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**Mathematics certificate**

**Session 2017**

**Asia Pacific**

**Exercise 1: (4 points)**

In the United States, temperature is measured in degrees Fahrenheit (°F).

In France, it is measured in degrees Celsius (in °C).

To make the conversions from one unit to another, a spreadsheet was used,

Here is a copy of the resulting screen:

1)What temperature in °F corresponds to a temperature of 20°C?

2) What temperature in °C corresponds to a temperature of 4L “F?

3) To convert the temperature from °C to °F, multiply the temperature in oC by

1.8 then add 32.

We wrote a formula in 83 and then copied it down.

What formula could have been entered in cell B3?

**Exercise 2 (5 points)**

In a class of 24 students, there are 1.6 girls.

1) Can either of the two diagrams below correctly represent the distribution of students in this class?

2) The distribution of students in this class was represented by a pie chart.

Write the calculation to determine the measure of the angle of the sector that represents

boys.

**Exercise 3 (6 points)**

Consider the figure below, which is not shown in full size.

Points A, B and E are aligned as well as points C, B and D.

1) In each of the following cases, indicate on the copy the answer that corresponds to the

length of the segment [AB] among the proposed answers. No justification is expected.

2) For one of the three cases only, justify the answer on the copy by

drafting.

**Exercise 4 (4 points)**

Margot has written the following program. It allows you to draw with three keys of the keyboard.

1) Of the following three drawings, only one cannot be made with this program.

Which one? Explain

2) Julie has modified Margot’s program (see below).

What happens to drawing 3 with the program modified by Julie?

**Exercise 5 (8 points)**

To measure precipitation, Météo France uses two types of rain gauges:

– direct reading rain gauges;

– electronic rain gauges.

The measurement of precipitation is expressed in millimeters. We give the height of water H in which fell using the formula :

where V is the volume of water falling on a surface S.

For H expressed in mm , V is expressed in and S in .

**Part I: Direct reading rain gauges.**

These rain gauges consist of a receiving cylinder and a graduated conical tank.

1) Check with the formula that when 1 mm of rain fell, it corresponds to 1 L of water falling on a surface

of 1 m².

2) A rain gauge indicates 10 mm of rain. The surface that receives rain is 0.01 m².

What is the volume of water in this rain gauge?

**Part II: Electronic rain gauges.**

During a rainy episode, the following graph was obtained using an electronic rain gauge.

1) The rainy episode started at 5:15 pm.

At what time did the rain stop?

2) We qualify the different rainy episodes as follows:

Using the information given in the graph and table above, this rain

would it be described as weak, moderate or strong?

**Exercise 6 (7 points)**

Gaspard creates patterns with white and grey mosaic tiles in the following way

following :

Gaspard forms a square with gray tiles and then borders it with white tiles.

1) How many white tiles will Gaspard use to border the gray square of pattern 4 (a square with 4 gray tiles on each side)?

2) a) justify that Gaspard can make a pattern of this type using exactly 144 gray tiles.

b) How many white tiles will he then use to edge the resulting gray square?

3) A pattern in which a square of n gray squares is bordered is called a “pattern n”,

Three students each came up with an expression to calculate the number of white tiles needed to make “pattern n” :

Expression #1-:

Expression #2:

Expression #3:

Only one of these three expressions is not appropriate. Which one?

**Exercise 7 (6 points)**

The coach of a track and field club recorded the performance of her shot putters over five throws.

Here are some of the readings he took (one pitcher is missing three performances):

The characteristics of the series of one of the pitchers are known:

1) Explain why these characteristics are not relevant to either Solenne’s or Rachida’s results.

2) The characteristics given are therefore those of Sarah. His best throw is 19.5m.

Indicate on the copy what Sarah’s three missing throws might be?

**Exercise 8 (5 points)**

The figure below represents a solid made of the assembly of four cubes:

– three cubes of edge 2 cm;

– a cube of edge 4 cm.

1) What is the volume of this solid?

2) we have drawn two views of this solid face (they are not full size).

Draw the **right-hand view** of this solid at **full size**.

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