Soal Latihan Matematika : Taiwan Imso - 2005 ( 2 )

1. If a, b, c and d are positive integers such that

What is the value of a + b + c + d ?

2.Alan has a stride 75 cm. If he travels by walking 5 steps forward and one step back, what is the least number of steps he needs to reach a spot 24 metres away?

3.N is a positive integer such that N and N + 97 are both perfect squares. What is the positive integer N ?

4.Five students sit for an exam which has a maximum score of 100. The average of the five scores achieved by the students in the exam was 89. What could the minimum score be gained?

5.In Figure, OX = OY =10 are radii of a circular quadrant. A semi-circle is drawn on XY as shown. T, S and C denote the resulting triangles, segment and crescent. What is the area of C ?

6.A large watermelon weighs 12 kg, with 97% of its weight being water. It is left to stand in the sun, and some of the water evaporates so that now only 90% of its weight is water. What does it now weigh?

7.What is the number of lines of symmetry in the plane of the diagram?

8.What is the value of x in the diagram?

9.When 10²⁰⁰⁵－2005 is express as a single number, what is the sum of the digits?

10.The length of the sides of a triangle PQR are PQ = 5, QR = 3 and RP = 4. The bisectors of the angles P and Q meet at the point I. What is the area of the triangle PQI?

11.A cube with edge of length 10 is painted. The cube is then divided into 1000 unit cubes. Among these small cubes, how many cubes which have one or two painted faces?