# Math test on affine functions in 3rd grade.

A math test on affine functions in ninth grade (3ème) will help you progress further. In addition, this proctored assignment on affine functions is intended for teachers but also for students who want to review a proctored assignment on affine functions in ninth grade (3ème).

## Exercise 1 (4points) ‘affine functions

A circus offers two admission prices: one for adults and one for children.

A group of three children with one adult pays 53 €.

Another group of five children with four adults pays 128 €.

a) Write a system of two equations and solve it, specifying the unknowns.

b) Give the price of an admission for a child and the price of an admission for an adult.

## Exercise 2: (4points)Consider the expression:

a ) Expand and reduce C.

b ) Factor the expression C.

c) Solve the equation: ( 3 x 5 ) ( 2 x )=0

d) Calculate C for x=

## Problem: (12 points)

An Internet service provider offers its customers 2 subscription options:

• A formula with a fixed subscription of 20 € per month plus the price of communications at the preferential rate of
• 2 € per hour.
• A formula B offering free access to the Internet but for which the price of communications is 4 € for one hour of connection.

In both cases, communications are charged in proportion to the connection time.

1. Peter goes online 7 h 30 min per month and Annie 15 h per month.

Calculate the price paid by each of the two people if they choose option A or option B. Advise each person which option is more advantageous for them.

2. We note x the connection time of a customer, expressed in hours.

We callPA the price to be paid in euros with formula A andPB the price to be paid in euros with formula B.

ExpressPA andPB as functions of x.

3. In an orthogonal reference frame, draw :

* the line (d), graphic representation of the function f : x |¾® 2x + 20

* the line (d’), graphic representation of the function g : x |¾® 4x

(we will take as units 1 cm for 1 h on the abscissa axis and 1 cm for 10 € on the ordinate axis)

a. Coralie, who had chosen formula A, paid 36 €. How long was she connected? (show the necessary lines on the previous graph)

b. Check by calculation

1. Solve the inequation: 4x 2x + 20.
What can be determined by solving this inequation in the context of the problem?

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