Activities
P.o.t.W. #15
■ No GDC ■ for SL and HL students Show that the area, \(A, of a regular polygon with \(n sides that is inscribed within a circle of radius \(r is given by the formula \(A = \frac{{n{r^2}}}{2}\sin \left(...
Activities
P.o.t.W. #14
■ No GDC ■ for HL students An empty well is situated at the center of a village. Initially, at time \(t = 0 minutes, the well contains no coins. At \(t = 1 minute, a single coin is dropped into the...
Activities
P.o.t.W. #13
■ GDC is allowed ■ for SL and HL students The three sides of a triangle have lengths of 3 cm, 7 cm and \(x cm. Find all possible values of \(x such that the degree measures of the three angles of...
Activities
P.o.t.W. #12
■ No GDC ■ for SL and HL students (a) Consider a unit square (each side is one unit) such that points A and B are two of the vertices of the square. Point C is a randomly chosen point in the interior...
Activities
P.o.t.W. #11
■ No GDC ■ for SL and HL students The first, fourth and eighth terms of an arithmetic sequence are also three consecutive terms of a geometric sequence. If the eight terms of the arithmetic sequence...
Activities
P.o.t.W. #10
■ No GDC ■ for SL and HL students Consider an isosceles triangle with the characteristics shown in the figure below where the angle marked \(\theta is between the two equal sides of length \(x, and...
Activities
P.o.t.W. #9
■ No GDC ■ for SL and HL students Consider a parabola with equation \(y = a{x^2} such that \(a > 0. Such a parabola is intersected by a line at two distinct points having coordinates \(\left( {b,a{b^2}}...
Activities
P.o.t.W. #8
■ No GDC ■ for HL students The diagram shows a circle with centre C and radius 1 unit that is tangent to the graph of \(y = k\left| x \right| at two points. The shaded region is bounded by the circle...
Activities
P.o.t.W. #7
■ GDC is allowed ■ for SL and HL students (a) Given the figure below and the indicated lengths and angles, express {\theta } as a function of x and \alpha. (b) Let \alpha = 20^\circ. Use a graph...
Activities
P.o.t.W. #6
■ No GDC ■ for SL and HL students The diagram below shows two circles each with a radius of one unit. One circle is fixed with its centre at the origin \(\left( {0,\,0} \right). The other circle has...