629 results for "quadratic".
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Exam (20 questions) in Evi's workspace
A portfolio of NUMBAS questions created for first year Natural Sciences students. The questions cover the topics:
- Linear functions
- Quadratic functions
- Differentiation
- Integration
- Explonatial and logarithms
- Further differentiation
- Further Integration
- Trigonometric Functions
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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
Graph a linear or quadratic function and state its domain and range. Part of HELM Book 2.2.1.
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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 Ting-Ying's workspace
No description given
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Question in MfEP Progress Quizzes
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.
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Question in MfEP Progress Quizzes
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.
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Question in MfEP Progress Quizzes
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.
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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
Finding the stationary point (maximum) of a quadratic equation in a contextualised problem.
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Question in MASH Bath: Question Bank
Calculating the gradient of a quadratic equation at a specific point and finding the stationary point (maximum) in a contextualised problem.
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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
Estimating the proportion of sodium carbonate in a solutionat a specific timepoint and vice versa, depicted as a quadratic graph.
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Question in Skills Audits for Maths and Stats
Multiple choice - select the quadratic graph.
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Question in Skills Audits for Maths and Stats
A question to practice simplifying fractions with the use of factorisation (for binomial and quadratic expressions).
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Question in Skills Audits for Maths and Stats
Factorising a quadratic expression of the form $a^2x^2-b^2$ to $(ax+b)(ax-b)$, using the difference of two squares formula.
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Question in Skills Audits for Maths and Stats
Factorise a quadratic equation where the coefficient of the $x^2$ term is greater than 1 and then write down the roots of the equation
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Question in Skills Audits for Maths and Stats
Solving a quadratic equation via factorisation (or otherwise) with the $x^2$-term having a coefficient of 1.
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Question in Skills Audits for Maths and Stats
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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Question in Skills Audits for Maths and Stats
Solving a pair of simultaneous equations of the form $a_1x+y=c_1$ and $a_2x^2+b_2xy=c_2$ by forming a quadratic equation.
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Question in How-tos
The student is asked to give the roots of a quadratic equation. They should be able to enter the numbers in any order, and each correct number should earn a mark.
When there's only one root, the student can only fill in one of the answer fields.
This is implemented with a gap-fill with two number entry gaps. The gaps have a custom marking algorithm to allow an empty answer. The gap-fill considers the student's two answers as a set, and compares with the set of correct answers.
The marking corresponds to this table:
There is one root There are two roots Student gives one correct root 100% 50%, "The root you gave is correct, but there is another one." Student gives two correct roots impossible 100% Student gives one incorrect root 0% 0% Student gives one incorrect, one correct root 50% "One of the numbers you gave is not a root". 50% "One of the numbers you gave is not a root". Student gives two incorrect roots 0% 0% -
Question in How-tos
The student is given a quadratic formula and asked to fill in a table of values of $f(x)$ for a given range of $x$.
The table uses the spreadsheet extension.
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Question in How-tos
The student is given a quadratic formula and asked to fill in a table of values of $f(x)$ for a given range of $x$.
There is also a plot of the points, which updates when the table is filled in, or the student can move the points to fill in the table.
The table uses the spreadsheet and JSXgraph extensions.
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Question in HELM books
Calculate R = ap^2 for given positive values of a and p.
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Question in DIAGNOSYS
No description given
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Question in DIAGNOSYS
No description given
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Question in HELM books
Simplify an algebraic fraction where the numerator is a factor of the quadratic on the denominator. Posed as a yes/no question, is this fraction equivalent to this simplified form? The answer is always yes. Part of HELM Book 1.4
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Question in Radu Dragomir's workspace
Tags: algebra, equations (linear), equations (quadratic)
Last updated Sep 2019