177 results for "constant".
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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 Skills Audits for Maths and Stats
Simplify (qx+a)/(rx+b) +/- (sx+c)/(tx+d)
x is a randomised variable. a,b,c,d,q,r,s,t are randomised integers. a,b,c,d run from -5 to 5, including 0. q,r,s,t run from -3 to 3, and can be 0 if the constant term is nonzero, but are mostly 1.
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Question in CHY1201 - SpectroscopyThe reduced masses are pre-calculated for this question and included in a list. It would be more elegant to program Numbas to permute atoms together to generate diatomic molecules while constraining the permutations to those which are chemically/physically reasonable, so as to allow calculation of each reduced mass directly from the atomic masses- but organising this with high computational efficiency might be a significant programing task (add to "to do" list).
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Question in HELM books
Given f(x)=1/(a-x)^2, evaluate f(x/z) where a is a randomised constant, and z is a randomised letter.
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Question in HELM books
Give f(x)=ax^2+b a simple function input (like 6x-3) and evaluate. Constants and variables, and the function input are all randomised.
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Question in How-tos
A custom marking algorithm picks out the names of the constants of integration that the student has used in their answer, and tries mapping them to every permutation of the constants used in the expected answer. The version that agrees the most with the expected answer is used for testing equivalence.
If the student uses fewer constants of integration, it still works (but they must be wrong), and if they use too many, it's still marked correct if the other variables have no impact on the result. For example, adding $+0t$ to an expression which otherwise doesn't use $t$ would have no impact.
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Question in HELM books
Simplify (qx+a)/(rx+b) +/- (sx+c)/(tx+d)
x is a randomised variable. a,b,c,d,q,r,s,t are randomised integers. a,b,c,d run from -5 to 5, including 0. q,r,s,t run from -3 to 3, and can be 0 if the constant term is nonzero, but are mostly 1.
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Question in Engineering Statics
Pulley supported by a cable, so the tension in the rope is constant. Advice is a youtube video showing how to solve the problem.
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Question in HELM books
Simplify, if possible,
(a) $\frac{2}{3}x^2 + \frac{x^2}{3}$, (b) $0.5x^2 + \frac{3}{4}x^2 - \frac{11}{2}x$, (c) $3x^3 - 11x + 3yx + 11$, and (d) $-4\alpha x^2 + \beta x^2$ where $\alpha$ and $\beta$ are constants.The numbers and letters are all randomised.
Part of HELM Book 1.3
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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 HELM books
Given either (a) ax+bx+cy+dy, or (b) ax^2+bx+c, (c) ax^2+bx^2+cx^2, where a,b,c,d are randomised constants, and x and y are randomised letters, simplify by collecting like terms (if possible).
Part of HELM Book 1.3
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Question in HELM books
Is this polynomial a quadratic, linear or constant? Part of HELM Book 1.2
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Question in HELM books
Expand (x+a)(x+b)(x+c), where x is a randomised variable, and a,b,c are randomised integers.
Note that the pattern restriction in the marking checks that there are no brackets and that the expression is simplified to at most a single x^3, x^2, x and constant term; but it will let you get away with an additional -x^2 and/or -x term. (e.g., you could write 3x as 4x -x and the marking would accept this. This was to stop the pattern matching getting too complicated.
Part of HELM Book 1.3
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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 Julie's workspace
Laplace of constants and powers of t
rebelmaths
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Question in NCL MAS2803
Find the dimensions of the gravitational constant.
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Question in Standard Maths
Students are given an exponential equation and asked to identify the y-intercept from a list of choices.
The constants in the exponential equation have been randomised.
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Question in Standard Maths
Students are given an exponential equation and asked to evaluate it at two points.
The constants in the exponential are randomised.
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Question in Clodagh's workspace
Integration by susbtitution. Use the letter C for the constant.
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Question in MASH Bath: Question Bank
Rearraning the constant acceleration equation $v^2=u^2+2as$ to make $s$ the subject.
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Question in MASH Bath: Question Bank
Rearraning the constant acceleration equation $v^2=u^2+2as$ to make $a$ the subject.
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Question in MASH Bath: Question Bank
Rearraning the constant acceleration equation $v^2=u^2+2as$ to make $u$ the subject.
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Question in MASH Bath: Question Bank
Rearraning the constant acceleration equation $s=ut+\frac{1}{2}at^2$ to make $a$ the subject.
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Question in MASH Bath: Question Bank
Rearraning the constant acceleration equation $s=ut+\frac{1}{2}at^2$ to make $u$ the subject.
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Question in MASH Bath: Question Bank
Rearraning the constant acceleration equation $v=u+at$ to make $t$ the subject.
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Question in MASH Bath: Question Bank
Rearraning the constant acceleration equation $v=u+at$ to make $a$ the subject.
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Exam (7 questions) in MASH Bath: Moodle quizzes and TS
No description given
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Question in MASH Bath: Question Bank
Given 3 vectors $\mathbf a$, $\mathbf b$ and $\mathbf c$, find the constants $p$, $q$ and $k$ such that $ p\mathbf a + q \mathbf b = \mathbf c$, where $k$ is an unknown component of $\mathbf c$ .
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Question in MASH Bath: Question Bank
Given 3 vectors $\mathbf v$, $\mathbf a$ and $\mathbf b$, find the constants $c_1$ and $c_2$ such that $\mathbf v = c_1 \mathbf a + c_2 \mathbf b$ .
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Question in MASH Bath: Question Bank
Given an equation of the form $m=m_0 e^{-kt}$ to model the mass of a radioactive material, calculate the decay constant $k$ and the time taken for the material to reach a certain percentage of its initial mass.