233 results authored by Michael Proudman - search across all users.
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Calculation of quadratic discriminants.
State nature of roots.
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Structured questions with instructions.
Use for coaching not assessment.
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Questions asking for the factoring of simple case (a=1)
These first need to be changed to standard form.
Then use factors to solve.
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Questions asking for the factoring of simple case (a=1)
Then using factors to find roots.
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Questions asking for the factoring of simple case (a=1)
These first need to be changed to standard form.
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Questions asking for the factoring of simple case (a=1)
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Simple application of "Power Rule" to differentiate polynomials.
Some co-efficients and powers are non-integer and some may be negative.
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Simple application of "Power Rule" to differentiate single term functions.
Some co-efficients and powers are non-integer and some may be negative.
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Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant
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These practice questions cover:
- resolving axial forces in a truss structure
- stress & strain in a closed thin-walled pressure vessel (an example of 2D plane stress)
- use of Mohr's circle for determining principal stresses for a 2D plane stress case
- calculation of invariants for general 3D stress case, leading to von Mises stress and principal stresses
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Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.
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A function which renders the factorisation of a number in LaTeX.
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Rearrange equations to make $x$ the subject.
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Rearrange equations to make $x$ the subject.
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Substitute a given value into a formula, and substitute an expression in terms of $x$ into a formula.
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Two questions on solving systems of simultaneous equations.
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Simple exercise in collecting terms in different powers of \(x\)
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9 questions: Expanding out expressions such $(ax+b)(cx+d)$ etc.
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As it says on the tin!
Random terms including powers of x.
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Quotient and remainder, polynomial division.
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Dividing powers of x - set out as a fraction
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Split $\displaystyle \frac{ax+b}{(cx + d)(px+q)}$ into partial fractions.
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Looking at gradients and values for x and y for straight-line graphs
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This uses an embedded Geogebra graph of a sine curve $y=a\sin (bx+c)+d$ with random coefficients set by NUMBAS.
