$I$ 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 $I$

$I$ compact interval, $g:I\rightarrow I$, $g(x)=(x-a)(x-b)^2$. Stationary points in interval. Find local and global maxima and minima of $g$ on $I$. 

$g: \mathbb{R} \rightarrow \mathbb{R}, g(x)=\frac{ax}{x^2+b^2}$. Find stationary points and local maxima, minima. Using limits, has $g$ a global max, min? 

$I$ compact interval. $\displaystyle g: I \rightarrow I, g(x)=\frac{ax}{x^2+b^2}$. Find stationary points and local maxima, minima. Using limits, has $g$ a global max, min? 

No description given

No description given

No description given

No description given

No description given

No description given

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.

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 $x$ direction but the positive $y$. 

Find the $x$ and $y$ components of the resultant force on an object, when multiple forces are applied at different angles.

Another example of finding the $x$ and $y$ components when multiple forces are applied at different angles to a particle.

Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.

Find the mean, median and mode of a list of 10 test scores.

rebelmaths

Given the derivatives of a cubic function at a point, find the value of the function at another point.

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.

Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

rebelmaths

Find the area under a porabola.

Find the area under a curve. The step is given.

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

Use $\cos^2\theta+\sin^2\theta=1$ and/or an understanding on the unit circle definitions to determine $\cos\theta$ given $\sin\theta$ and the quadrant theta is in.

Use $\cos^2\theta+\sin^2\theta=1$ and/or an understanding on the unit circle definitions to determine $\sin\theta$ given $\cos\theta$ and the quadrant theta is in.

Given a geometric sequence, find the common ratio (negative in this question), write down the formula for the nth term and use it to calculate a given term.

Given the probability that a basketball shot misses the hoop, find the probability that it's on target - use the law of total probability.

Given the probabilities that each of four out of five friends will win a round of mini-golf, work out the probability that the fifth friend won't win, then use that to find the probability that they will win.

Given the first four terms of a quadratic sequence, write down the formula for the $n^\text{th}$ term.

Given a formula for a sequence, calculate a given term.