53 results authored by cormac breen - search across all users.

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Introduction to using the product rule

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A basic introduction to differentiation

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Simple Indefinite Integrals

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Use the rule $\log_a(n^b) = b\log_a(n)$ to rearrange some expressions.

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Two questions testing the application of the Cosine Rule when given two sides and an angle. In these questions, the triangle is always acute and both of the given side lengths are adjacent to the given angle.

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Two questions testing the application of the Cosine Rule when given two sides and an angle. In these questions, the triangle is always acute and both of the given side lengths are adjacent to the given angle.

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Use the rule $\log_a(n^b) = b\log_a(n)$ to rearrange some expressions.

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Use the rule $\log_a(n^b) = b\log_a(n)$ to rearrange some expressions.

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Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.

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No description given

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Dividing a cubic polynomial by a linear polynomial. Find quotient and remainder.

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No description given

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No description given

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Express $\log_a(x^{c}y^{d})$ in terms of $\log_a(x)$ and $\log_a(y)$. Find $q(x)$ such that $\frac{f}{g}\log_a(x)+\log_a(rx+s)-\log_a(x^{1/t})=\log_a(q(x))$

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Two questions testing the application of the Sine Rule when given two angles and a side. In this question the triangle is obtuse. In one question, the two given angles are both acute. In the second, one of the angles is obtuse.

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A question testing the application of the Cosine Rule when given three side lengths. In this question, the triangle is always acute. A secondary application is finding the area of a triangle.

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Two questions testing the application of the Sine Rule when given two angles and a side. In this question, the triangle is always acute.

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This question takes the student through variety of examples of quadratic inequalities by asking them for the range(s) for which $x$ meets the inequality.

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In the first three parts, rearrange linear inequalities to make $x$ the subject.

In the last four parts, correctly give the direction of the inequality sign after rearranging an inequality.

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Factorise a quadratic equation where the coefficient of the $x^2$ term is greater than 1 and then write down the roots of the equation

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Practice finding parallel and perpendicular lines to a given line.

rebelmaths

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Integration by susbtitution, no hint given

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Maximising the volume of a rectangular box

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Chain rule

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Introduction to using the product rule

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Integration by susbtitution, no hint given

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A basic introduction to differentiation

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Simple Indefinite Integrals

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Implicit differentiation.

Given $x^2+y^2+ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.

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Quotient rule