◈ Oracle PrepSign Up Free
O-LevelAdditional MathematicsIndices and surds4037/22 · May/June 2014 · Q14 Marks

Without using a calculator, express (2 + √5)² / (√5 – 1) in the form a + b√5, where a and b are constants to be found.

  1. Without using a calculator, express (2 + √5)² / (√5 – 1) in the form a + b√5, where a and b are constants to be found.[4]

Mark scheme

Marking points from the official mark scheme (May/June 2014). The mark or mark type is shown in brackets.

  1. [M1] rationalise the denominator to get (2+√5) (√5+1) / 5-1 or better
  2. [M1] or squaring to get (4+4√5+5) / √5-1 or better
  3. [A1 + A1] or rationalising the denominator to get their(9+4√5)(√5+1) / 5-1 or better correct simplification Allow 29+13√5 / 4 etc.

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 →

About this question

Topic
Indices and surds, O-Level Additional Mathematics (syllabus 4037). Structured question, 4 marks.
Source
O-Level Additional Mathematics, May/June 2014 Paper 2 Variant 2, question 1.

Questions and mark schemes are from past examination papers and remain the copyright of the exam board. How Oracle Prep builds its content

Related Additional Mathematics questions

Indices and surdsMay/June 20144m

Without using a calculator, express 6(1 + √3)⁻² in the form a + b√3, where a and b are integers to be found.

Indices and surdsMay/June 20165m

Solve the equation 16^(3x−1) = 8^(x+2) .

Indices and surdsMay/June 20176m

Simplify √x³y¹⁰ ÷ √x³y⁻⁶, giving your answer in the form xᵃyᵇ, where a and b are integers.

Simultaneous equationsMay/June 20185m

Find the coordinates of the points where the line 2y - 3x = 6 intersects the curve x²/4 + y²/9 = 5.

Permutations and combinationsMay/June 20187m

Four parts in a play are to be given to four of the girls chosen from the seven girls in a drama class. Find the numb…

Vectors in two dimensionsMay/June 20186m

Vectors i and j are vectors parallel to the x-axis and y-axis respectively. Given that a = 2i + 3j, b = i – 5j and c …

← Browse all past-paper questions

© 2026 Oracle Prep