Calculating gradients

Calculating gradients

This question assesses the students ability to find the expected number of times an event occurs given the probability of the event occurring for a single trial and the total number of trials.

Algebra word problems using area and perimeter.

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Calculating wages using algebraic equations

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A small sequence of questions on calculating percentage increases and decreases. Moving from percentages of 100, to percentages of some random whole number, and onto calculating percentage changes in applied financial situations.

Calculating the volumes of different containers

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(Calculating estimate and actual value of temperature using given formulas, and hence finding the percentage error)

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Application of the binomial distribution given probabilities of success of an event.

Finding probabilities using the binomial distribution.

Application of the binomial distribution given probabilities of success of an event.

Finding probabilities using the binomial distribution.

Calculating particular harmonic components of a Fourier series expansion.

Calculating particular harmonic components of a Fourier series expansion.

Spearman rank correlation calculated. 8 paired observations.

Calculating rates and scaling rates. Drops per mL and drops per minute questions equivalent rate to unit rate.

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Students are given six graphs, corresponding to curves $\gamma(t)$. They must match each with its signed curvature function, $\kappa(t)$.

The graphs are generated by calculating $\theta(t)=\int \kappa(t) \mathrm{d}t$ (by hand: these are given to the question as functions of a variable '#', in string form), and solving $x^{\prime}=\cos(\theta(t)-\theta(0))$ and $y^{\prime}(t)=\sin(\theta(t)-\theta(0))$ numerically (using the RKF method) with a JavaScript extension.

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 integration by parts.

This question assesses the students ability to find the expected number of times an event occurs given the probability of the event occurring for a single trial and the total number of trials.

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.

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.

Calculate a rate of pay (in pounds per week) given the total pay over a given period of time.

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.

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.

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.

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.