Solve for $x$:  $\log_{a}(x+b)- \log_{a}(x+c)=d$

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).

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).

Apply and combine logarithm laws in a given equation to find the value of $x$.

Solve for $x$ each of the following equations: $n^{ax+b}=m^{cx}$ and $p^{rx^2}=q^{sx}$.

Solve for $x$: $\log(ax+b)-\log(cx+d)=s$

Solve for $x$: $\displaystyle 2\log_{a}(x+b)- \log_{a}(x+c)=d$. 

Make sure that your choice is a solution by substituting back into the equation.

Solve for $x$: $c(a^2)^x + d(a)^{x+1}=b$ (there is only one solution for this example).

Solve exponential equation of the form \[ a^{kx}=b^{kx+m}. \]

Solve exponential equation of the form \[ a^{kx}=a^{m}. \]

Try to solve some simultaneous equations using matrix inverses.

Integrate Paris Law equation to estimate life to failure.

Exercises in solving simultaneous equations with 2 variables.

Semi-worked example of solving simultaneous equations using matrices. Equation values are randomly generated. The student is walked through the steps needed to solve the equations.

This is a set of questions for students to practice identifying parabolas, hyperbolas and exponentials.

There are also a few questions asking students to draw graphs, and to evaluate the curves at specific points.

10 questions are selected from a larger pool. 

In the first question students are asked to identify the type of a graph.

In the second question students are asked to identify the type of an equation.

Then next 6 questions are basic questions about evaluating points on a curve or matching curves and equations.

The last 2 questions are applications - e.g. compound interest, displayed as an equation, a table or a graph.

Practise solving simultaneous linear equations graphically and algebraically.

No description given

Questions involving various techniques for rearranging and solving quadratic expressions and equations

Given the gradient of a slope and the coefficient of friction for a mass resting on it, use the equations of motion to calculate how it moves.

Includes a GeoGebra rendering of the model.

Solve $\displaystyle ay + b = cy + d$ for $y$.

Solve an exponential equation

Students are given a word problem and are asked to construct a line equation, evaluate it at a given point, and graph the line.

The line parameters and the given point are randomised.

Students are given a line equation in the form y=mx+b and asked to graph it.

m and b are randomised.

The question is not auto-marked, students need to "reveal answers" to see a sample graph that they can compare to their own.

Students are shown a graph and, in the context of a word problem, are asked to find the gradient and the y-intercept, to read points from the graph, and to identify the correct equation for the graph.

Students are shown to intersecting lines in the context of comparing the costs of services from two companies. They are asked to identify the y-intercept, the gradients, the point of intersection and are asked to interpret the graphs in the context of the word problem.

Students are given a word problem with the distance travelled and the time taken by a cyclist. They need to choose the correct form for the linear equation, compute the gradient, and plot the line.

The distance travelled and time taken are randomised.

Speed, distance and time are all integer values.

Students are given a line equation (where the coefficient of y is 1) and asked to rearrange it into gradient-intercept form.

Students need to substitute a value into an equation and solve it. The equation constant (gravity) and the value (time) are both randomised.

Students are given 2 equations of the form y=mx+b and asked to solve them using either the substitution or the elimination method. The lines are randomised but the solution coordinates are always integers.

Students are shown to intersecting lines in the context of a gym visiting program. They are asked to identify the y-intercept, the gradients, the point of intersection and are asked to interpret the graphs in the context of the word problem.