655 results for "part".

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• Integration revision

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

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• 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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• Factorise a quadratic

The student is asked to factorise a quadratic $x^2 + ax + b$. A custom marking script uses pattern matching to ensure that the student's answer is of the form $(x+a)(x+b)$, $(x+a)^2$, or $x(x+a)$.

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

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• Integration - Area Under a Graph 2

Three graphs are given with areas underneath them shaded. The student is asked to calculate their areas, using integration.  Q1 has a polynomial. Q2 has exponentials and fractional functions. Q3 requires solving a trig equation and integration by parts.

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• Integration by parts

Find $\displaystyle \int x\sin(cx+d)\;dx,\;\;\int x\cos(cx+d)\;dx$ and hence $\displaystyle \int ax\sin(cx+d)+bx\cos(cx+d)\;dx$

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• Fourier Series Step function.

Calculating particular harmonic components of a Fourier series expansion.

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• Mark the product of two matrices in a mathematical expression part

A mathematical expression part whose answer is the product of two matrices, $X \times Y$.

By setting the "variable value generator" option for $X$ and $Y$ to produce random matrices, we can ensure that the order of the factors in the student's answer matters: $X \times Y \neq Y \times X$.

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• Arithmetics of complex numbers III

Inverse and division of complex numbers.  Four parts.

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• Integration - By Partial Fractions

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.

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• Partial Fractions: simple linear factors

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