# 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.