Find upper and lower bounds on the number of codewords in three maximal codes given their codeword lengths and minimum distances.

Uses Hamming, Singleton and Gilbert-Varshamov bounds.

Given a 3x3 matrix with very big elements, perform row operations to find a matrix with single-digit elements. Then reduce that to an upper triangular matrix, and hence find the determinant.

Given constant demand for a product, with a single break point on the price, calculate the economic order quantity, and the minimum cost per year.

Express $\displaystyle b+  \frac{dx+p}{x + q}$ as an algebraic single fraction. 

Express $\displaystyle \frac{ax+b}{x + c} \pm  \frac{dx+p}{x + q}$ as an algebraic single fraction over a common denominator. 

Express $\displaystyle \frac{ax+b}{cx + d} \pm  \frac{rx+s}{px + q}$ as an algebraic single fraction over a common denominator. 

Poles, residues, and contour integral of a complex-valued function.  Single, simple pole.

Modulus and argument of a single complex number, where $\mathrm{Re}(z)=\mathrm{Im}(z)$.

Express $\displaystyle \frac{a}{(x+r)(px + b)} + \frac{c}{(x+r)(qx + d)}$ as an algebraic single fraction over a common denominator. The question asks for a solution which has denominator $(x+r)(px+b)(qx+d)$.

Find $\displaystyle \frac{a} {b + \frac{c}{d}}$ as a single fraction in the form $\displaystyle \frac{p}{q}$ for integers $p$ and $q$.

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.

Finding unknown sides/angles in right-angled triangles.  6 different combinations of unknowns are included in this single question. Makes my previous questions redundant

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Questions to test if the student knows the inverse of an odd power (and how to solve equations that contain a single power that is odd). 

Two particles connected by a string which passes over a pulley at the top of an inclined plane. Find the acceleration of the masses and the tension in the string. Can not model the whole system as a single particle.

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Questions to test if the student knows the inverse of an even power (and how to solve equations that contain a single power that is even). 

Questions to test if the student knows the inverse of fractional power or root (and how to solve equations that contain them). 

Questions to test if the student knows the inverse of an odd power (and how to solve equations that contain a single power that is odd). 

Inequality involving a single absolute value, question solution uses the piecewise nature of the absolute value function.

Testing whether students know how to use multiple log laws.

Replace two parallel forces with an equivalent single force

This question is made up of 10 exercises to practice the multiplication of brackets by a single term.

This question is made up of 10 exercises to practice the multiplication of brackets by a single term.

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.