General tests Algebra

Transcription

1 General tests Algebra Question () : Choose the correct answer : - If = then = a)0 b) 6 c)5 d)4 - The shape which represents Y is a function of is : - - V A B C D o - - y - - V o V o V o - -if the curve Y = log 4 (- a ) passes through (, - ) then a = a) b) c) 4 d) 8 4- From the following functions, the one to one function is : a) ( ) = + b) ( ) = c) ( ) = l l d) 4 ( ) = 5 5- If - = - then = a) b)- c) zero d) 6- If y = for all < 0 then the inverse function of y is = a) y = b) y = c) y = d) y = - 7- If is an odd function on [ -, ] then (-) + () = a) b) not defined c) - d) zero

2 8- The curve in the opposite figure is symmetric about the straight line whose equation is : a) = 0 b) y = 0 c) y=- d) = 9- The function f where () = { is symmetric about the point : a) (, 0 ) b) ( -, 0 ) c) ( 0, 0 ) d) (, - ) 0 The eponential function f where () =, ( a < ) then () < when a) R b) R + c) R - d) Z - The area included between the curves of the two functions ()=l+l g () = 0 equal. a) b) c) 4 d) 5 - If log 4= then equals. a) 4 b) c) d) - -The domain of the function () = log - is : a) < 0 b) > c)0 > > d) 0 4- If is a function where () = then the point of symmetry of the function Y (+) is : a) (,0) b) (0,) c) (-,0) d) (-,) 5- The opposite shows the function : X Y then a) b) - (4) = 5 < < y 4 c) 5 d) 7 7

3 6- The curve of the function g() = + 4 is the same curve of () = by displacement 4 units in direction.. a) b) c) d) 7- The function where () = represented by the figure: A B C D y y y y The epression is equivalent to : a) log b) log 7 c) log 8 d) log If () = then the domain of = a) [ -, ] b) ] -, [ c) [-, [ d) ] -, ] 0- If the function is an even over [ a, b ] then b equal : a) a b) -a c) a d) a

4 Question () :- - If : R R where () = -, : [ -,] R where () = then graph the function ( + ) () showing its domain then check its monotony. Question () : - Find in R the solution set of each of the following equations : a) log 4 = log 4 (-) b) l + l = l l Question (4) : - If () = a prove that the epression ( ) + ( ) has a constant value whatever the value of. - Find the domain of the function where () = log - - Draw the graph of each of each of the following functions then determine the domain, the range, monotonicity of each : a) () = b) () = l 4 + 5l, [0,4] Question (5) : - Simplify : log y + log y y. - If () = find the value of which satisfies the equation ( + ) - ( - ) = 4. Question (6) : - Write the rule of the function which represented by the straight line whose slope is and its y intercept is. - Graph the function where () = (-) ll and from the graph find its range and monotony. - Find in R the solution set of the equation l l = 4

5 Question (7) : - Graph the curve of the function : R R + where ()=, [-,4] and from the graph find approimated value of each of (-.5), 4 - Without using calculator find the value of log5 + - Find the solution set of the equation : l + l + = 0 Question (8) : A. Find the solution set for each of : ) = 9 ) B. Find in R the solution set of the equation : = 0 Question (9) : - Find the solution set of the inequality l l 7 in R - Find a, b, c which makes () = g () where () = (a + b) -, g() = + ( a + c ) + b then draw the function () and check its monotony. 5

6 " The answers " - Choose :- () D () C () A (4) A (5) D (6) B (7) D (8) B (9) C (0) B () C () B () C (4) C (5) A (6) D (7) D (8) C (9) A (0) B - [ -, ] -(a) {4} (b) { } 4-(a) Proof )], [ - {} 5- () () 4 6- f () = - + () Graph () { 7, -4 } 7- () 0,4, 50,5 () () {-} 8- (a) ) {, - } ) ], [ (b) S S = {,7} 9- () R - ], [ () A =, B = -, C = - 6

7 General tests Calculus Question () : Choose the correct answer. - lim ( ) = X A) B) C) D) - In triangle ABC, If 4 sin A = sin B = 6 sin C, then m ( C ) = A) 89 B) 9 C) 57 D) 8 - If f the function where () = { is continuous at =, then a = A) zero B) - C) D) 4- In triangle XYZ, the epression equals : A) cos X B) cos Y C) cos Z D) sin Z 5- lim = X A) B) C) D) 6- In triangle ABC, cos A = A) B) C) D) 7- ABC is a triangle in which = = then a : b : c = A) 6 : 5 : 8 B) 8 : 5 : 6 C) 7 : : 4 D) : 5 : 6 8- lim X = A) B) C) D) 7

8 9- lim = X A) 5 B) C) D) zero 0-In triangle ABC, if a = 6,m ( B ) = m ( A) = 80 then c = A) B) C) D) -lim = X A) B) () C) D) -In triangle X Y Z if : = = then the measure of biggest angle in the triangle is : A) 60 B) 75 C) 90 D) 0 - lim =. X A) 7 B) 8 C) 6 D) zero 4- In triangle A B C, = A) B) C) D) 5- If the function where () = { continuous at = 0, then a = A) B) C) D) 4 6- In triangle XYZ If = y then cos = A) B) C) D) 7- lim X a A) B) (a) n-m C) (a) n-m D) (a) n-m 8

9 8- In any triangle ABC, A) B) C) D) 9- lim = X A) B) C) 5 D) 0- The lengths of sides of a triangle are 6 cm, 0 cm and 4 cm then the measure of the greatest angle is. A) 0 B) 50 C) 5 D) 60 Question () : - Find a lim b lim - Solve the acute angled triangle ABC in which a = cm, a = 5 cm the length of the diameter of the circumcircle of triangle ABC equals 8 cm. Question () : - From the opposide graph find A) lim f() B) lim f() C) f () = X - Find the value of a which makes the function is continuous at = ( ) { Question (4) : X X 0 - If the function ( ) ={ is continuous at = -, find the value of a. X - ABC is a triangle = in which sin A = sin B = sin C. find m (< C), and if the perimeter of the triangle = 4 cm, find its surface area. - - y 4 0-9

10 Question (5) - Find : lim X 0 - Solve the triangle A B C in which a = 9 cm, b = 5 cm, m ( < C) = 06 Question (6) : - Find lim ( ) X - ABCD is a quadrilateral in which AB = 7 cm, BC = cm, CD = 8 cm, DA= cm, AC= 8 cm. Prove that bisects < BAD then find the areaof the shape ABCD. Question (7) : - If ( ) = { Discuss the eistence of lim ( ) X - ABC is a triangle in which m ( < A ) : m (< B) : m(< C) = : 4 : If a = 5cm. Find the perimeter of the triangle ABC > Question (8) : - Find a) b) - In the opposite figure, ABCD is a quadrilateral in which AB = 8cm, BC = 6cm, m(< B) = 90, DC = 5cm, m (< ACD ) = 60 Find the area of the circumcircle of triangle ADC. Question (9) : - Discuss the continuity of the function where C 6 cm B cm D A X > ( ) = at = - X - Solve the triangle ABC in which a = 5 cm, b = c = 8 cm. 0

11 Question (0) : - Find a) b) - ABC is a triangle in which m (<A) = 5, a = 8 cm, b= 6cm find m (<B) Question () : - Discuss the continuity of the function where () = at = - If the perimeter of a regular pentagon is 0 cm, find its surface area. Question () : - If the perimeter of the parallelogram ABCD is 0 cm and the ratio between the lengths of two adjacent sides is :, BD = 8 cm, find the length of. X 0 - If ( )= where ( ) = find value of a X < 0 X X <

12 The answers *Choose :- ) C ) B ) d 4) b 5) B 6) D 7) A 8) C 9) C 0)B ) d ) C ) A 4) C 5) C 6)B 7) C 8) B 9) C 0) A ) () a b) 7 ()A=48 5', B = 4 6' C = 68 ',A' = 6 cm. ) a) 0 b) c)0 () A= - 4) ) A=- ) m(<c) = 95, perimeter = cm. 5) ) ) c = 8 cm, B = 5 4 A=0 46' 6) ) 4. cm 7) ) - ) perimeter 0.9 cm 8) ) a) b) ) 5 cm 9) ) discontinuous C= 4 48' ) B= 5 6 ', A=0 45' 0) ) a) b) ) 4 0' ) ) Continuous ) 4 cm ) 4.8 cm )

13 ) Two forces of magnitudes 8 and F newton, are applied to a point and the angle between them of measures 0 0 if the magnitude of their resultant is F newton, find F [ 4 newton ] )Two forces of magnitudes 4 and F newton act at a particle and the measure of the angle between them is 5 0. If the line of action of their resultant inclines at angle of measure 45 0 to the force F, find the value of F. [ 4 N ] )Two forces of magnitudes, newton act at a particle. If the magnitude of their resultant is newton, find the measure of the angle between them. [ 0 0 ] 4) Two forces of magnitudes 8, 6 newton act at a particle. Find the measure of the angle between them, if their resultant is perpendicular to the first force. [ 0 0 ] 5)A weight of 6 newton is suspended at one end of a light string fied from its other end to a point on a vertical wall. The weight has been pulled away from the wall by a force perpendicular to the string to become in equilibrium when the string makes an angle of measure 0 0 with the wall. Find the magnitude of the force and the tension in the string. [ 8, 8 N ] 6) A body of weight 80 gm.wt is suspended by a light string whose other end is fied to the ceiling of a room. It is pulled by a horizontal force such that the string is inclined at an angle of 0 0 to the vertical in the state of equilibrium. Find the magnitudes of the horizontal force and the tension in the string. [, gm.wt]

14 7) A body of weight 90 gm. wt is placed on a smooth plane inclined at angle of measure 0 0 to the horizontal and is kept in equilibrium by a force F acting upwards along the line of the greatest slope of the plane. Find the magnitude of F and the reaction of the plane on the body. [45, 45 gm.wt] 8) A uniform smooth sphere of weight 00 gm. wt, and the length of its radius 0 cm is suspended from a point on its surface by a string of length 0 cm and its other end is fied to a point on a vertical smooth wall. Find the tension in the string and the reaction of the wall [5, 75 gm. wt] 9) A body of weight W newton is placed on a smooth plane inclined to the horizontal with an angle of measure 0 0 and the body is maintained in equilibrium under the influence of a force of magnitude 6 newton acting upwards along the line of greatest slope of the plane. Find the weight of the body and the reaction of the plane, [7, 6 N] 0) ABCD is a rectangle in which AB = 6 cm, BC = 8 cm. A point H such that BH = 6 cm. Forces of magnitudes, 0, 5, gm.wt act along,,, respectively. Find the magnitude of the resultant force, then show that its line of action passes by the point H. [ 4 gm.wt ] ) Four forces of magnitudes, 0, 5, 7N, act ot a point, the first is towards east and the measure of the angle between the first and the second is θ where cos θ = /5 and θ is positive acute angle, and, the third force lies between north and, west and perpendicular to the second force, and the fourth is towards south. Find magnitude of their resultant, and its direction. [ 4 due the east-north ] 4

15 ) Four forces of magnitudes 40, 0, 0, 50 gm. wt, act on a particle, the first is due east, the second is in the direction 0 0 west of north, the third is due west, and the fourth is in direction 60 0 south of west. Find magnitude and direction of the force which is in equilibrium with these forces. [40 gm. wt, 60 0 north of east] )ABC is an equilateral triangle, M is the point of intersection of its medians.three forces of magnitude 6, 8, 0N, act along,, respectively. Find magnitude of the resultant of these forces, and prove that it is parallel to [ N ] 4) Coplanar forces of magnitudes F,, and newton are applied at a point, such that the first force acts towards east and the measure of the angle between the first and second force is 45 0 and between the second and third force l05 0 and between the third and fourth force 0 0. If the magnitude of the resultant of the forces is equal to newton. Find the value of F and measure of the angle between the line of action of the resultant and the first force. [ Newton, 45 0 ] 5) A regular quadrilateral pyramid whose base area 700cm. and its slant height 0 cm, find its volume. [ 500 cm ] 6) A regular quadrilateral pyramid whose volume is 400 cm. and its height cm., find its lateral area. [ 60 cm.] 7) A regular quadrilateral pyramid, the side length of its base is 8 cm., and its volume is 96 cm. Find its slant height and its lateral surface area. [ 5 cm., 540 cm.] 5

16 8) find to the nearest tenth, the total area of the right circular cone in which the diameter length of its base is 0 cm. and its height is cm. [8.7 cm] 9) find the volume of the right circular cone where the circumference of its base is 44cm. and its height is 5 cm. [8.8 cm ] 0) Find the radius length of the base of a right circular cone where its total area = 66 cm. and the length of its drawer is 0 cm. [4 cm.] ) A piece of chocolate is in the shape of a right circular cone of volume 7 cm., and the circumference of its base is 6 cm. find its height. [9 cm.] 6