27 results authored by Kevin Bohan - search across all users.

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• Exam (5 questions)
A collection of questions on solving equations and revising manipulation of small matrices for 2nd year students
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More work on differentiation with trigonometric functions

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Chain rule

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Simplifying indices.

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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.

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Simplifying indices.

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Graphs are given with areas underneath them shaded. The student is asked to select the correct integral which calculates its area.

• Exam (5 questions)

5 questions on definite integrals - integrate polynomials, trig functions and exponentials; find the area under a graph; find volumes of revolution.

• Question

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)

Use the quotient rule to differentiate various functions.

• Exam (11 questions)

Use the product rule to differentiate various functions.

• Question

No description given

• Matrices 1
Draft
Question

No description given

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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

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.

• Quadratics
Draft
Exam (6 questions)

Questions involving various techniques for rearranging and solving quadratic expressions and equations

• Exam (12 questions)

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

Missing: Application with bacteria, turning points, difficult chain rule

• Integration
Draft
Exam (13 questions)

Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.

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Find $\displaystyle \int x(a x ^ 2 + b)^{m}\;dx$

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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.

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Find $\displaystyle \int x\sin(cx+d)\;dx,\;\;\int x\cos(cx+d)\;dx$ and hence $\displaystyle \int ax\sin(cx+d)+bx\cos(cx+d)\;dx$

• Max & Mins
Draft
Question

Finding the stationary points of a cubic with two turning points

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This exercise will help you solve equations of type ax-b = c.

• Exam (4 questions)

Refresher questions on topics in algebra that students beginning a maths undergraduate course should be familiar with.

• Question

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 $q(x)=0$.

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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)
If you find manipulating fractions tricky, then work through this problem set to get more familiar with them.