334 results for "which".

Maria's copy of Roots of a quartic real polynomial
Given two complex numbers, find by inspection the one that is a root of a given quartic real polynomial and hence find the other roots.
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Last modified 10/10/2019 13:43
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Last modified 09/10/2019 15:35
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Integration  Area under a curve 1
Graphs are given with areas underneath them shaded. The student is asked to select the correct integral which calculates its area.
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Last modified 19/09/2019 12:10
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Andreas's copy of MA100 MT Week 9
This is the question for week 9 of the MA100 course at the LSE. It looks at material from chapters 17 and 18.
Description of variables for part b:
For part b we want to have four functions such that the derivative of one of them, evaluated at 0, gives 0; but for the rest we do not get 0. We also want two of the ones that do not give 0, to be such that the derivative of their sum, evaluated at 0, gives 0; but when we do this for any other sum of two of our functions, we do not get 0. Ultimately this part of the question will show that even if two functions are not in a vector space (the space of functions with derivate equal to 0 when evaluated at 0), then their sum could nonetheless be in that vector space. We want variables which statisfy:
a,b,c,d,f,g,h,j,k,l,m,n are variables satisfying
Function 1: x^2 + ax + b sin(cx)
Function 2: x^2 + dx + f sin(gx)
Function 3: x^2 + hx + j sin(kx)
Function 4: x^2 + lx + m sin(nx)
u,v,w,r are variables satifying
u=a+bc
v=d+fg
w=h+jk
r=l+mn
The derivatives of each function, evaluated at zero, are:
Function 1: u
Function 2: v
Function 3: w
Function 4: r
So we will define
u as random(5..5 except(0))
v as u
w as 0
r as random(5..5 except(0) except(u) except(u))
Then the derivative of function 3, evaluated at 0, gives 0. The other functions give nonzero.
Also, the derivative of function 1 + function 2 gives 0. The other combinations of two functions give nonzero.We now take b,c,f,g,j,k,m,n to be defined as \random(3..3 except(0)).
We then define a,d,h,l to satisfy
u=a+bc
v=d+fg
w=h+jk
r=l+mnDescription for variables of part e:
Please look at the description of each variable for part e in the variables section, first.
As described, the vectors V3_1 , V3_2 , V3_3 are linearly independent. We will simply write v1 , v2 , v3 here.
In part e we ask the student to determine which of the following sets span, are linearly independent, are both, are neither:both: v1,v2,v3
span: v1,v1+v2,v1+v2+v3, v1+v2+v3,2*v1+v2+v3
lin ind: v1+v2+v3
neither: v2+v3 , 2*v2 + 2*v3
neither:v1+v3,v12*v3,2*v1v3
neither: v1+v2,v1v2,v12*v2,2*v1v2Question Draft
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Last modified 11/09/2019 07:45
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Exam (6 questions) Ready to use
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Last modified 09/09/2019 11:29
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Aoife's copy of Intro to Numbas
5 questions which introduce the student to the Numbas system.
rebelmaths
Exam (6 questions) Draft
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Last modified 04/09/2019 16:24
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Getting Started with Numbas Quizzes
5 questions which introduce the student to the Numbas system.
rebelmaths
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Last modified 30/08/2019 15:52
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Leonardo's copy of Solve equations which include a single odd power (e.g. x^odd=blah)
Questions to test if the student knows the inverse of an odd power (and how to solve equations that contain a single power that is odd).
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Last modified 30/08/2019 13:59
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Ed's copy of Masses connected through a pulley
Two particles connected by a string which passes over a pulley at the top of an inclined plane. Find the acceleration of the masses and the tension in the string. Can not model the whole system as a single particle.
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Last modified 14/08/2019 11:28
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Resolve a force into $x$ and $y$ components
Find the $x$ and $y$ components of a force which is applied at an angle to a particle. Resolve using $F \cos \theta$. The force acts in the positive $x$ and positive $y$ direction.
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Last modified 08/08/2019 10:37
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