Additional Mathematics

Mathematics students a more seamless transition to the advanced thinking and skills needed for CAPE unit 1 Mathematics courses, although a good SEC Mathematics student should still be able to meet the skills and thinking demands of the CAPE Unit 1 Mathematics course. The examinations consist of three papers: C] paper 01 -? a 45 – item multiple choice paper; C] Paper 02 -? a structured, ‘essay-type’ paper consisting of 8 questions; II Paper 031 or Paper 032 -? Paper 03 represents an School-Based Assessment (SABA) project component for candidates in schools, and paper 032 an alternative to the SABA for out-of-school candidates.

The Additional Mathematics syllabus (EX. 37/G/SLYLY 10) tests content in four main topic areas divided as follows: Section 1 -? Algebra and Functions, Section 2 -? Coordinate Geometry, Vectors and Trigonometry, Section 3 Introductory Calculus, and Section 4 -? Basic Mathematical Applications. Paper 01 tests content from Sections 1, 2 and 3 of the syllabus. This paper carries 45 items which are weighted up to 60 for the overall examination. Paper 02 tests content from all four sections of the syllabus.

This year the paper consisted Of four sections, divided as described previously for the outline of the syllabus. Each section contained TTY. Or problem-solving type questions. The questions in Sections 1 , 2 and 3 were all compulsory. The TV questions in these sections were worth a total of 28, 24 and 28 marks respectively. Section 4 also contained two questions, one on Data Representation and Probability and the other on Kinematics worth 20 marks each; candidates were to choose one question from this section. Paper 03 represents the SABA component of the examination.

Candidates can do a reject chosen from two project types, a mathematical modeling project (Project A) and a data handling/statistical analysis project (Project B). The SABA component is worth 20 marks. Alternatively, candidates can sit an alternative to the SABA paper, Paper 032, which consists of a more in-depth extended question from Sections 1, 2 and/or 3 of the syllabus. This paper carries 20 marks. DETAILED COMMENTS paper 01 -? Structured Essay Questions This was a 45 – item paper covering Sections 1, 2 and 3 of the syllabus.

A total of 1 720 candidates sat this paper of the examination. Candidates scored a mean of 23. 22, with standard deviation 8. 77. Paper 02 – Structured Essay Questions No formula sheet was provided for this sitting of the examination. However, in cases where it was suspected that candidates might have been affected by the absence of a formula sheet the mark scheme was adjusted so that candidates were awarded follow through marks if they used an incorrect reasonable formula, and were not penalized for this wrong formula.

For future examinations, a formula sheet will be provided for papers 01 and 02. Section 1: Algebra and Functions Question 1 This question tested candidates’ ability to: C] determine a composite function, its range and inverse; C] make use of the Factor Theorem; C] use the laws of indices to solve exponential equations in one unknown; and C] apply logarithms to reduce a relationship to linear form. There were 1746 responses to this question. The mean mark was 5. 2 with standard deviation 3. 26. Thirty-nine candidates obtained full marks. Candidates performed best on Parts (a) (I), (iii) and (b) which required them to determine the composite function g(f(x)) of given functions f(x) and g(x), and the inverse of the composite function. In Part (a) (iii) some candidates experienced difficulty at the interchange step, that is, 1) g(f(x)) = xx + 6; Let y = g(f(x) y 3 0 x 6*њD commonly seen error 01 Part (b) was generally well done by candidates.

However, some of them did have difficulty here. The following common errors were seen: Substituting x = 2 into f(x) rather than x = -2; Some candidates who did correctly substitute x = -?2 then made errors in their manipulation of the directed numbers; A few candidates attempted long division approach to solving this problem; however they very often encountered some difficulty with this.

Parts (a) (ii), (c) and (d) presented the most difficulty to candidates. In part (a) (ii), which required candidates to state the range of the composite function, generally candidates were unable to do this, or stated discrete values for the range, that is, {6, 7, 14, 33}, not recognizing it as the infinite set Of Real Numbers, 6 g(f(x)) 33. In Part (c), many candidates attempted to solve the given equation xx 8 without (appropriate) substitution.