Kafr El-Sheikh Governorate Subject: Algebra and Trigonometry
Motobis Educational Zone Time: 2 hours
Math Supervision
First term examination for the first form Secondary (2013 - 2014)

Calculators are permitted :
Answer the following questions: (1) Complete:

(1) The quadratic equation in the set of the complex numbers whose roots are –2 i, 2 i is-------------------
(2) The function f: [- 4, 7]  R where f(x) = 6 – 2 x has a positive sign in the interval --------------------
) = ---- (3) If 4 sin²   3 = 0, where [0˚, 90˚], then m (∠  (4) the range of the function f(x) = 2 sin3 x is -----------

(2) Choose the correct answer from the given answer
(1) The simplest form of the imaginary number i²³= ----
(A) -1 (B) 1 (C) -i (D) i

(2) if ∠ A and ∠ B are two acute angles where sin A = cos B , then sin ( A + B ) = --------
(A) -1 (B) 1 (C) 0 (D) 90˚

(3) The length of the arc that is subtended by a central angle of measure 210˚ in a circle of diameter length 12  cm is --------- cm
(A) 14 (B) 14 (C) 7 (D) 7

(4) If one root of the equation 2 x 2 + (a – 2) x – 7 = 0 is equal to the additive inverse of the other; then the value of a = ------
(A) 2 (B) - 2 (C) 7 (D) 0
(3) (a)(1) Determine the sign of the function:
f ( x ) = – x 2+ 7 x – 10

(2) Find the solution set of the inequality in R:
x 2+ 3 x – 4  0

(b) If 180 ˚ <  < 270˚, where cos  = – 
Find the value of :
sin  cos ( –  ) + cos (–  ) sin (  - 270 )


(4)(a) If L, M are the roots of the equation x (2x – 3) = 5 Find the equation whose roots are L2 , M 2

(b) Without using Calculator Find the value of :
sin 120 ˚ cos 330 ˚ – cos 420 ˚ sin (– 30 ˚)


(5) (a) If x = 3 + 2i and y =

, then find x + y in the form of a complex number.



(b) A B is an arc in a circle
of radius 10 cm and A B = 16 cm.
Find in radian measure,
Then find the length of the arc A B