L L G Advanced Math and Science Pilot Class

Paris – Abu Dhabi Mathematics, Grade 10

2013 – 2014

NAME : ……………………………………………………………………

SecondTrimesterExamination- Correctversion

Time : 2 hours and 30 minutes. Calculator and dictionary allowed. All the answers have to be justified.

The exercises can be solved in any order and all the questions can be answered assuming the results

of the previous questions.

Exercise 1: (10 marks) The numbers race :

(a)What is the area of a square if its perimeter is ?(2 marks)

The perimeter is then the side is and the area is .

(b)What is the absolute value of the diﬀerence between the squares of 5 and 3 ?(2 marks)

(c)A right angled triangle has an area of 24 and one side of the right angle is 8cm. What is the length of its hypotenuse ? (2 marks)

The area is wher is the other side of the right angle. Then .

So using Pythagoras Theorem, the hypotenuse measures :. Then

(d)7 falafels cost 2.10 €, how much cost 5 falafels ?(2 marks)

One falafel costs € then for 5 we pay €.

(e)A vehicle moves at , how much is that velocity in kilometres per hour ?(2 marks)

per second gives us per hour.

(f)BONUS : After an increase of 20% a jewel costs 18 000 AED, how much was its original price ?

Let’s call the original price : then AED.

(g)BONUS : The external area of a cube is , how much is the sum of its sides ?

Each of the 6 faces of the cube has an area of . Then each side is . So the sum of the 12 sides is

(h)BONUS : The mean of the four numbers and is . What is the value of?

We have . So .

Exercise 2: (20 marks) Equations and inequations :

The two questions are independent

Solve the inequation: (10 marks)

Using a sign table, solve the inequality : (10 marks)

Exercise 3: (28 marks) Algebra and function

Let be the function deﬁned on by with graph .

1. Prove that can be written and (6 marks)

2. Choose the best expression to answer each of the following questions :

(a) Solve the equation . (4 marks)

(b) Calculate the image of 0 by . (2 marks)

We’ll solve :

The counter image of is .

(d) Calculate the image of . Give the answer in the form with ∈ (3 marks)

(e) Find the counter image(s) of by . (4 marks)

We’ll solve :

The counter mages of are and .

(f) Give the coordinates of the intersection point between and the axis. (3 marks)

We have . Then the intersection point between and the axis is .

(g) Find the coordinates of the intersection point(s) between and the axis. (2 marks)

We know that for and . Then the intersection points between and theaxis are and .

Exercise 4: (30 marks) Graphs and functions : ANSWER THIS EXERCISE ON THIS TEST SHEET

Part 1 :We consider the graph of a function below ; answer the following questions without justifying :

(a)What is the domain of . . . . ....... (3 marks)

(b)Complete :...... ...... ...... (3marks)

(c)Give all the counter images of : . . . . ....... (4 marks)

(d)Complete : The maximum of over is 3 . . . reached at . . . . . (2 marks)

(e)Draw the table of variation of the function . (4 marks)

(f)Solve graphically the equation : . ....... (3 marks)

(g)BONUS :Solve graphically the inequation : . . ..

Part 2 : Draw the graph of a function with the following properties : (11 marks)

The domain of is .
.
The 3 solutions of are ; and .
The image of is .
The counter images of areand .
The minimum of over is reached at .

NAME: ......

Exercise 5 : Applied Math (10 marks)

Answer on thisworkingsheet and giveit back withyour exam workingsheet

a)Construct, the image of by the translation with vector . What can you say about the quadrilateral ? (1 mark)

……………………………………..………………………..………………………………………………………………………………….……………..

b)Construct, the image of by the translation withvector and, the image of by the translation with vector . (1 mark)

c)Constructvector such that . (1 mark)

d)Usingonly the points on the figure, find a vectorequalto . (1 mark)

………………………………………………

e)Write in terms of the vector . (1 mark)

f)Construct point such that . (1 mark)

g)Complete, usingonly the points or the vectors of the figure : (4 marks)