Solve a Differential equation with 3 simple linear factors

Solve equation involving exponential function

Solve equation involving exponential function.

Solve equation involving exponential function.

Solve equation involving logarithmic function.

Solve equation involving logarithmic function.

Set up and solve an equation = 1, to ensure a function is a CRV

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Solve a trigonometric equation

Solve a trigonometric equation involving a conversion to tangent by division by cosine.

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

Some quadratics are to be solved by factorising

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Find the $x$ and $y$ components of a force which is applied at an angle to a particle. Resolve using $F \cos \theta$. The force acts in the positive $x$ and positive $y$ direction.

Find the $x$ and $y$ components of a force which is applied at an angle to a particle. Resolve using $F \cos \theta$. The force is applied in the negative $x$ and negative $y$ direction.

Part (a): Given two cubic functions $g(x)$ and $h(x)$ of the form $ax^3+bx^2+cx+d$, give an expression for the function $f(x)$, where $f(x)=g(x)-2h(x)$. 

Part (b): Solve $f(x)=0$.

Given two cubic functions $g(x)$ and $h(x)$ of the form $ax^3+bx^2+cx+d$, solve the equation $g(x)=2h(x)$, giving all possible solutions for $x$. 

Using Gaussian Elimination to solve 3X3 systems of equations

Solving a system of three linear equations in 3 unknowns using Gaussian Elimination (or Gauss-Jordan algorithm) in 5 stages. Solutions are all integers. Introductory question where the numbers come out quite nice with not much dividing. Set-up is meant for formative assessment. Adapated from a question copied from Newcastle.

Solving a system of three linear equations in 3 unknowns using Gaussian Elimination (or Gauss-Jordan algorithm) in 5 stages. Solutions are all integers. Introductory question where the numbers come out quite nice with not much dividing. Set-up is meant for formative assessment. Adapated from a question copied from Newcastle.

Solve simple two step linear equations with feedback.

Solve for $x$: $\displaystyle ax+b = cx+d$

Solve for $x$: $\displaystyle \frac{s}{ax+b} = \frac{t}{cx+d}$

Solve for $x$: $\displaystyle \frac{a} {bx+c} + d= s$

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Solve for an angle which will result in equilibrium for a triangle subjected to three couples.   A trial and error solution is recommended.

Some quadratics are to be solved by factorising

Apply the quadratic formula to find the roots of a given equation. The quadratic formula is given in the steps if the student requires it.

Matrix multiplication. Has automatically generated "unresolved" matrix product to write in the solution, which is the interesting part of this implementation.

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve.