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Shaheen's copy of Functions of two variables: Locate stationary point
Ready to use
Question in WM175_A1_24 by Shaheen Charlwood and 1 other

Find the stationary point $(p,q)$ of the function: $f(x,y)=ax^2+bxy+cy^2+dx+gy$ . Calculate $f(p,q)$ .
CF Maths January test mock paper finding stationary points
Ready to use
Question in Deactivated user's workspace by Jinhua Mathias

$I$ compact interval, $g:I\rightarrow I,\;g(x)=ax^3+bx^2+cx+d$ . Find stationary points, local and global maxima and minima of $g$ on $I$
CF Maths In class test two mock paper question 4
Ready to use
Question in Deactivated user's workspace by Jinhua Mathias

$I$ compact interval, $g:I\rightarrow I,\;g(x)=ax^3+bx^2+cx+d$ . Find stationary points, local and global maxima and minima of $g$ on $I$
Ugur's copy of Maclaurin series (three terms)
Ready to use
Question in Ugur's workspace by Ugur Efem and 1 other

Find the first 3 terms in the MacLaurin series for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$ .
Ugur's copy of Taylor series (three terms)
Ready to use
Question in Ugur's workspace by Ugur Efem and 1 other

Find the first 3 terms in the Taylor series at $x=c$ for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$ .
DIfferentiation: product rule
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

Differentiate the function $f(x)=(a + b x)^m e ^ {n x}$ using the product rule. Find $g(x)$ such that $f^{\prime}(x)= (a + b x)^{m-1} e ^ {n x}g(x)$ .
Differentiation: quotient rule
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Differentiate $f(x) = (a x + b)/ \sqrt{c x + d}$ and find $g(x)$ such that $f^{\prime}(x) = g(x)/ (2(c x + d)^{3/2})$ .
Chain rule - trig and quadratic
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 2 others

Differentiate $\displaystyle \cos(e^{ax}+bx^2+c)$
Sine and Cosine Functions
Draft
Question in DIAGNOSYS by Christian Lawson-Perfect and 3 others

No description given
Sine and Cosine
Draft
Question in DIAGNOSYS by Christian Lawson-Perfect and 3 others

No description given
Probability mass function of string of heads from weighted coin,
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

A weighted coin with given $P(H),\;P(T)$ is tossed 3 times. Let $X$ be the random variable which denotes the longest string of consecutive heads that occur during these tosses. Find the Probability Mass Function (PMF), expectation and variance of $X$ .
Calculate expectation and a probability from a frequency table, , ,
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Given a probability mass function $P(X=i)$ with outcomes $i \in \{0,1,2,\ldots 8\}$ , find the expectation $E$ and $P(X \gt E)$ .
Julie's copy of Second order differential equations 1
Draft
Question in Julie's workspace by Julie Crowley

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+(a^2+b^2)y=0,\;y(0)=1$ and $y'(0)=c$ .

rebelmaths
Julie's copy of Second order differential equations 2
Draft
Question in Julie's workspace by Julie Crowley

Method of undermined coefficients:

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+a^2y=0,\;y(0)=c$ and $y(1)=d$ . (Equal roots example). Includes an interactive plot.

rebelmaths
Chain rule - binomial
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

Differentiate $\displaystyle (ax^m+b)^{n}$ .
Solve a linear programming problem
Has some problems
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 2 others

Student is given a set of constraints for a linear program. Asked to enter the constraints as inequalities, and then to identify the optimal solution.

Problem with solving the simultaneous equations gven by the constraints - too unwieldy and not given enough marks for doing so. Best if the point of intersection is given graphically by putting the mouse over the intersection.
Graphs: Horizontal scale transformation
Ready to use
Question in Graphing and Polynomials by Ben Brawn

of a random cubic spline
Graphs: Vertical scale transformation
Ready to use
Question in Graphing and Polynomials by Ben Brawn

of a random cubic spline
Graphs: Random Single Transformation
Ready to use
Question in Graphing and Polynomials by Ben Brawn

Horizontal and vertical shifts and scales of a random cubic spline
Graphs: Vertical shift transformation
Ready to use
Question in Graphing and Polynomials by Ben Brawn

of a random cubic spline
Graphs: Three random transformations
Ready to use
Question in Graphing and Polynomials by Ben Brawn

Horizontal and vertical shifts and scales of a random cubic spline
Graphing: Four random transformations
Ready to use
Question in Graphing and Polynomials by Ben Brawn

Horizontal and vertical shifts and scales of a random cubic spline
Graphs: Two random transformations
Ready to use
Question in Graphing and Polynomials by Ben Brawn

Horizontal and vertical shifts and scales of a random cubic spline
Graphs: Horizontal shift transformation
Ready to use
Question in Graphing and Polynomials by Ben Brawn

of a random cubic spline
Chain rule - product of two functions
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

The derivative of $\displaystyle x ^ {m}(ax^2+b)^{n}$ is of the form $\displaystyle x^{m-1}(ax^2+b)^{n-1}g(x)$ . Find $g(x)$ .
Chain rule - square root of polynomial
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics and 1 other

Differentiate

$\sqrt{a x^m+b})$
Logarithms: Solving equations 5
Ready to use
Question in Bill's workspace by Bill Foster

Given $\rho(t)=\rho_0e^{kt}$ , and values for $\rho(t)$ for $t=t_1$ and a value for $\rho_0$ , find $k$ . (Two examples).
Chain rule - power of a quadratic,
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Differentiate $\displaystyle (ax^m+bx^2+c)^{n}$ .
Chain rule - log of binomial
Ready to use
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Differentiate $\displaystyle \ln((ax+b)^{m})$
Indefinite integral by substitution
Draft
Question in Bill's workspace by Bill Foster

Find $\displaystyle \int \sin(x)(a+ b\cos(x))^{m}\;dx$

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