Four sinusoidal graphs are given. Student should select the one which is sine and cosine.

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

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

Used for LANTITE preparation (Australia). NA = Number & Algebra strand. Students are given the total cost, insurance fee and daily hire charge (all randomly generated). They need to calculate the number of days hired.

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trig equation that uses cos2x=c^2-s^s

solve trig equation that requires use of s^s+c^2=1. with worked solutions.

solve trig equation involving sin2x=2sinxcosx in a given interval

Solving cosx in given interval. With random variation and worked solutions.

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Differentiate $x^m\cos(ax+b)$

Differentiate $\displaystyle \cos(e^{ax}+bx^2+c)$

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The student is given a value of $\cos(\theta)$ and has to find $\theta$.

Shows how to use subexpressions to represent randomly-chosen fractions of $\pi$ and surds, and have them displayed nicely.

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

rebelmaths

Find $\displaystyle \frac{d}{dx}\left(\frac{m\sin(ax)+n\cos(ax)}{b\sin(ax)+c\cos(ax)}\right)$. Three part question.

Used for LANTITE preparation (Australia).  SP = Statistics & Probability strand. Students are shown an unuaual chart and asked one of seven possible questions. The Advice for this question is general in nature.

This is a set of practice questions for the non-right-angle trig component of the Australian year 12 Mathematics Standard 2 course.

It asks questions about

• finding sides and angles of right angle triangles,
• finding areas of triangles,
• using the sine rule,
• using the cos rule,
• bearings, and
• radial surveys.

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This question is the one described in method 1 of the example "Apply a standard integral" in the Numbas documentation.

The student is shown a randomly chosen function to integrate. The function is one of $e^{kx}$, $x^k$, $\cos(kx)$, $\sin(kx)$, with $k$ a randomly chosen integer.

Demonstration of adaptive marking: the student must first add up the number of apples to buy, then work out how much that would cost. Adaptive marking carries an incorrect number of apples into the cost calculation.

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

Differentiate $x^m\cos(ax+b)$

Students are shown to intersecting lines in the context of comparing the costs of services from two companies. They are asked to identify the y-intercept, the gradients, the point of intersection and are asked to interpret the graphs in the context of the word problem.

A bill (for a random amount) is divided equally between a number of people.

Students evaluate the per-person cost for a random number of people.

They then complete a table showing the cost per person for various numbers of people.

Finally they are asked to identify the shape of the graph that represents this function. They are given 2 exponentials, a hyperbola and a line to choose from.