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The test consists of five exercises.

NATIONAL PATENT DIPLOMA – ASIA PACIFIC

SESSION 2021

MATHEMATICS

General series

Duration of the test: 2 hours

Exercise 1 (24 points)

For each of the following six statements, write the question number and answer on the copy

chosen. There is only one correct answer per statement. Remember that all answers must be

be justified.

Exercise 2 (21 points)

The quadrilateral ABCD is a square with side length 1 cm. is noted square O.

The points A, B, E and H are aligned, as are the points A, D, G and J.

We build a sequence of squares (square 1, square 2, square 3, …) by doubling the length

of the side of the square, as shown below for the first three squares.

The figure is not full size.

1) Calculate the length AC.

2) We choose a square from this sequence of squares.

No justification is required for questions 2)a) and 2)b).

a) What is the magnification factor of the lengths to go from this square to the square

next?

b) What type of transformation is used to go from this square to the next square?

3) The statement “the length of the diagonal of square 3 is three times greater than the

Is the length of the diagonal of the 1” square correct?

4) Using a calculator, determine an approximate value for the measure of the angle

to the nearest degree.

Exercise 3 (23 points)

Here is an algorithm:

1) Justify that if we choose the starting number N equal to 18, the final result of this algorithm

is 28.

2) What is the final result if we choose 14 as the starting number N?

3) By applying this algorithm, two different starting numbers allow to obtain 32

as the final result. What are these two numbers?

4) We program the previous algorithm:

5) A prime number between 10 and 25 is chosen at random as the starting number N.

What is the probability that the algorithm will return a multiple of 4 as the final result?

Exercise 4 (16 points)

In physical education and sports (PE) class, your 24 students in a third grade class

are involved in long-distance running.

Students perform the half-Cooper test: they must travel the greatest distance

possible in six minutes. Each student then calculates his or her average speed over this race.

The result obtained is called MAV (Maximum Aerobic Speed).

I) After her warm-up, Chloe performs this half-cooper test. It runs through

1,000 meters in 6 minutes. Show that his MAV is equal to 10 km/h.

2) The teacher collected the results and obtained the following documents 1 and 2:

Say whether the following statements are true or false.

Remember that all answers must be justified.

a) **Assertion 1: **

The range of the Statistical Series of the girls’ MAVs in the class is more

than that of the Statistical Series of VMA of the boys in the class.

b) **Statement 2:** More than 25% of the students in the class have an AMV less than or equal to

11.5 km/h.

c) The teacher wants half the class to compete.

It therefore selects the twelve with the highest VMA.

**Statement 3:** Lisa is participating in the competition.

Exercise 5 (16 points)

Part 1

By placing several unit cubes, we build this solid:

Question: How many unit cubes are needed to complete this solid and

get a right block?

Part Two

A 3D game contains the seven pieces shown below.

Each piece is made of identical cubes with an edge of 1 dm.

1) Draw a top view of the part n°4 (taking 2 cm on the drawing to represent

1 dm in reality).

2) Using all seven pieces, it is possible to build a large cube without

empty space.

a) What will be the volume (in ) of this large cube?

b) What is the length of an edge (in dm) of this large cube?

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