CIE IAL · Mathematics · 2014 May/June

9709/22 May/June 2014

This Mathematics 9709 Paper 2 (Pure Mathematics 2) paper contains 8 questions worth 50 marks. The profile below reports five mark-weighted difficulty and complexity measures, and every question row repeats them. Full question text and mark scheme open in the Interactive Practice Hub.

CIE IAL 9709 P2 8 questions 50 marks Free paper

Practise this paper All 9709 P2 papers

Core finding

9709/22 May/June 2014 is a past paper for CIE IAL Mathematics 9709 Paper 2 (Pure Mathematics 2), with 8 questions worth 50 marks. Its mark-weighted Difficulty Measure is 0.40 on a 0.20–0.75 scale, with a Difficulty Deviation of 0.14 and a mark split of 26.0% Easy, 64.0% Medium and 10.0% Hard. Algebraic complexity averages 0.45; text density and modelling average 0.23. All five measures use 14 part-level tags, not candidate results. Every question row below repeats them and opens the Interactive Practice Hub for that question.

Difficulty & complexity profile

All five measures are mark-weighted and calculated from 14 parts carrying 50 part marks. Difficulty tags cover 14 parts, algebraic tags 14 and text-density tags 14. Tags are internal metadata, not official exam-board ratings.

Difficulty Measure 0.40 0.20–0.75 · nearer Medium

Difficulty Deviation 0.14 0 = uniform; higher = more mixed

Difficulty Ratio 26.0 / 64.0 / 10.0 % Easy / Medium / Hard

Algebraic Complexity Measure 0.45 0.20–0.75 · nearer Medium

Text Density and Modelling Measure 0.23 0.20–0.75 · nearer Low

Scale: Easy 0.20 · Medium 0.45 · Hard 0.75, and Low 0.20 · Medium 0.45 · High 0.75 for the two complexity measures. How each band is defined and how the values are calculated →

Definitions and calculation

Measure	Paper value	Formula
Difficulty Measure	0.40	Σ(d_i × w_i) / Σw_i, with d = 0.20 / 0.45 / 0.75
Difficulty Deviation	0.14	√(Σw_i(d_i − μ)² / Σw_i)
Difficulty Ratio	26.0% Easy / 64.0% Medium / 10.0% Hard	marks in band / all tagged marks
Algebraic Complexity Measure	0.45	Σ(c_i × marks_i) / Σmarks_i, with c = 0.20 / 0.45 / 0.75
Text Density and Modelling Measure	0.23	Σ(t_i × marks_i) / Σmarks_i, with t = 0.20 / 0.45 / 0.75

w_i equals the part marks, except for a Hard part worth 4 or more marks, where w_i = marks^0.75 to offset the accessible starter steps inside long structured questions.

Question list

Each measure is recalculated from the parts of that question and uses the same weights as the paper profile.

Question	Topic	Marks	Difficulty Measure	Algebraic Complexity Measure	Text Density and Modelling Measure	Practice
Q1 FRQ	1 Algebra	4	0.20Easy	0.33Medium	0.20Low	Go to Practice Hub
Q2 FRQ	3 Trigonometry	4	0.45Medium	0.45Medium	0.20Low	Go to Practice Hub
Q3 FRQ	5 Integration	5	0.35Medium	0.35Medium	0.20Low	Go to Practice Hub
Q4 FRQ	4 Differentiation	6	0.45Medium	0.45Medium	0.20Low	Go to Practice Hub
Q5 FRQ	2 Logarithmic and exponential functions	6	0.45Medium	0.45Medium	0.45Medium	Go to Practice Hub
Q6 FRQ	1 Algebra	7	0.38Medium	0.38Medium	0.20Low	Go to Practice Hub
Q7 FRQ	5 Integration	9	0.31Easy	0.31Low	0.20Low	Go to Practice Hub
Q8 FRQ	3 Trigonometry	9	0.59Medium	0.75High	0.20Low	Go to Practice Hub

Topics in this paper

1 Algebra 2 Logarithmic and exponential functions 3 Trigonometry 5 Integration 4 Differentiation 6 Numerical solution of equations

Paper FAQ

How are the difficulty and complexity measures calculated?: Each part is weighted by its official marks. Difficulty uses Easy 0.20, Medium 0.45 and Hard 0.75; algebraic complexity and text density and modelling use Low 0.20, Medium 0.45 and High 0.75. A Hard part worth 4 or more marks is down-weighted to marks^0.75, so the accessible starter steps inside a long structured question do not inflate the difficulty result. This paper's Difficulty Measure is 0.40 from 14 parts.
What does the Difficulty Deviation show?: It is the mark-weighted standard deviation of the part difficulty values around the paper mean. A value of 0 would mean every tagged part has the same difficulty; this paper's deviation is 0.14, so its parts are more mixed than a single-level paper.
Is the Difficulty Ratio based on question counts or marks?: It is based on official marks, not question counts. This paper's shares are 26.0% Easy, 64.0% Medium and 10.0% Hard; the three shares sum to 100% before rounding.
Are these official difficulty ratings?: No. They are derived from the platform's part-level difficulty and static-question-profile tags. They are not exam-board grade boundaries and are not calculated from candidate outcomes. Use them to compare the demand profile of papers, not to predict a grade.
Why does each question row show its own measures?: Each row recalculates the same mark-weighted formula from that question's parts. A single-part MCQ therefore shows the tag value directly, while a multi-part structured question blends the tags of its parts using the same Hard-part decay as the paper profile.