# Corrections to Past Exam Solutions

## Mathematics IA

**2016**

- Q2)b) Algebra: The solution should say linearly Independent, not dependent as det neq 0
**2013**- Q3)a) Algebra: the value of c is -2. There is a transcription error where \(\frac{-1}{2}\) changed to \(\frac{1}{2}\). If you follow through the working with this correction, you should get c = -2.
- Q3)a) Calulus: The final answer should be 3x^2 arcsin(x^3) not 3x^2 arcsin(3x^3).
- Q4)b) Algebra: Firstly, the vertex at (0,6) is ignored. Secondly, g is not maximised at either (3,6) or (5,4), but at any point along the line from (3,6) to (5,4).
- 5 b) (i) of Algebra: The dimension should be 3, not 2.
- Q5) Calculus: there should be a constant of integration (typically written as +C) with each answer.

**2012**- Q1)b) Calculus: there should be rounded parentheses () instead of square brackets [] for the domain.
- Q4) Calculus: last value after the expansion should be +e^-2x not -e^-2x

## Mathematics IB

**2016 Algebra**- 2 (a)(ii): The last term should not have a 3 at the front, Due to this ,v3' was also calculated wrongly.

**2013**- Algebra 1 (b) (i): The normalizing vectors on the denominators of the Gran-Schimt process should not be v_1's.
- 2 (b): The range of F should be taking the columns of the original matrix but the solutions take the columns of the rref matrix.
- 6 (b): We need to normalise the vector (3,4) first to get (3/5,4/5), which means the rate of change is 3/5.

## Numerical Method II

**2013**- Q1 c): There is a minor typo, should be x_j not x_j+1

**2013**- Q3 (b) x1 = (1,0,2)^T should be x1 = (1,-2,2)^T

## Engineering Mathematics IIB

**Practice Exam 1**- Q2 b): Should be d(phi)/dy = exp(2x)+6y instead of exp(2x)

## Engineering Mathematics IIA

**Practice Exam 1**- Q1 a): The characteristic equation should have -2 not +2.

**Practice Exam 2**- Q1 e) i) & ii): Function should be with respect to t not x.

**Practice Exam 3**- Q3 : dw/dt was accidently mis-written as dx/dt (Start of page 16).

**Practice Exam 4**- Q5 (b) : The minus has been dropped when evaluating the integral at 0, the corret answer is -4pi/3.

**Practice Exam 5**- Q1 e) i) & ii): Function should be with respect to t not x.

- Q2 e): The (-4B-C+D) should be (-4B-C+2D), this changes the solution to D=5/4.

## Differential Equations

**2013**- Q2 d): Due to the missing negative sign \(w=Ax\) should be \(w=A/x\).

- Q4 b): The \(\frac{2}{\pi}\) factor for \(b_{n}\) (seen outside the integral expression on the left hand side of the page) was accidentaly omitted later in the question.