Tag: worked math problems

Posted in Math blogs

Math Problems for K-12 with solution

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Math Problems for K-12 is my new site that contains problems with solutions, explanations and common errors students commit in solving the problem.  Sample students answers are shown with the corresponding marks. The posts are written for students but teachers, I’m sure, will also find them helpful. You can say this is the student version of Math for Teaching blog. The problems are categorized according to math area and year level. Here is a sample problem for middle school algebra. Click the image to go to the site.

And here’s another for high school mathematics. This post links equation solving and graphing functions, a key concept in algebra.

If you are a teacher and wishes to contribute a problem you have done with your class, feel free to share it here together with students’ solutions. It would be great if you can also show how you marked it together with comments. It is through assessment and marking that we communicate to students what we value. Email me at mathforteaching@gmail.com so I can invite you as author. Thank you.

Posted in Calculus

Differentiation problem in parametric context with solution

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This is hot off the press-a question taken from the recently concluded 2011 September Preliminary Examinations of a school in Singapore. It deals with applications  of differentiation in the parametric context. Extensive trigonometry is employed here together with the manipulation of surd forms. I have personally worked out everything for your (the student’s) reference.

If you want a real calculus challenge, the problem below should satisfy your appetite. Peace.

QUESTION :

The parametric equations of a curve  are

x = sin2t and y= a cos t

where is a positive constant \frac{-\pi}{2} \le t \le\frac{\pi}{2}

(i) Find the equation of the tangent to the curve at the point P  where t= \frac{\pi}{4}.

(ii) The normal to the curve at the point Q where t = \frac {\pi}{3} intersects the axis at R. Find the coordinates of R and hence show that the area enclosed by the normal at Q , the tangent P and the x-axis is

differentiation

Author

Frederick Koh is a teacher residing in Singapore who specialises in teaching the A level maths curriculum. He has accumulated more than a decade of tutoring experience and loves to share his passion for mathematics on his personal site www.whitegroupmaths.com.

Mr Koh is also the author of the post Working with summation.

I have created a GeoGebra applet to visualize Question 1 above.