Maria Aneiros

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These practice questions can help you revise basic mathematical concepts needed to succeed when studying STEM programs.

Applications of Derivatives 2

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Just what the title says, I guess.

Just what the title says, I guess.

Just what the title says, I guess.

Just what the title says, I guess. I couldn't find a 0^0 that didn't converge to 1 except things like x^(1/ln(x)) as x->0, but they just need the e^ln() transformation, not L'hopital's rule!

Find the first 3 terms in the Taylor series at $x=c$ for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$.

Find the first 3 terms in the MacLaurin series for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$.

Use two points on a line graph to calculate the gradient and $y$-intercept and hence the equation of the straight line running through both points.

The answer box for the third part plots the function which allows the student to check their answer against the graph before submitting.

This particular example has a positive gradient.

Use two points on a line graph to calculate the gradient and $y$-intercept and hence the equation of the straight line running through both points.

The answer box for the third part plots the function which allows the student to check their answer against the graph before submitting.

This particular example has a negative gradient.

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Maths 1 B week 1 to week 6 content

Questions on differentiation from first principles, and continuity and differentiability.

Problem on a closed cylindrical tank having minimum surface area

Another practical application of differentiation

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Compute a table of values for a quadratic function. A JSXgraph (the graph paper) plot shows the curve going through the entered values. The student input is now disconnected from the graph so that they slide the points usually after they input the values and the answer fields are not updated.

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Given two complex numbers, find by inspection the one that is a root of a given quartic real polynomial and hence find the other roots. 

Find the determinant of a $4 \times 4$ matrix.

Find the determinant of a $3 \times 3$ matrix.

Basic rules of derivatives

Given a randomised log function select the possible ways of writing the domain of the function.

Rearranging equations to change the subject

Find the inverse of a composite function by finding the inverses of two functions and then the composite of these; and by finding the composite of two functions then finding the inverse. The question then concludes by asking students to compare their two answers and verify they're equivalent.

A few simple functions are provided of the form ax, x+b and cx+d. Values of the functions, inverses and compositions are asked for. Most are numerical but the last few questions are algebraic.

Substitute values into formulae for the area or volume of various geometric objects.