Calculate the Pearson correlation coefficient on paired data and comment on the significance.

Spearman rank correlation calculated. 10 paired observations.

Spearman rank correlation calculated. 8 paired observations.

Questions on Pearson and Spearman correlation coefficients.

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+(a^2+b^2)y=0,\;y(0)=1$ and $y'(0)=c$. 

Find a regression equation given 12 months data on temperature and sales of a drink. 

This question tests the students ability to factorise simple quadratic equations (where the coefficient of the x^2 term is 1) and use the factorised equation to solve the equation when it is equal to 0.

This question tests the student's knowledge of the remainder theorem and the ways in which it can be applied.

Factorise a quadratic equation where the coefficient of the $x^2$ term is greater than 1 and then write down the roots of the equation

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

A quadratic function $ax^2+bs+c$ is given. Six parabolas are sketched. Question is to select the correct parabola.  Need to consider the y-intercept, the coefficient of x^2, and the x-coordinate of the minimum/maximum point.

Given the gradient of a slope and the coefficient of friction for a mass resting on it, use the equations of motion to calculate how it moves.

Includes a GeoGebra rendering of the model.

This uses an embedded Geogebra graph of a line $y=mx+c$ with random coefficients set by NUMBAS.

Given the gradient of a slope and the coefficient of friction for a mass resting on it, use the equations of motion to calculate how it moves.

Includes a GeoGebra rendering of the model.

Given the gradient of a slope and the coefficient of friction for a mass resting on it, use the equations of motion to calculate how it moves.

Includes a GeoGebra rendering of the model.

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

This question tests the student's knowledge of the remainder theorem and the ways in which it can be applied.

Expand $(ax+b)(cx+d)$.

rebelmaths

This uses an embedded Geogebra graph of a sine curve $y=a\sin (bx+c)+d$  with random coefficients set by NUMBAS.

This uses an embedded Geogebra graph of a sine curve $y=a\sin (bx+c)+d$  with random coefficients set by NUMBAS.

Straightforward question: student must find the general solution to a second order constant coefficient ODE. Uses custom marking algorithm to check that both roots appear and that the solution is in the correct form (e.g. two arbitrary constants are present). Arbitrary constants can be any non space-separated string of characters. The algorithm also allows for the use of $e^x$ rather than $\exp(x)$.

Unit tests are also included, to check whether the algorithm accurately marks when the solution is correct; when it's correct but deviates from the 'answer'; when one or more roots is incorrect; or when the roots are correct but constants of integration have been forgotten.

Let $P_n$ denote the vector space over the reals of polynomials $p(x)$ of degree $n$  with coefficients in the real numbers.

Let the linear map $\phi: P_4 \rightarrow P_4$ be defined by:

$\phi(p(x))=ap(x) + (bx + c)p'(x) + (x ^ 2 + dx + f)p''(x)$

Using the standard basis for range and domain find the matrix given by $\phi$.

Let $P_n$ denote the vector space over the reals of polynomials $p(x)$ of degree $n$  with coefficients in the real numbers. Let the linear map $\phi: P_4 \rightarrow P_4$ be defined by: \[\phi(p(x))=p(a)+p(bx+c).\]Using the standard basis for range and domain find the matrix given by $\phi$.

No description given

A quadratic function $ax^2+bs+c$ is given. Six parabolas are sketched. Question is to select the correct parabola.  Need to consider the y-intercept, the coefficient of x^2, and the x-coordinate of the minimum/maximum point.

This uses an embedded Geogebra graph of a cubic polynomial with random coefficients set by NUMBAS.  Student has to decide what kind of map it represents and whether an inverse function exists.

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

This uses an embedded Geogebra graph of a cubic polynomial with random coefficients set by NUMBAS.  Student has to decide what kind of map it represents and whether an inverse function exists.

This uses an embedded Geogebra graph of a cubic polynomial with random coefficients set by NUMBAS.  Student has to decide what kind of map it represents and whether an inverse function exists.