503 results for "fraction".

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• Exam (13 questions)

Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.

• Brøker
Draft
Question

Add, subtract, multiply and divide numerical fractions.

• Question

Add, subtract, multiply and divide algebraic fractions.

• Question

Add, subtract, multiply and divide algebraic fractions.

• Question

No description given

• Question

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• Question

Split $\displaystyle \frac{ax+b}{(cx + d)(px+q)}$ into partial fractions.

• 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.

• Mixed fractions
Doesn't work
Question in How-tos

No description given

• Question in How-tos

Lay out gapfills so the student has to enter either the numerator or denominator of a fraction.

• Question in How-tos

Some custom CSS restyles the matrix input so it looks like a fraction, with input boxes on top and bottom.

Ideally, there should be a fraction input part type, or an option for the number entry part to display a fraction input.

• Question in How-tos
Shows how to use the sqrtSquare simplification rule to display a randomly-chosen fraction involving surds on either the top or bottom.
• Question in How-tos

Display a fraction, given as a numerator and a denominator, as a mixed fraction when appropriate.

• Question in How-tos

The student's answer is a fraction of two polynomials. First check that the student's answer is a fraction, then check that the numerator is of the form $x+a$.

To find the script, look in the Scripts tab of part a.

• Question

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• Question

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• Find the angle between planes
Has some problems
Question

Find angle between plane $\Pi_1$, given by three points, and the plane $\Pi_2$ given in Cartesian form.

The calculation of $cos(\alpha)$ at the end of Advice has fractionNumbers switched on and so the result is presented as a fraction, which can be misleading. Best if calculation is followed through without using fractionNumbers.

• Question

Four questions on finding least upper bounds and greatest lower bounds of various sets.

• Question

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• Question

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• Question

Eight questions on finding least upper bounds and greatest lower bounds of various sets.

• Question

Two numbers are drawn at random without replacement from the numbers m to n.

Find the probability that both are odd given their sum is even.

• Question

Question on $\displaystyle{\lim_{n\to \infty} a^{1/n}=1}$. Find least integer $N$ s.t.  $\ \left |1-\left(\frac{1}{c}\right)^{b/n}\right| \le10^{-r},\;n \geq N$

• Question

$\displaystyle \int \frac{bx+c}{(ax+d)^n} dx=g(x)(ax+d)^{1-n}+C$  for a polynomial $g(x)$. Find $g(x)$.

• Question

Find $\displaystyle\int \frac{ax^3-ax+b}{1-x^2}\;dx$. Input constant of integration as $C$.

• Question

Find $\displaystyle \int \frac{nx^3+mx^2+nx + p}{1+x^2}\;dx$. Solution involves $\arctan$.

• Question

Find $\displaystyle \int \frac{nx^3+mx^2+px +m}{x^2+1} \;dx$

• Question

Find the polynomial $g(x)$ such that $\displaystyle \int \frac{ax+b}{(cx+d)^{n}} dx=\frac{g(x)}{(cx+d)^{n-1}}+C$.

• Question

Integrate $f(x) = ae ^ {bx} + c\sin(dx) + px^q$. Must input $C$ as the constant of integration.

• Exam (4 questions)

Find the integral of an improper fraction.