490 results for "linear".

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• Question

Studnents are asked to write down equations for cost and income for a business.

They are then asked to graph the two lines.

• Question in 1202

A graph is drawn. A student is to identify the derivative of this graph from four other graphs.

• Question

Students are given equations for a line, a parabola, a hyperbola and an exponential, and their respective graphs and are asked to match them.

• exponential curve
Question

Students are shown an exponential curve and asked to identify it as either linear, parabolic, hyperbolic or exponential.

• Question

Dividing a cubic polynomial by a linear polynomial. Find quotient and remainder.

• Question

Express a sum of linear terms in $x$ and $y$ as a single linear term in $x$ and $y$.

• Question

Expand $ax(cx+d)$ and expand $(rx+s)(px)$

• Question

Expand $(ax+b)(cx+d)$.

• Question

Expand $(pw+q)(aw^2+bw+c)$.

• Question

Expand $(az^2+bz+c)(pz+q)$.

• Question

The data is fitted by linear and quadratic regression.  First, find a linear regression equation for the $n$ data points, $20 \le n \le 35$.

They then are shown that the quadratic regression is often a better fit as measured by SSE. Also users can experiment with fitting polynomials of higher degree.

• Question

Factorise $\displaystyle{ax ^ 2 + bx + c}$ into linear factors.

• Question

Abstract linear combinations. "Surreptitious" preview of bases and spanning sets, but not explicitely mentioned. There is no randomisation because it is just an abstract question. For counter-examples, any valid counter-example is accepted.

• 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".

• Question in 1202

A graph is drawn. A student is to identify the derivative of this graph from four other graphs. There are four version of this question: I: cubic, II: linear, III: quadratic, IV: sinusoisal.

• Question

Solving a system of three linear equations in 3 unknowns using Gaussian Elimination (or Gauss-Jordan algorithm) in 5 stages. Solutions are all integers. Set up so that sometimes it has infinitely many solutions (one free variable), sometimes unique solution. Scaffolded so meant for formative. The variable d determines the cases (d=1: unique solution, d-0: infinitely many solutions). The other variables are set up so that no entries become zero for some randomisations but not others.

• Question

Solve for $x$: $\displaystyle ax+b = cx+d$

• Question

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• Question

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• Question

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• Question

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.

• Linear Functions 1
Needs to be tested
Question
Rearrange to give for y = mx + c, find gradient and realise that a parallel line has the same gradient (find x_intercept)
• Functions - Intersections
Needs to be tested
Question
Finding x and y intercapts and intersections of two graphs, one linear one exponential.
• Question

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• Question

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• Given a generator matrix for a linear code, write a parity check matrix, compute the syndrome of a word, and decide if it's a codeword.

• Numbas demo: video
Question in Demos

Customised for the Numbas demo exam

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.

• Question
For using as a practice in solving system of linear equations in two variables.
• Exam (4 questions)
Questa è una verifica creata per testare la conoscenza del piano cartesiano e dei sistemi lineari.
• Question

Linear combinations of $2$ dimensional vectors.