618 results for "linear".
-
Question in Andrew's workspace
Solving a system of three linear equations in 3 unknowns using Gaussian Elimination (or Gauss-Jordan algorithm) in 5 stages. Solutions are all integers. Introductory question where the numbers come out quite nice with not much dividing. Set-up is meant for formative assessment. Adapated from a question copied from Newcastle.
-
Exam (5 questions) in Ed's workspace
Solve simple two step linear equations with feedback.
-
Question in Ed's workspace
No description given
-
Question in XE420
Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix.
-
Question in XE420
Solve for $x$: $\displaystyle ax+b = cx+d$
-
Question in Julia Goedecke's contributions
Example of an explore mode question. Student is given a 3x3 matrix and is asked to find the characteristic polynomial and eigenvalues, and then eigenvectors for each eigenvalue. The part asking for eigenvectors can be repeated as often as the student wants, to be used for different eigenvalues.
Assessed: calculating characteristic polynomial and eigenvectors.
Feature: any correct eigenvalue will be recognised by the marking algorithm, even multiples of the obvious one(s) (which can be read off from the reduced row echelon form)
Randomisation: Not randomised, just using particular matrices. I am still working on how to randomise this for 3x3; a randomised 2x2 version exists. I have several different versions for 3x3 (not all published yet), so I could make a random choice between these in a test.
The implementation uses linear algebra functions such as "find reduced echelon form" or "find kernel of a reduced echelon form", from the extension "linalg2".
-
Question in Mobius ENG - summative test
Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix.
-
Question in Julia Goedecke's contributions
Educational calculation tool rather than "question".
This allows the student to input a linear system in augmented matrix form (max rows 5, but any number of variables). Then the student can decide to swap some rows, or multiply some rows, or add multiples of one row to other rows. The student only has to input what operation should be performed, and this is automatically applied to the system. This question has no marks and no feedback as it's just meant as a "calculator".
It has some rounding to 13 decimal places, as otherwise some fraction calculations become incorrectly displayed as a very small number instead of 0.
It would be possible to extend to more than 5 rows, one just has to put in a lot more variables and so on. I just had to choose some place to stop.
-
Question in Linear Algebra 1st year
This allows the student to input a linear system in augmented matrix form (max rows 5, but any number of variables). Then the student can decide to swap some rows, or multiply some rows, or add multiples of one row to other rows. The student only has to input what operation should be performed, and this is automatically applied to the system. This question has no marks and no feedback as it's just meant as a "calculator".
-
Question in Julia Goedecke's contributions
Example of an explore mode question. Student is given a 2x2 matrix with eigenvalues and eigenvectors, and is asked to decide if the matrix is invertible. If yes, second and third parts are offered where the student should give the eigenvalues and eigenvectors of the inverse matrix.
Assessed: remembering link between 0 eigenvalue and invertibility. Remembering link between eigenvalues and eigenvectors of matrix and its inverse.
Randomisation: a random true/false for invertibility is created, and the eigenvalues a and b are randomised (condition: two different evalues, and a=0 iff invertibility is false), and a random invertible 2x2 matrix with determinant 1 or -1 is created (via random elementary row operations) to change base from diag(a,b) to the matrix for the question. Determinant 1 or -1 ensures that we keep integer entries.
The implementation uses linear algebra functions such as "find reduced echelon form" or "find kernel of a reduced echelon form", from the extension "linalg2".
-
Question in rhaana's workspace
Based on Chapter 8, quite loosley.Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix.
-
Question in Ugur's workspace
This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve.
-
Question in SPF Math1060
Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.
-
Question in Mash's workspace
No description given
-
Exam (6 questions) in .Graphing
No description given
-
Question in .Algebra
Split $\displaystyle \frac{ax+b}{(cx + d)(px+q)}$ into partial fractions.
-
Question in .Algebra
No description given
-
Exam (5 questions) in .Graphing
Looking at gradients and values for x and y for straight-line graphs
-
Question in Assessment Exercises
Solving pair of simultaneous (linear) equations
-
Question in .Statistics
Find a regression equation.
-
Question in Ugur's workspace
This exercise will help you rearrange a linear equation to find the value of a given variable
-
Question in Ugur's workspace
This exercise will help you rearrange a linear equation to find the value of a given variable
-
Question in Ugur's workspace
Factorising basic quadratics into linear expressions
-
Question in Ugur's workspace
Factorising further basic quadratics into linear expressions
-
Question in PHYS1010
Use a piecewise linear graph of speed against time to find the distance travelled by a car.
Finally, use the total distance travelled to find the average speed.
-
Question in Demos
A 2D linear programming problem: optimise the profit from producing two different kinds of product, which both use the same limited resources.
A JSXGraph diagram illustrates the problem and can be used to find an answer.
-
Question in Marie's linear algebra workspace
Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix.
-
Exam (15 questions) in NC Math 4Plot linear functions and identify key characteristics.
-
Question in NC Math 4
No description given
-
Question in Will's workspace
No description given