In an NBA basketball game, a player scores 44 points, 5 of which come from 5 foul shots (each shot scores 1 point). He makes more 2-point shots than 3-point shots. Of the following number, which cannot possibly be the total number of 2-point and 3-point shots made by this player?
（A）15 （B）16 （C）17 （D）18 （E）19
A diagram shows a large cube formed of eight identical small cubes (imagine as a 2*2*2 cube). The surface area of the large cube is 216 square centimetres less than the total surface areas of the eight small cubes. What is the length, in centimetres, of a side of a small cube?
（A）2 （B）3 （C）4 （D）5 （E）6
The given diagram shows the calendar for the month of November, 2011. Three numbers from the same column are chosen. Of the following number, which can be the sum of three such numbers?
（A）21 （B）37 （C）38 （D）40 （E）54
The given diagram shows how a square ABCD with side length 40 may be dissected into six pieces by three straight cuts AC, BD and EF, where E and F are the respective midpoints of AB and BC. The pieces are then rearranged to form the given shape. What is the total area, in square centimetres, of the shaded part of the given shape?
（A）200 （B）400 （C）600 （D）800 （E）1000
A greengrocer is having an apple sale. The price is $6 per kilogram. If the total purchase exceeds 3 kilograms, a 20% discount is applied to the portion over 3 kilograms. There is no discount if the total purchase does not exceed 3 kilograms. If Leith buys 8 kilograms of apples from this greengrocer, how much does he pay?
Around 550 BC, the Greek mathematician Pythagoras discovered and proved a theorem which now bears his name. To celebrate this achievement, he had 100 cows killed for a feast. Thus the result is also known as the One Hundred Cows Theorem. What is the anniversary of this result in 2011? (There is no Year 0.)
（A）2562 （B）2560 （C）2561 （D）1460 （E）1461
The temperature on the shady side of a certain planet is −253°C. The temperature on its sunny side is only −223°C. Which of the following statement is an accurate description of the relation between the temperatures on the shady side and on the sunny side?
（A）The temperature of its sunny side is 30°C higher than its shady side;
（B）The temperature of its sunny side is 30°C lower than its shady side;
（C）The temperature of its sunny side is 476°C higher than its shady side;
（D）The temperature of its sunny side is 476°C lower than its shady side;
（E）The temperature of its sunny side is the same as its shady side.
In this web - Mathulike mostly is algebraic and only few geometry. So I will post some exercises of geometry.
1. Given ABCD rectangle with AB = 2AD, call E, I in turn is the midpoint of AB and CD. Connect D to E. Draw the Dx beam perpendicular to DE, the Dx beam to the opposite ray of the CB ray at M. On the opposite side of the CE beam take the K point so that DM = EK. Let G be the intersection of DK and EM.
a) Calculate DBK angle.
b) Let F be the right-angled foot from K to BM. Prove that four points A, I, G, H are in the same line.