655 results for "part".

Integration revision
Questions on integration using various methods such as parts, substitution, trig identities and partial fractions.
Exam (13 questions) Draft
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Last modified 11/10/2019 22:18
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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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Last modified 10/10/2019 13:43
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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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Last modified 03/10/2019 16:00
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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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Last modified 26/09/2019 09:26
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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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Last modified 25/09/2019 11:49
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Fourier Series Step function.
Calculating particular harmonic components of a Fourier series expansion.
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Last modified 24/09/2019 15:49
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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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Last modified 24/09/2019 15:27
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Last modified 23/09/2019 23:49
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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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Last modified 19/09/2019 11:55
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Last modified 19/09/2019 11:18
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