Application of the Poisson distribution given expected number of events per interval.

Finding probabilities using the Poisson distribution.

rebelmaths

The student is given a connected graph and must find a minimum spanning tree.

rebelmaths

Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

rebelmaths

The dimensions of a rectangle are given in m and cm. Compute the area or perimeter.

Simple probability question. Counting number of occurrences of an event in a sample space with given size and finding the probability of the event.

rebelmaths

The student is asked to give the roots of a quadratic equation. They should be able to enter the numbers in any order, and each correct number should earn a mark.

When there's only one root, the student can only fill in one of the answer fields.

This is implemented with a gap-fill with two number entry gaps. The gaps have a custom marking algorithm to allow an empty answer. The gap-fill considers the student's two answers as a set, and compares with the set of correct answers.

The marking corresponds to this table:

The student is given a quadratic formula and asked to fill in a table of values of $f(x)$ for a given range of $x$.

There is also a plot of the points, which updates when the table is filled in, or the student can move the points to fill in the table.

The table uses the spreadsheet and JSXgraph extensions.

Student estimates, then calculates exactly and symbolically the value of $k$ for a parabola $y = k x^2$ which passes through a given point.

Given f(x)=1/(a-x)^2, evaluate f(x/z) where a is a randomised constant, and z is a randomised letter.

Given one of ax^2, ax^3, a/x (where a is a positive integer), calculate f(x+h) and f(x+h)-f(x) 

Evaluate a given, randomised, linear function at a given, randomised, value.

Given a function definition in words, evaluate the function with various variable and numeric inputs

Rearrange an equation for a variable e in k.1/(1-e) and then evaluate for e, given values for the variables.

Given the formula for a cone or a cylinder, and values for r and h, find the volume.

evaluate a function (4a)/(pi*b^2cd) given random values for a,b,c,d.

Evaluate pi / (2r+s) given values for r and s (r>0, s positive or negative)

Compute P = 3/(QR) given values for Q and R.

Calculate R = ap^2 for given positive values of a and p.

evaluate the function y=ax+b for given values of a,b and x, each of which may be positive or negative.

Given 2 or 3 fractions such as A/(2x+5), add them.

There are 5 possible versions.

Given an equation with variable x in the power on two different bases, students must solve for x. Hints are included in the question to aid the student as needed.

Given an equation where x is the base of a log term, the student must solve for x. Hints are included in the question to aid the student as needed.

Given an equation involving x as a power on e, the student must solve for x. Hints are included in the question to aid the student as needed.

Given an equation with log terms added together, the student must solve for x. Hints are included in the question to aid the student as needed.

Given an equation with log terms added together, the student must solve for x. Hints are included in the question to aid the student as needed.

Given the original formula the student enters the transformed formula

Working 26_10_16

Given the original formula the student enters the transformed formula

Student is given two points defined symbolically, and must find the equation of the line they define, then use integration to find an equation for the area under the line, bounded by the x-axis and vertical lines through the two points.   

In the first part, the student must write an R function to compute the first $n$ terms of the series $\frac{1}{k!}$.

In the second part, they must use that function to calculate an approximation to $e$ using a given number of terms of the series.