◈ Oracle PrepSign Up Free
O-LevelAdditional MathematicsIndices and surds4037/22 · Oct/Nov 2017 · Q15 Marks

If z = 2 + √3 find the integers a and b such that az² + bz = 1 + √3.

  1. If z = 2 + √3 find the integers a and b such that az² + bz = 1 + √3.[5]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

  1. [B1] z² = 7+4√3; Accept 4+3+4√3
  2. [M1] a(7+4√3)+b(2+√3)=1+√3; Equate both √3 terms and constant terms to obtain two equations in a and b.
  3. [A1] 7a+2b=1; 4a+b=1; Both correct. Accept equation with a multiple of √3
  4. [M1] Attempt to solve a pair of linear simultaneous eqns to a = or b =; M1dep
  5. [A1] a =1 and b = -3

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, 5 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2017 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 20144m

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.

Indices and surdsMay/June 20165m

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

Quadratic functionsMay/June 20205m

DO NOT USE A CALCULATOR IN THIS QUESTION. Find the positive solution of the equation (5+4√7)x²+(4-2√7)x-1 = 0, giving…

Differentiation and integrationMay/June 20206m

Find the equation of the tangent to the curve y = ln(3x²-1) / (x+2) at the point where x = 1. Give your answer in the…

Straight line graphsMay/June 20208m

The line y = 5x+6 meets the curve xy = 8 at the points A and B.

← Browse all past-paper questions

© 2026 Oracle Prep