**math certificate**Report an error / Note?

**A 2016 math patent topic that is a blank common assignment to help students review the 2016 college patent in math.**

*All answers must be justified.*

*For each question, if the work is not completed, leave a record of the research. **a record of the research. *

*It will be taken into account in the scoring.*

**Exercise 1: ( 3 points)**

In one ski school, there are 2,346 children enrolled and 966 adults for the period March 18-25, 2015.

The instructors would like to have identical groups of adults and children.

All registrants must belong to one group and one group only.

- What is the maximum number of groups they can do? Explain.
- Calculate the number of children and adults in each group.

**Exercise 2: (4.5 points)**

For her birthday, Vanessa received an archery set.

She shoots an arrow. The trajectory of the tip of this arrow is shown below.

The curve gives the height (in meters) as a function of the horizontal distance (in meters)

covered by the arrow.

**1)** In this section, answers will be given through **graphic readings**.

**a) **From what height is the arrow shot?

**b) **At what distance from Vanessa does the arrow fall to the ground?

**c) **Determine the image of by the function *f*.

**d** ) Determine the antecedent(s) of 1 by the function *f .*

**2) **In this part, answers will be justified by **calculations: **

The curve above represents the function *f *defined by *f **(x*) = -0.^{1×2+0}.*9x *+1.

**a) **Calculate *f *(4.5).

**b) **Can the boom rise to more than 3m in height?

**Exercise 3: (3.5 points)**

The figure below is drawn freehand. It is not accurate.

Calculate the measure of the angle rounded to the nearest degree.

Are the points E, A and B aligned? Justify your answer.

** Exercise 4: (3.5 points)**

Joachim must cross a river with a group of friends.

He would like to install a rope so that people who are insecure can hold on.

He wants to know the width of the river at this point (named D) to determine if the rope he has is long enough. To do this he located a tree (named A) on the other side of the river.

He travels 20 meters along the straight bank where he is located and finds a new landmark: a rock (named R).

Then it continues for 12 meters and then moves away from the river, __at right angles__, until the rock

is aligned with the tree from its observation point (named B).

It covers 15 meters for that. He is then satisfied: he thinks that his 30 meters long rope

is long enough for him to install it between points D and A.

Using the figure, confirm your decision.

** ***The figure is not to scale.*

**Exercise 5: ( 4 points)**

Four statements are made below.

For each, indicate whether it is true or false by justifying the answer.

**Exercise 6: (2.5 points)**

Valentin invented an exercise subject. It begins as follows:

“ABC is a right triangle such that AB = 4 cm, AC = 8 cm and BC = 7 cm …”

Her classmate Nadia, who is very good at mental arithmetic, immediately interrupts her and says:

“We won’t be able to do your exercise because there is a mistake from the beginning! I don’t even need

to start making the figure.”

Explain how Nadia can be so confident.

**Exercise 7: (4 points)**

We consider these two calculation programs:

**1) a **) Show that if we apply the program A to the number 10, the result is 190.

**b) **Apply program B to the number 10.

**2) **A spreadsheet was used to calculate the results of these two programs. Below are the results obtained.

**a) **What formula was entered in cell C2 and copied down?

**b) **What conjecture can be made from this table?

**c) **Prove this conjecture.

**Exercise 8: (4 points)**

For her comfort, Elise wants to install a triangular shade sail in her garden.

The area of this one must be of 6 m² minimum.

**Which of the following three sails would be suitable?**

** ***The diagrams below are not to scale.*

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