Power rule

Power rule

An experiment is performed twice, each with $5$ outcomes

$x_i,\;y_i,\;i=1,\dots 5$ . Find mean and s.d. of their differences $y_i-x_i,\;i=1,\dots 5$.

This question provides a sample of 20 data values and requires the calculation of mean, median, and standard deviation. The data are presented as a column so they can be easily copy-pasted into a spreadsheet.

First Real Exam on Wednesday 1st March 2017

This is a set of questions designed to help you practice adding, subtracting, multiplying and dividing fractions.

All of these can be done without a calculator.

Integration by susbtitution, no hint given

Step by step solving for integration by substitution

Antiderivatives

rebel 

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Simple Indefinite Integrals

Basic indefinite integrals, Basic definite integrals, integration by substitution

Missing: Area type question, solving diff eq application

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

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No description given

This question aims to test understanding and ability to use the laws of indices.

Harder implicit differentiation requiring both chain rule and product rule.

No description given

Critical points, absolute minimum, local maximum and minimum points, increasing and decreasing, concavity

rebel

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Critical points, absolute minimum, local maximum and minimum points, increasing and decreasing, concavity

rebel

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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.

Implicit differentiation.

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

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

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Match the question with the correct formula.

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Laplace of constants and powers of t

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No description given

Two column vectors are given, with one entry unknown. Given that the vectors are perpendicular, question is to determine the unknown entry.

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Laplace transform of e^{at}

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Indices

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Practice using the log rules to add and subtract logarithms

This question provides a list of data to the student. They are asked to find the mean, median, mode and range.