27 results authored by Kevin Bohan  search across all users.

Exam (5 questions) in Kevin's workspaceA collection of questions on solving equations and revising manipulation of small matrices for 2nd year students

Question in Kevin's workspace
More work on differentiation with trigonometric functions

Question in Kevin's workspace
Chain rule

Question in Kevin's workspace
Simplifying indices.

Question in Kevin's workspace
Three graphs are given with areas underneath them shaded. The student is asked to calculate their areas, using integration. Q1 has a polynomial. Q2 has exponentials and fractional functions. Q3 requires solving a trig equation and integration by parts.

Question in Kevin's workspace
Simplifying indices.

Question in Kevin's workspace
Graphs are given with areas underneath them shaded. The student is asked to select the correct integral which calculates its area.

Exam (5 questions) in Kevin's workspace
5 questions on definite integrals  integrate polynomials, trig functions and exponentials; find the area under a graph; find volumes of revolution.

Question in Kevin's workspace
Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Exam (8 questions) in Kevin's workspace
Use the quotient rule to differentiate various functions.

Exam (11 questions) in Kevin's workspace
Use the product rule to differentiate various functions.

Question in Kevin's workspace
No description given

Question in Kevin's workspace
No description given

Question in Kevin's workspace
Implicit differentiation.
Given $x^2+y^2+dxy +ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.
Also find two points on the curve where $x=0$ and find the equation of the tangent at those points.

Question in Kevin's workspace
Implicit differentiation.
Given $x^2+y^2+dxy +ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.
Also find two points on the curve where $x=0$ and find the equation of the tangent at those points.

Exam (6 questions) in Kevin's workspace
Questions involving various techniques for rearranging and solving quadratic expressions and equations

Exam (12 questions) in Kevin's workspace
Differentiation of polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.
Missing: Application with bacteria, turning points, difficult chain rule

Exam (13 questions) in Kevin's workspace
Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.

Question in Kevin's workspace
Find $\displaystyle \int x(a x ^ 2 + b)^{m}\;dx$

Question in Kevin's workspace
Two quadratic graphs are sketched with some area beneath them shaded. Question is to determine the area of shaded regions using integration. The first graph's area is all above the $x$axis. The second graph has some area above and some below the $x$axis.

Question in Kevin's workspace
Find $\displaystyle \int x\sin(cx+d)\;dx,\;\;\int x\cos(cx+d)\;dx $ and hence $\displaystyle \int ax\sin(cx+d)+bx\cos(cx+d)\;dx$

Question in Kevin's workspace
Finding the stationary points of a cubic with two turning points

Question in Kevin's workspace
This exercise will help you solve equations of type axb = c.

Exam (4 questions) in Kevin's workspace
Refresher questions on topics in algebra that students beginning a maths undergraduate course should be familiar with.

Question in Kevin's workspace
Complete the square for a quadratic polynomial $q(x)$ by writing it in the form $a(x+b)^2+c$. Find both roots of the equation $q(x)=0$.

Question in Kevin's workspace
A quadratic is given and sketched. Based on the sketch, task is to determine the number of solutions to the equation $f(x)=0$.

Exam (1 question) in Kevin's workspaceIf you find manipulating fractions tricky, then work through this problem set to get more familiar with them.