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• Question

Student is asked to find the distance from a given point, A, to a house, given the distance between A and another point B, and the angles at A and B. Requires use of the sine rule. Distance and angles are randomised.

• House distance
Question

Student is asked to find the distance from a given point, B, to a house, given the distance between B and another point A, and the angles at A and B. Requires use of the sine rule. Distance and angles are randomised.

• Heat flow formula
Question

Two part question, student has to rearrange the heat flow formula (stated in the question) to make T_1 or T_2 the subject (variable is chosen randomly), then find the value of this variable when values of the other variables in the formula are given. These values are randomly chosen.

Note that the advice for this question has two versions, the one displayed to the student depends on which variable is selected by the question.

• Exact value sine
Question

Question about use of trig identities, student has to use identities to find exact value of $\sin \frac{\pi}{12}$. Question is used in exam where student has to write out the solution and upload it for grading.

• Exact value cosine
Question

Question about use of trig identities, student has to use identities to find exact value of $\cos \frac{7\pi}{12}$. Question is used in exam where student has to write out the solution and upload it for grading.

• Energy use
Draft
Question

Students need to solve a quadratic equation and recognise that only the positive root has physical significance. Roots are randomised with one always negative and one positive. Equation can be factorised fairly easily or the quadratic formula can be used to find the solution. Advice gives solution by factorisation.

• Question

Simultaneous equation problem as circuit analysis to find unknown currents. Students need to solve the equations and type in the solutions for each variable. Advice is given in terms of solution by elimination.

• Electronic circuit
Question

Simultaneous equation problem as circuit analysis to find unknown voltages. Students need to solve the equations and type in the solutions for each variable. Advice is given in terms of solution by elimination.

• Diving board
Draft
Question

Student needs to solve a quadratic equation to calculate time taken for a diver to hit the water after diving from a diving board. Height of the board and initial upward velocity of the diver are randomly generated values. student needs to know that surface of the water is height 0, and only positive root of quadratic has physical meaning. Question is set to always give one positieve and one negative root.

• Question

Given some random finite subsets of the natural numbers, perform set operations $\cap,\;\cup$ and complement.

• Fault Analysis 5 Bus
Question

No description given

• Question

Question requires students to determine if the smallest angle of a triangle is smaller than a given value. Answer is Yes/No but students need to use cosine rule to find the smallest angle and to know that smallest angle is oppositeshortest side (otherwise they will need to find all angles of the triangle). Designed for a test where students upload handwritten working for each question as a check against guessing. Also designed to make it difficult for students to google or use AI to find the answer.

• Question

Question requires students to determine if the largest angle of a triangle is smaller than a given value. Answer is Yes/No but students need to use cosine rule to find the largest angle and to know that largest angle is opposite longest side (otherwise they will need to find all angles of the triangle). Designed for a test where students upload handwritten working for each question as a check against guessing. Also designed to make it difficult for students to google or use AI to find the answer.

• Question

A two part question. Students are first given the formula for the time for a ball to come to rest after being dropped on a block. Part a) asks the students to rearrange the formula to make e, the coefficient of restitution, the subject of the formula. Part b) gives students realistic values for variables in the formula and asks them to calculate the coefficient of restitution using the formula derived in part a).

• Car window 2
Question

Students are given lengths of 3 sides of a triangle (all randomised) and asked to find one of the angles in degrees. Requires use of the cosine rule.

• Car window
Question

Students are given two angles and the length of the side between them, they are asked to find the length of the side opposite angle A. Can be completed with the ine rule.

• Question

Students are asked to solve two simulatineous linear equations in an application of mixing two liquids to arrive at a given final volume and concentration. Students are expected to write up working for their solution and upload it seperately. Final volume, final concentration and concentrations of each solution are randomised.

• Bending moments
Question

Question asks student to find zeros of a quadratic equation. In this version students are expected to write up their working and submit it seperately to the Numbas question. Students are expcted to recognise that only the positive solution has physical significance.

• Ball height
Question

Question asks students to find the time taken for an object thrown vertically upward from a platform to reach the ground. Set up randomly chooses environment to be on Earth, Mars or the Moon and uses appropriate acceleration due to gravity. The initial velocity of the body and height of the platform above the ground are randomly selected. In this version students are expected to write up their working and submit it seperately to the Numbas question. Students are expcted to recognise that only the positive solution has physical significance.

• Border area
Draft
Question

This question is an application of a quadratic equation. Student is given dimensions of a rectangular area, and an area of pavers that are available. They are asked to calculate the width of a border that can be paved around the given rectangle (assuming border is the same width on all 4 sides). The equation for the area of the border is given in terms of the unknown border width. Students need to recognise that only one solution of the quadratic gives a physically possible solution.

The dimensions of the rectangle, available area of tiles and type of space are randomised. Numeric variables are constructed so that resulting quadratic equation has one positive and one negative root.

• Question

Using given information to complete the equation $c= A \cos{ \left( \frac{2 \pi}{P} \left( t-H \right) \right) }+V$ that describes the concentration, $c$, of perscribed drug in a patient's drug over time, $t$. Calculating the maximum concentration and the concentration at a specific time.

• Question

Solving a separable differential equation that describes the rate of decay of radioactive isotopes over time with a known initial condition to calculate the mass of the isotope after a given time and the time taken for the mass to reach $m$ grams.

Decay Constant - Radioactivity - Nuclear Power (nuclear-power.com)

• Question

Calculating the rate of change of the temperature during a chemical reaction using the chain rule in a function of the form $T=ate^{-t}$, and finding the maximum temperature of the reaction.

• Question

Using basic derivatives to calculate the gradient function of a hill $y=-e^{x}+b\ln{\left(x\right)+c$, and then substituting values to find the gradient at specific distance from the sea.

• Question

Knowing the half-life of Carbon-14 and the initial mass of Carbon-14 when a tree was cut (a) write an expression that describes the relationship between the remaining mass and time, (b) calculate the remaining mass after $t$ years, and (c) given the remaining mass calculate how many years ago the tree was cut down.

• Question

Knowing the doubling time of a population and the population on day $t$, calculate the initial population and the number of days required for the population to reach a threshold.

• Question

Calculating area under curves of the form $ax^2+bx$ and $ax^4+bx^3+cx^2+dx+e$ in a contextualised problem.

• Question

Finding the stationary point (maximum) of a quadratic equation in a contextualised problem.

• Question

Calculating the gradient of a quadratic equation at a specific point and finding the stationary point (maximum) in a contextualised problem.

• Question

The relationship between the frequency of an allele A, $x$, at a genetic locus in a diploid population and the fitness of a population with this frequency of allele A, $w$, is described by the function $w=ax^2+x(b-x)+c(b-x)^2$ . The aims are (a) ti simplify the algebraic expression, (b) calculate the fitness of a population with a given allele A frequency, and (c) calculate the allele A frequency when the fitness of the population is given.