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Matlab Lab 4: Differentiation, Integration, Solving Differentiation equations
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Exam (3 questions) in ENG1002 - Matlab Lab 4: Differentiation, Integration, Solving Differentiation equations by Alex Boote

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Question in ENG1002 - Matlab Lab 4: Differentiation, Integration, Solving Differentiation equations by Alex Boote

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Task B
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Question in ENG1002 - Matlab Lab 4: Differentiation, Integration, Solving Differentiation equations by Alex Boote

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Task C
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Question in ENG1002 - Matlab Lab 4: Differentiation, Integration, Solving Differentiation equations by Alex Boote

For ENG1002 - Matlab Lab 4: Differentiation, Integration, Solving Differentiation equations.
Problem solving in GCSE mathematics q 37
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Question in Demos by Christian Lawson-Perfect and 1 other

Taken from question 37 of the book Problem Solving in GCSE Mathematics by Daniel Griller.
Given bearings and lengths of two straight lines, work out the bearing and distance back to the starting point.
A Eukleides diagram shows the setup visually.
Algebra: exp and log, graphs, solving equations
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Question in All questions by Lovkush Agarwal

$f(x)= ae^{-bt}+c$ is given and plotted. A few points are plotted on the curve. $x$ -coordinates are provided for two of them and $y$ -coordinate provided for third. Student is required to determine other coordinates.
Algebra: Solving quadratics by factorising
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Question in All questions by Lovkush Agarwal

Some quadratics are to be solved by factorising
Algebra: solving a quadratic equation graphically.
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Question in All questions by Lovkush Agarwal

A quadratic equation (equivalent to $(x+a)^2-b$ ) is given and sketched. Three equations are given that can be solved using the graph. There is a chance there will only be one solution.
Algebra: Solving quadratics by completing the square
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Question in All questions by Lovkush Agarwal

A few quadratic equations are given, to be solved by completing the square. The number of solutions is randomised.
John's copy of Algebra: Solving quadratics by factorising. shorter
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Question in John's workspace by John Wick and 1 other

Some quadratics are to be solved by factorising
Quadratic simultaneous equations
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Question in Maths support by Simon Thomas

Solving 1 linear and 1 quadratic simultaneous equations
Integration: Area bounded by the graph of a cubic
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Question in All questions by Lovkush Agarwal

Question is to calculate the area bounded by a cubic and the $x$ -axis. Requires finding the roots by solving a cubic equation. Calculator question
Matrices revision
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Exam (5 questions) in Kevin's workspace by Kevin Bohan and 2 others

A collection of questions on solving equations and revising manipulation of small matrices for 2nd year students
Shaheen's copy of Andrew's copy of Matrices: Inverse Matrix Method
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Question in Shaheen's workspace by Shaheen Charlwood and 1 other

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix.
Portfolio Task 1 Q4
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Question in Ruth's workspace by Ruth Allison

Solving equations for x
Min_max_v1
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Question in Anna's workspace by Anna Strzelecka and 3 others

Calculate the local extrema of a function ${f(x) = e^{x/C1}(C2sin(x)-C3cos(x))}$
The graph of f(x) has to be identified.
The first derivative of f(x) has to be calculated.
The min max points have to be identified using the graph and/or calculated using the first derivative method. Requires solving trigonometric equation
Algebra: Solving quadratics by factorising. shorter
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Question in All questions by Lovkush Agarwal

Some quadratics are to be solved by factorising
Solve a pair of congruences
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solving a pair of congruences of the form $\begin{align}x &\equiv b_1\;\textrm{mod} \;n_1\\x &\equiv b_2\;\textrm{mod}\;n_2 \end{align}$ where $n_1,\;n_2$ are coprime.
Solve a pair of congruences
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solving two simultaneous congruences:

$\begin{eqnarray*} c_1x\;&\equiv&\;b_1\;&\mod&\;n_1\\ c_2x\;&\equiv&\;b_2\;&\mod&\;n_2\\ \end{eqnarray*}$ where $\operatorname{gcd}(c_1,n_1)=1,\;\operatorname{gcd}(c_2,n_2)=1,\;\operatorname{gcd}(n_1,n_2)=1$
Solve congruence in given range
Has some problems
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solving an equation of the form $ax \equiv\;b\;\textrm{mod}\;n$ where $\operatorname{gcd}(a,n)|r$ . In this case we can find all solutions. The user is asked for the two greatest.
Solve three congruences using Chinese Remainder Theorem
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solving three simultaneous congruences using the Chinese Remainder Theorem:

$\begin{eqnarray*} x\;&\equiv&\;b_1\;&\mod&\;n_1\\ x\;&\equiv&\;b_2\;&\mod&\;n_2\\x\;&\equiv&\;b_3\;&\mod&\;n_3 \end{eqnarray*}$ where $\operatorname{gcd}(n_1,n_2,n_3)=1$
Solve three congruences with the Chinese Remainder Theorem
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solving three simultaneous congruences using the Chinese Remainder Theorem:

$\begin{eqnarray*} x\;&\equiv&\;b_1\;&\mod&\;n_1\\ x\;&\equiv&\;b_2\;&\mod&\;n_2\\x\;&\equiv&\;b_3\;&\mod&\;n_3 \end{eqnarray*}$ where $\operatorname{gcd}(n_1,n_2,n_3)=1$
Methods for solving differential equations
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Exam (9 questions) in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Questions used in a university course titled "Methods for solving differential equations"
Solve a pair of simultaneous equations
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solve for $x$ and $y$ : $\begin{eqnarray} a_1x+b_1y&=&c_1\\ a_2x+b_2y&=&c_2 \end{eqnarray}$

The included video describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.
Solving equations
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solve $\displaystyle ax + b = cx + d$ for $x$ .
Solving equations
Has some problems
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solve for $x$ : $\displaystyle ax ^ 2 + bx + c=0$ .
Solving equations
Has some problems
Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solve for $x$ : $\displaystyle \frac{a} {bx+c} + d= s$
Solving equations
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solve for $x$ and $y$ : $\begin{eqnarray} a_1x+b_1y&=&c_1\\ a_2x+b_2y&=&c_2 \end{eqnarray}$
Solve linear equations in the rationals and Z_n
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Question in Content created by Newcastle University by Newcastle University Mathematics and Statistics

Solving simple linear equations in $\mathbb{Q}$ and $\mathbb{Z}_n$ for $n= 13, \;17$ or $19$ .
Solving linear inequalities
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Question in Transition to university by Bradley Bush and 1 other

In the first three parts, rearrange linear inequalities to make $x$ the subject.

In the last four parts, correctly give the direction of the inequality sign after rearranging an inequality.

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