Straightforward solving linear equations question

Using e to solve equations involving the natural log

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.

A question to practise the following skills in the context of Earth Sciences:

• graph-reading skills
• using a graph to find the equation of a line
• used adpative marking

Questions to test if the student knows the inverse of an even power (and how to solve equations that contain a single power that is even). 

Questions to test if the student knows the inverse of fractional power or root (and how to solve equations that contain them). 

Questions to test if the student knows the inverse of an odd power (and how to solve equations that contain a single power that is odd). 

Given an equation or a worded formula determine if it is a function or not

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.

Factorise a quadratic expression of the form $x^2+akx+bk^2$ for $x$, in terms of $k$. $a$ and $b$ are constants.

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

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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. 

set up x- and y axises.

set linear equations and solve the simulatenous equations.

Solving a Linear and a Non-linear system of equations

Solve a system of three simultaneous linear equations

Solve a logarithmic equation

Solve an exponential equation

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

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.

Recognising the equation of a circle.

A parabolic graph is given. The question is to determine the equation of the graph. Non-calculator. Advice is given.

Simple procedures are given and student is asked to carry them out or un-do them.

Version 1: bi and bii have the same answer. biii and biv both have two answers.

Version 2: bi and bii have different answers. biii has two answers, biv has one answer.

Version 3: bi and bii have different answer. biii has one answer, biv has two answers.

Version 4: bi and bii have the same answer. biii has one answer, biv has two answers.

Simple procedures are given and student is asked to carry them out or un-do them.

Version 1: i and ii have the same answer. iii and iv both have two answers.

Version 2: i and ii have different answers. iii has two answers,biv has one answer.

Version 3: i and ii have different answer. iii has one answer, iv has two answers.

Version 4: i and ii have the same answer. iii has one answer, iv has two answers.

Simple procedures are given and student is asked to carry them out or un-do them.

Version 1: i and ii have the same answer. iii and iv both have two answers.

Version 2: i and ii have different answers. iii has two answers,biv has one answer.

Version 3: i and ii have different answer. iii has one answer, iv has two answers.

Version 4: i and ii have the same answer. iii has one answer, iv has two answers.

Simple procedures are given and student is asked to carry them out or un-do them.

Version 1: i and ii have the same answer. iii and iv both have two answers.

Version 2: i and ii have different answers. iii has two answers,biv has one answer.

Version 3: i and ii have different answer. iii has one answer, iv has two answers.

Version 4: i and ii have the same answer. iii has one answer, iv has two answers.

Simple procedures are given and student is asked to carry them out or un-do them.

Version 1: i and ii have the same answer. iii and iv both have two answers.

Version 2: i and ii have different answers. iii has two answers,biv has one answer.

Version 3: i and ii have different answer. iii has one answer, iv has two answers.

Version 4: i and ii have the same answer. iii has one answer, iv has two answers.

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.

Three graphs are given with areas underneath them shaded. Student is asked to determine the minimum and maximum $x$-values of the regions. This will involve solving a linear equation and two trigonmetric equations.