{26}{20}\) (both numerators correct) or \(\dfrac{30}{40}, \dfrac{54}{40}\) (one numerator incorrect) |
| Two correct fractions with valid common denominator and \(\dfrac{3}{4}\) oe | A1 | eg \(\dfrac{15}{20}\) and \(\dfrac{26}{20}\) and \(\dfrac{3}{4}\) oe or \(\dfrac{7.5}{10}\) and \(\dfrac{13}{10}\) and \(\dfrac{3}{4}\) oe |
| Alternative method 4 | ||
| Converts \(\dfrac{1}{4}\) and \(\dfrac{3}{10}\) to valid common denominator with at least one numerator correct | M1 | eg \(\dfrac{5}{20}, \dfrac{6}{20}\) (both numerators correct) or \(\dfrac{10}{40}, \dfrac{16}{40}\) (one numerator incorrect) |
| Two correct fractions with valid common denominator and \(\dfrac{3}{4}\) oe | A1 | eg \(\dfrac{5}{20}\) and \(\dfrac{6}{20}\) and \(\dfrac{3}{4}\) oe or \(\dfrac{2.5}{10}\) and \(\dfrac{3}{10}\) and \(\dfrac{3}{4}\) oe |
Additional guidance
| If answer line blank allow \(\dfrac{3}{4}\) to be indicated by eg circling the correct fraction | |
| Allow \(\dfrac{3}{4}\) to be given as a correct equivalent form eg Alt 1 0.75 and 1.3 and answer 0.75 | M1A1 |
| Ignore + or − when calculating difference from 1 eg Alt 2 accept 0.25 and \(-0.3\) or \(-0.25\) and 0.3 or \(-0.25\) and \(-0.3\) | |
| In Alt 1 if further work is seen eg to calculate the differences then these must be correct and comparable for the A1 | |
| eg 0.75 and 1.3 and 25 and 30 (correct change to %) Answer \(\dfrac{3}{4}\) | M1A1 |
| eg 0.75 and 1.3 and 0.25 and 30 (not comparable) Answer \(\dfrac{3}{4}\) | M1A0 |
| eg 0.75 and 1.3 and 0.15 and 0.3 (one incorrect) Answer \(\dfrac{3}{4}\) | M1A0 |
| Diagrams are acceptable if clear eg  and answer \(\dfrac{3}{4}\) | M1A1 |
| NB the reciprocal of \(\dfrac{3}{4}\) is 1.3… which may be seen truncated to 1.3 | M0 |
| \(1 - 0.75 = 0.25\), \(1 + 0.25 = 1.25\) and 1.3 seen and answer \(\dfrac{3}{4}\) | M1A1 |
| \(1.3 - 1 = 0.3\), \(1 - 0.3 = 0.7\) and 0.75 seen and answer \(\dfrac{3}{4}\) | M1A1 |
| Alt 3 eg \(\dfrac{15}{20}\) and \(1\dfrac{6}{20}\) and answer \(\dfrac{3}{4}\) | M1A1 |