385 results for "first".
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Question in MESH
Some students believe a decimal is larger if it is longer, some believe a decimal is larger if its first non-zero digit is larger.
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Question in How-tos
In the first part, the student must write any linear equation in three unknowns. Each distinct variable can occur more than once, and on either side of the equals sign. It doesn't check that the equation has a unique solution.
In the second part, they must write three equations in two unknowns. It doesn't check that they're independent or that the system has a solution. The marking algorithm on each of the gaps just checks that they're valid linear equations, and the marking algorithm for the whole gap-fill checks the number of unknowns.
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Question in How-tos
The student must solve a pair of simultaneous equations in $x$ and $y$.
The variables are generated backwards: first $x$ and $y$ are picked, then values for the coefficients of the equations are chosen satisfying those values.
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Question in HELM books
Choice of 2 formulae. The first is a fraction of the form y=(r+x)(1-rx). The second is of the form y=sqrt[(1-x)/(1+x) ]. Rearrange to make x the subject.
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Question in Christian's workspace
The student is asked to calculate a division by the method of long division, which they should enter in a grid.
The process is simulated and the order in which cells are filled in is recorded, so the marking feedback tries to identify the first cell that the student got wrong, or should try to fill in next.
They're asked to give the quotient as a plain number in a second part, to check that they can interpret the finished grid properly.
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Question in HELM books
Simplify an algebraic fraction where both numerator and denominator must first be factorised. Part of HELM Book 1.4
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Question in HELM books
Simplify an algebraic fraction where the numerator and denominator first need to be factorised (the common factor is an integer). Part of HELM book 1.4
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Question in Demos
In the first part, the student must write an R function to compute the first $n$ terms of the series $\frac{1}{k!}$.
In the second part, they must use that function to calculate an approximation to $e$ using a given number of terms of the series.
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Question in Demos
Given a randomly-generated list, the student must write code to return its first value.
There's an alternative to check if they get the second item, which they might do if they don't realise Python lists are zero-indexed.
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Question in Demos
In four parts, the student builds up the definition of a class representing a rectangle. First they write the constructor, then add methods to compute area and perimeter.
In the final part, they must use the methods to write a function which determines if a rectangle's area is larger than its perimeter.
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Question in Brendan's workspace
Separable equation for integration.
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Question in Brendan's workspace
Separable equation for integration.
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Question in Brendan's workspace
First order integral.
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Question in Brendan's workspace
First order integral.
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Question in Ugur's workspace
Find the first 3 terms in the MacLaurin series for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$.
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Question in Ugur's workspace
Find the first 3 terms in the Taylor series at $x=c$ for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$.
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Question in Brendan's workspace
Solving first order differentials by separation of variables.
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Exam (7 questions) in Foundation Year
First assessment in 2021/22 for Foundation Mathematics, counts 5% towards the module total.
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Question in Don's workspace
Dummy question to test random() function when first decimal place of upper limit of range is 4, and test of currency() function.
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Question in HELM books
The first task in HELM book 1.4 section 1.
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Question in DemosAn interactive experiment about probability: the student must first 'design' the experiment by deciding how many times they're going to flip a coin, and define what number of heads would make them believe the coin is biased. They must then enter the results of their coin flips, calculate the percentage of heads, and finally decide if the coin is biased, using the condition they specified in the design stage. There are optional hints at each stage.
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Question in Foundation Maths
Given a factor of a cubic polynomial, factorise it fully by first dividing by the given factor, then factorising the remaining quadratic.
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Question in Foundation Maths
Find the first 3 terms in the MacLaurin series for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$.
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Question in Emil's workspace
Derivatives from first principles, quadratic
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Question in Musa's workspace
Two quadratic graphs are sketched with some area beneath them shaded. Question is to determine the area of shaded regions using integration. The first graph's area is all above the $x$-axis. The second graph has some area above and some below the $x$-axis.
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Question in Musa's workspace
Recovering original function given some information such as derivative and value at some point.
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Question in Musa's workspace
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.
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Exam (4 questions) in George's workspace
A couple of questions. Some hard, some easy.
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Question in All questions
Two quadratic graphs are sketched with some area beneath them shaded. Question is to determine the area of shaded regions using integration. The first graph's area is all above the $x$-axis. The second graph has some area above and some below the $x$-axis.
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Exam (12 questions) in .Differential CalculusDesigned to instill a systematic method. The first 6 questions are scaffolded (step by step) followed by 2 randomly selected questions that only ask for a final answer.