Activities
P.o.t.W. #35
■ GDC allowed ■ for SL and HL students There are two fair coins labelled A and B. Coin A is flipped three times and coin B is flipped four times. Find the probability that the number of times coin...
Activities
P.o.t.W. #34
■ No GDC ■ for SL and HL students Consider the function h\left( x \right) = ax + b, where a and b are real numbers. Given that h\left( {h\left( {h\left( x \right)} \right)} \right) = 8x + 21, find...
Activities
P.o.t.W. #33
■ No GDC ■ for HL students Find the exact area of the region bounded by the curve y = x\arctan x, the x-axis and the vertical line x = 1. The region is shaded in the figure below. PDF: P.o.t.W. #33...
Activities
P.o.t.W. #32
■ No GDC ■ for SL and HL students The two isosceles triangles, A and B, shown below have equal areas. Both triangles have two sides with the same length x. The angle between the two equal sides in...
Activities
P.o.t.W. #31
■ No GDC ■ for HL students Consider the following polynomial where x is a variable and a is a non-zero constant. 2a{x^2} - 4ax + a + 1 The polynomial has two roots. One root is three times the other...
Activities
P.o.t.W. #30
■ GDC allowed ■ for HL students 33 people are in a classroom. Everyone in the room shakes hands once with everyone else in a very organized manner such that the time from the start of one handshake...
Activities
P.o.t.W. #29
■ GDC allowed ■ for SL and HL students Find the exact area of the circle below. PDF: P.o.t.W. #29...
Activities
P.o.t.W. #28
■ No GDC ■ for SL and HL students The quadrilateral PQRS shown below is a trapezium where the parallel sides PQ and SR have lengths \(a and \(b respectively. The diagonal QS is shown as a dashed line...
Activities
P.o.t.W. #27
■ No GDC ■ for SL and HL students Consider the figure below containing triangle PQR and two circles – one with center at C, and the other with center at B. \(\left[ {{\textrm{AP}}} \right] is perpendicular...
Activities
P.o.t.W. #26
■ No GDC ■ for HL students (a) (i) Show that \(\displaystyle\int_0^a {{x^2}{\textrm{d}}x} = \frac{1}{3}{a^3} (ii) Find \(\displaystyle\frac{{\textrm{d}}}{{{\textrm{d}}a}}\left( {\frac{1}{3}{a^3}}...