1702 results for "given".
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Question in HELM books
Find the gradient of a line through 2 given points. Part of HELM Book 2.5.2.
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Question in HELM books
Given one of ax+b, a/x, x^(1/a), a, is it a straight line. a is a randomised integer.
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Question in HELM books
Given the period of a repeating function, determine the number of repeats in a given amount of time. Part of HELM Book 2.4.
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Question in HELM books
Given a piecewise function determine whether the limit exists at two points. Part of HELM Book 2.4.1.
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Question in HELM books
Given a linear or a quadratic function and asked whether it is continuous. Part of HELM Book 2.4.
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Question in HELM books
Given parametric equations, graph the function and obtain an explicit equation. Part of HELM Book 2.2.2.
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Question in HELM books
Use parametric equations to find x for a given value of y. Part of HELM Book 2.2.2.
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Question in HELM books
Given f(x)=(x+a)/(x+b) and g(x) = 1/x, compute f(g(x)) and g(f(x)).
a and b are randomised integers.
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Question in HELM books
Given 2 randomised functions f(x) (linear) and g(x) (quadratic), find one of f(f), f(g), g(f) or g(g) at a randomised integer x-value
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Question in HELM books
Given 2 randomised functions f (linear) and g (quadratic), find one of f(f), f(g), g(f) or g(g)
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Question in MfEP Progress Quizzes
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.
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Question in MfEP Progress Quizzes
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.
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Question in MfEP Progress Quizzes
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.
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Question in MfEP Progress Quizzes
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.
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Question in MfEP Progress Quizzes
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.
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Question in Peter's workspace
Given some random finite subsets of the natural numbers, perform set operations $\cap,\;\cup$ and complement.
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Question in MfEP Progress Quizzes
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.
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Question in MfEP Progress Quizzes
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.
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Question in MfEP Progress Quizzes
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).
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Question in MfEP Progress Quizzes
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.
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Question in MfEP Progress Quizzes
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.
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Question in MfEP Progress Quizzes
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.
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Question in MfEP Progress Quizzes
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.
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Question in MASH Bath: Question Bank
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.
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Question in MASH Bath: Question Bank
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)
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Question in MASH Bath: Question Bank
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.
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Question in MASH Bath: Question Bank
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.
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Question in MASH Bath: Question Bank
The proportion of the sodium carbonate, $p$, which has dissolved by time $t$ seconds is given by the formula $ p=\frac{bt-at^2}{c}$. The aim is to calculate the proportion of sodium carbonate in a solution at a given time and vice versa.
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Question in MASH Bath: Question Bank
Interpreting line graphs depicting the melting temperature of DNA depending on the percentage of GC content. Estimating the melting temperature given a GC percentage and vice versa.
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Question in MASH Bath: Question Bank
Interpreting line graphs depicting the decrease of temperature in a mixture over time. Estimating the temperature of the mixture at a given time point and vice versa.