O-LevelAdditional MathematicsIndices and surds4037/22 · Oct/Nov 2013 · Q24 Marks
Do not use a calculator in this question. Express (4√5-2)² / (√5-1) in the form p√5 + q, where p and q are integers.
- (a)Express (4√5-2)² / (√5-1) in the form p√5 + q, where p and q are integers.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2013). The mark or mark type is shown in brackets.
- [M1] (4√5-2)² = 80-16√5+4 Attempt to expand, allow one error, must be in the form a+b√5.
- [M1] Multiply top and bottom by √5+1 Must be attempt to expand top and bottom.
- [A1] (68√5+4)/4 Allow A1 for (68√5+4)/C
- [A1] 17√5+1
- OR
- [M1] (4√5-2)² = 80-16√5+4
- [M1] (√5-1)(p√5+q)=5p-q+√5(q-p) Must get to a pair of simultaneous equations for this mark
- [A1] Leading to 5p-q = 84, q − p = −16
- [A1] p=17 q=1
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →