Given a generator matrix for a linear code, write a parity check matrix, compute the syndrome of a word, and decide if it's a codeword.

Given percentages of males and females working on a project, and the percentage of the total staff who are male (or female), find the percentage of all staff working on the project.

Based on question 3 from section 3 of the maths-aid workbook on numerical reasoning.

Find the solution of a constant coefficient second order ordinary differential equation of the form $ay''+by=0$. Complex roots.

Matrix addition, multiplication. Finding inverse. Determinants. Systems of equations.

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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. 

Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.

A question testing the application of the Cosine Rule when given three side lengths. In this question, the triangle is always acute. A secondary application is finding the area of a triangle.

Curl and divergence of a vector field.  Determine whether the vector field is irrotational or solenoidal.

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.

Given  $P(A)$, $P(A\cup B)$, $P(B^c)$ find $P(A \cap B)$, $P(A^c \cap B^c)$, $P(A^c \cup B^c)$ etc..

Find $\displaystyle \int \frac{a}{(bx+c)^n}\;dx$

Download a file and scan the values into R to obtain a numeric vector of values. Then use R to explore your numeric vector in order to find the answers to these questions.

Multiplication and division of upper and lower bounds.

Question is to calculate the area bounded by a cubic and the $x$-axis. Requires finding the roots by solving a cubic equation. Calculator question

$X \sim \operatorname{Binomial}(n,p)$. Find $P(X=a)$, $P(X \leq b)$, $E[X],\;\operatorname{Var}(X)$.

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Matrix addition, multiplication. Finding inverse. Determinants. Systems of equations.

Find modulus and argument of two complex numbers.

Then use De Moivre's Theorem to find powers of the complex numbers.

Matrix addition, multiplication. Finding inverse. Determinants. Systems of equations.

rebelmaths

Matrix addition, multiplication. Finding inverse. Determinants. Systems of equations.

rebelmaths

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