Foundation November 2019 Paper 1 Q12
12 A college has
a total of 105 teachers
19 more female teachers than male teachers.
What proportion of the teachers are female? [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(x + x + 19 = 105\) or \(\dfrac{105 - 19}{2}\) or \(\dfrac{86}{2}\) or 43 | M1 | oe equation any letter may be implied by second mark |
| \(\dfrac{105 - 19}{2} + 19\) or 62 | M1dep | oe 62 seen is M2 (unless clearly from incorrect working) |
| \(\dfrac{62}{105}\) or 0.59(0…) or 59.(0…)% | A1 | oe SC2 \(\dfrac{43}{105}\) or 0.41 or 41% or better |
| Alternative method 2 | ||
| \(y + y - 19 = 105\) | M1 | oe equation any letter may be implied by second mark |
| \(\dfrac{105 + 19}{2}\) or \(\dfrac{124}{2}\) or 62 | M1dep | 62 seen is M2 (unless clearly from incorrect working) |
| \(\dfrac{62}{105}\) or 0.59(0…) or 59.(0…)% | A1 | oe SC2 \(\dfrac{43}{105}\) or 0.41 or 41% or better |
| Alternative method 3 | ||
| \(\dfrac{105}{2}\) and \(\dfrac{19}{2}\) or 52.5 and 9.5 | M1 | |
| their 52.5 + their 9.5 or \(105 -\) (their \(52.5 -\) their 9.5) or 62 | M1dep | 62 seen is M2 (unless clearly from incorrect working) |
| \(\dfrac{62}{105}\) or 0.59(0…) or 59.(0…)% | A1 | oe SC2 \(\dfrac{43}{105}\) or 0.41 or 41% or better |
Additional guidance
| Ignore any attempts to simplify or convert a correct fraction | |
| Trial and Improvement leading to 62 (may go on to score full marks) | at least M1M1 |
| Trial and Improvement not leading to 62 or the correct answer | M0M0A0 |
| \(\dfrac{19}{105}\) or \(\dfrac{86}{105}\) | M0M0A0 |
| 62 : 105 or 62 : 43 or 62% or 62 out of 105 | M1M1A0 |