lماذا تقرأ ليلة الامتحان

[mr.eid abass]

First the arithmetic sequence

1. A.S. its third term 8 and the sixth term is 17 find this seq. and the sum of the fist ten terms.

2. Find the A.S. in which the sum of its first and third terms= 22 and the sum of third and fourth terms= 7then find the sum of first twenty terms

3. Find the A.S. such that the sum of second and third terms=-7 and the sum of their squared =29 ,the sum of the first ten terms

4. If T2 of A.S. =129 , T5 =141 find the order of the term whose value=161 then find the sum of first twenty terms

5. Find the order of the first (-ve) term in theA.S.( 95,92,89,……….) then
find the sum of the(+ve) terms.

6. Insert 7 A. means between (5,29)then find the sum of this sequence

7. Find the terms should be taken from A.S.(9,12,15,…….)starting from the

First term for the sum = 106

8. A.S .T20= 41 , T3+ T6 – T9=1 ,find the A.S. and the terms should be taken
from A.S starting from the first term for the sum = 440

9. A.S consists of 15 terms and the middle term =23,and the sum of last three terms =123 find this seq. and the. Sum of its terms.

10. A.S it's first term = 12 , and it's last term = -26 , and the sum of it's terms = - 140 , Find the Seq.

11. The sum of third and fifth terms of an increasing A.S = 24 , and the squared of sixth term = 324 , Find the Seq , then
Find the sum of first twenty terms of it.

12. A decreasing A.S , the sum of fifth and seventh terms = 64 and the result of multiplication of them = 1008 , Find the seq.

13. A.S the sum of it's first fifteen terms = 150 , T4 , T5 and T7 in G. seq ,

Find the Seq.

14. A.S first term = 33 , T3 = 5 T8 . Find A.S , and how many terms should be taken from it to make the sum is maximum

15. Insert n. of A. mean between 3 , 21 such that the ratio between the sum of first two means to the sum of last mean is 1 : 3 then Find the seq.

16. A.S the T1+T3 = 20 , T5 + T8 = 60 , Find the seq. and the sum of first 20 terms in it.

17. A.S T3 + T5 = 24 , ( T6 )2 = 324 , Find this Seq. and the sum of first 20 terms.

18. A.S. the sum of the first three terms are 15 and the product of the first and third term is 21 find the seq.

19. G.s it's terms are positive , the A. mean of third and fifth terms = 30 , and the G. mean of them is 24 , Find the seq..

20. IfT4 =5 of G.S. and the A. mean of third and fifth term= 13prove that there are two seq. and one of them should determine the S∞..

21. G.S. its first term =2 and its last term = 256 , the sum of its terms =510. Find the G.S.

22. An infinite G.S. S∞ =96 and T1 exceeds T2 by 24 .find the G.S.

23. G.S .its fourth term=32 and its seventh term= -256 find this seq. and the sum of first five terms

24. If T2 exceeds T1 by 4 in G.S. T4 exceeds T1 by 124 find this seq. and the sum of the fist ten terms.

25. The sum of the first and second terms of G.S.= 3 and the sum of the first and the fourth terms =63 find this seq. where (r< 1)

26. Find the terms should be taken from G.S.(2,4,8,…….)starting from the first term for the sum = 510

27. Insert 5 G. means between ,

28. Insert 8 G. means between (243, )

29. If ( 1 , X , Y , ……….. ) is an A.S , and ( 1 , Y , X , …….. ) is a G.S , Find the value of X , Y where X ≠ Y ≠ 1

30. Find the A.S.in which the sum of its first and third terms= 22 and the sum of third and fourth terms= 7

31. G.seq. the sum of the first three terms is 21 and their productis 216 ,
Find this G.seq. and the sum of the first ten terms

32. G.seq. the sum of infinity terms from the first term 25 and the difference between second and first term equal oneFind this G.seq.

33. Three numbers forms a.seq. their 15 and if we add 1,1,4,the result forms g.seq.find this numbers.

34. A .seq.the sumof the first five terms= 25 and the first,second ,fifth term form a G.seq .find the A.seq.

35. G.seq.the sum of the fist for terms = 280 and the fifth term exceedsthe second term by 560 find this seq.

36. Prove that (Tn) such that Tn=5 Tn+1 is a G. seq.and find the sum of
infinity terms starting from the first term

37. Prove that (Tn) such that T2 = 5, 2 Tn+1= Tn. is a G. seq.and find the sum
of infinity terms starting from the first term

38. A.seq.T3 = 5 , Tn=19 , T2n=39Find the A.seq. Find the terms should be taken from this seq. starting from the first term for the sum = 400.

The functions

1- Draw the curve of function :

1) f(x) = x2 + 1

2) f(x) = 1 – x2

3) f(x) = ( x -1 )2

4) f(x) = 2 – ( x + 1 ) 2

5) f (x) = x2 – 4x + 6

6) f (x) = | x | 2

2- Draw the curve of function :

1) f(x) = x3 + 1

2) f (x) = ( x – 1 )3

3) f (x) = ( x – 2 ) 3 + 1

4) f (x) = 1 – ( x – 2 )3

5) f (x) = | x3 | + 2

6) f (x) = 2 – x |x2|

3- draw the curve of function :

1) f(x) =

2) f(x) =-

3) f(x) =

4) f(x) =

5) f(x) =

6) f(x) =

7) f(x) =

8) f(x) = + 3

4- Draw the curve of function :

1- f(x) = |x| + 2

2- f(x) = |x -1| + 2

3- f(x) = 2 -|x|

4- f(x) = |x|2 + 2

5- f(x) = 1 - |x+2|

6- f(x) = |x3| + 1

5- Draw the curve of function :

1) f(x) = 2x where x [ -3 , 3 ]

2) f(x) =( ) x where x [ -2 , 2 ]

3) f(x) = where x [ , ]

6- Draw the curve of function :

2 – x2 , x < 0

(1) f(x) = -3x + 2 , x > 0

, x > 0

(2) f(x) = - , x < 0

, x > -2

(3) f(x) = - , x < -2

, x < 0

(4) f(x) = x 2 , x > 0

(5) f1(x) = ,f2(x) =x2 –x – 6 ,find the domain of
f1 . f2 (x)

(6)Determine the type of function in which even or odd
F(x) = x f(x) =(x-2)2 +3

F(x) = f(x) =

Find the s.s. of the following:

(1) =7 (2) <7

>5 (4)

(6) =7 + x (7) =

(7) - 6 + 5 =0 (8) x

The exponent and logarithm

+ =150 (9) - = 18

(10) +26( )-125=0 (11) +50( )-50=0

(12) + ( )-8=0 (13) + 27)=12

(14) If f(x) = then find the value of x if
f(x) = f(x+1 ) +f(x-1) =90

15) f1(x) = , f2(x) = then find
f1(2x-1) + f2(x+1 ) =756

16) If f(x) = then find the value of x if
f(x) = f(2x+1 ) -f(2x-1) =120

17) Without using calculator find

(1) 2

(2) 3

(3)

(4)

(5)

(6)

18) Find the value of x :

1-

2-

19) If :

Prove that : x y = 6 .

20) If : , Prove that : .

21) Find the value of x :

22) Prove that :

23) Find the value of x , if :

24) Find S.S of the equation : 3 5x – 2 = 7 x + 1

3 2x – 3 = 11 1 – x

5x + 1 = 6 x – 2

25) Find S.S of the equation :

26) If : y = Prove that : y = x , from that find the
value of : .

27) Prove that = from that Prove that:
(-1 + (-1 = 1

With my best wishes

Mr. Eid Abbas

[عبدة قورة]