Given one point and the gradient determine the equation of the line.

Given a description in words of the costs of some items in terms of an unknown cost, write down an expression for the total cost of a selection of items. Then simplify the expression, and finally evaluate it at a given point.

The word problem is about the costs of sweets in a sweet shop.

Uses JSXGraph to generate a plot for a cubic, with given critical points, along with three other incorrect graphs with modified properties. JSXGraph code is commented.

Find the equation of a straight line which has a given slope or gradient $m$ and passes through the given point $(a,b)$.

There is a video in Show steps which goes through a similar example.

Calculate the midpoint of two points.

Identifying y=mx+b given two points

Calculate the midpoint of two points.

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Given one point and the gradient determine the equation of the line.

No description given

No description given

Given two 3 dim vectors, find vector equation of line through one vector in the direction of another. Find two such lines and their point of intersection.

Construct a line through two points in a GeoGebra worksheet. Change the line by setting the positions of the two points when the worksheet is embedded into the question.

Find the stationary point $(p,q)$ of the function: $f(x,y)=ax^2+bxy+cy^2+dx+gy$. Calculate $f(p,q)$.

Find the coordinates of the stationary point for $f: D \rightarrow \mathbb{R}$: $f(x,y) = a + be^{-(x-c)^2-(y-d)^2}$, $D$ is a disk centre $(c,d)$.

Find the stationary points of the function: $f(x,y)=a x ^ 3 + b x ^ 2 y + c y ^ 2 x + dy$ by choosing from a list of points.

Turning points of a cubic function

Turning points of a cubic function

Critical points, absolute minimum, local maximum and minimum points, increasing and decreasing, concavity

rebel

rebelmaths

Critical points, absolute minimum, local maximum and minimum points, increasing and decreasing, concavity

rebel

rebelmaths

Implicit differentiation.

Given $x^2+y^2+dxy +ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.

Also find two points on the curve where $x=0$ and find the equation of the tangent at those points.

Find a regression equation.

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.

Factorise $x^2+bx+c$ into 2 distinct linear factors and then find $\displaystyle \int \frac{a}{x^2+bx+c }\;dx$ using partial fractions or otherwise.

Find $\displaystyle\int \frac{ax+b}{(x+c)(x+d)}\;dx,\;a\neq 0,\;c \neq d $.

Factorise $x^2+cx+d$ into 2 distinct linear factors and then find $\displaystyle \int \frac{ax+b}{x^2+cx+d}\;dx,\;a \neq 0$ using partial fractions or otherwise.

Video in Show steps.

Factorise $x^2+bx+c$ into 2 distinct linear factors and then find $\displaystyle \int \frac{a}{x^2+bx+c }\;dx$ using partial fractions or otherwise.

Find $\displaystyle\int \frac{ax+b}{(x+c)(x+d)}\;dx,\;a\neq 0,\;c \neq d $.

Finding the stationary points of a rational function with specific features.

Finding the stationary points of a cubic with two turning points