Students enter equation and turning point

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Students enter equation and turning point

Students enter equation and turning point

This question allows you to practice identifying the coordinates of points on graphs.

A mass is hanging from a string, tethered to two points. A horizontal force applied to the mass holds it directly underneath one of the points. Given the magnitude of the force, find the tension in the string and the mass of the bag.

Functional value of a function at a point. 

Find the equation of a straight line parrarell to a given straight line passes through a given point.

Obtain the equation of a straight line that passes through 2 points.

Finding the stationary points of a cubic with two turning points

Finding the stationary points of a cubic with two turning points

Finding the stationary points of a cubic with two turning points

A question testing the application of the Sine Rule when given two sides and an angle.  In this question the triangle is obtuse and the first angle to be found is obtuse.

Give the student three points lying on a quadratic, and ask them to find the roots.

Then ask them to find the equation of the quadratic, using their roots. Error in calculating the roots is carried forward.

Finally, ask them to find the midpoint of the roots (just for fun). Error is carried forward again.

Using differentiation to find the tangent and normal to a line at a given point

Given the vector equations of two straight lines, find the coordinates of the point of intersection

$I$ compact interval. $\displaystyle g: I\rightarrow I, g(x)=\frac{x^2}{(x-c)^{a/b}}$. Are there stationary points and local maxima, minima? Has $g$ a global max, global min? 

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

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

$I$ 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, $g:I\rightarrow I,\;g(x)=ax^3+bx^2+cx+d$. Find stationary points, local and global maxima and minima of $g$ on $I$

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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.

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Statistics and probability. 2 questions. Both simple regression. First with 8 data points, second with 10. Find $a$ and $b$ such that $Y=a+bX$. Then find the residual value for one of the data points.

3 questions. Finding the stationary points of functions of 2 variables.

Partial differentiation.

3 questions. Finding the stationary points of functions of 2 variables.

Partial differentiation.

Statistics and probability. 2 questions. Both simple regression. First with 8 data points, second with 10. Find $a$ and $b$ such that $Y=a+bX$. Then find the residual value for one of the data points.