Algebra
SECONDARY TWO
Post-Session Classwork
THREE
Revision Sheet 1
(1) the function 𝒇(𝒙)= 𝟒𝒙𝟐 − 𝟖𝒙 + 𝟏𝟓 is symmetric around the straight line whose
equation is …….
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a) x=2
b) x=4
c) x=1
d) x=y
(2) the function 𝒇(𝒙)= 𝟗𝒙𝟐 – 𝟏𝟐𝒙 + 𝟗 it’s vertex is …….
a) (2,5)
b) (3,2)
𝟐
c) ( , 5)
d) (3,5)
𝟑
(3) If f , g are two real functions , 𝒇(𝒙) = 𝒙𝟐 – 𝟒 , 𝒈(𝒙) =✓( 𝒙 − 𝟏) , find the domain for
each
(1) (f + g) is
a) R , b) [ 1 , ∞ [ , c) R ~ {1} , d) ] - ∞ , ∞ [ .
(2) (f/g) is
a) R , b) ] 1 , ∞ [ , c) [ 1 , ∞ [ , d) R ~ {1} .
(3) (f • g) is
a) R , b) ] 1 , ∞ [ , c) [ 1 , ∞ [ , d) R ~ {1} .
𝟐𝒙 + 𝒙𝟐 , 𝒙 ≤ 𝟎
(4)
the function 𝒇(𝒙) =
a) even
b) odd
is …….
𝟐𝒙 − 𝒙𝟐 , 𝒙 > 𝟎
c) nether even nor odd
d) both (a) and (b) .
(5) which of the following is one to one function
a) 𝒇(𝒙) = (𝒙 + 𝟑)𝟐 , b) 𝒇(𝒙) =
𝟏
, c) 𝒇(𝒙) = 𝟒 – 𝟓𝒙 , d) 𝒇(𝒙) = 𝟓 .
𝒙𝟐 −𝟒
(6) the function 𝒇(𝒙) = (𝒙 − 𝟑 )𝟐 + 𝟓 is increasing on …….
a) ] - ∞ , 𝟑 ]
b) [ 3 , ∞ [
c) [ 5 , ∞ [ , d) none of the previous
(7) the function 𝒇(𝒙) = 𝒙𝟐 − 𝟓 , 𝒙 ≥ 𝟎 is decreasing when 𝒙 € ……
a) ] - ∞ , 0 ] , b) [ 0 , ∞ [ , c) [ -5 , ∞ [ , d) there is no answer .
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Algebra
SECONDARY TWO
THREE
(8) the s.s of the inequality (✓(𝒙 + 𝟐)𝟐 ) + |𝟐𝒙 + 𝟒| ≥ 𝟔 is …….
a) [ -4 , 0 ] , b) R ~ [ -4 , 0 ] , c) R ~ ] -4 , 0 [ , d) ] -4 , 0 [ .
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(9) if 𝒇(𝒙) is even function and 𝒇(𝟑) = 𝟐𝒇(−𝟏) , so 𝒇(−𝟑) = …….
a) 𝒇(𝟏) , b) 𝒇(−𝟏) , c) 𝟐𝒇(𝟑) , d) 𝟐𝒇(𝟏) .
(10) if 𝒇(𝒙) is 1-1 and odd function 𝒇(𝟑) = 𝒇(𝒂) , so 𝒇(−𝒂) = …….
a) 𝒇(𝟑) , b) 𝒇(𝒂) , c) −𝒇(𝟑) , d) no answer .
(11) 𝟓 |𝟑 − 𝒙| − 𝟐 √𝒙𝟐 − 𝟔𝒙 + 𝟗 = 𝟏𝟐 it’s s.s is …….
a) { 3 , 2 } , b) { 7 , -1 } , c) R , d) { -2 , 7 } .
(12) The s.s of 𝐥𝐨𝐠 𝟐 (𝟑𝒙 − 𝟑𝒙−𝟐 ) = 𝟑 𝒊𝒔 … … … … .
a) {2}
b) {-2}
c) both (a) & (b)
d) none of the previous
(13) The s.s of 𝐥𝐨𝐠 𝟗 𝐥𝐨𝐠 𝟑 𝐥𝐨𝐠 𝒙 𝟐𝟕 = 𝟎 𝒊𝒔 … … . .
a) {4}
b) {3}
c) {2}
d) none of the previous
(14) s.s of 𝒙𝐥𝐨𝐠 𝒙 = 𝟏𝟎𝟎𝟎𝟎 is ……..
a) 100 b) 0.01
c) both (a) & (b)
𝟑
d) none of the previous
𝟑
(15) The s.s of 𝐥𝐨𝐠 √𝟑𝒙 − 𝟏 + 𝐥𝐨𝐠 √𝒙 − 𝟐 = 𝐥𝐨𝐠 𝟐𝟎 − 𝟏 is ……..
a) {3}
b) {-3}
c) {43}
d) none of the previous
(16) 𝐥𝐨𝐠 𝒕𝒂𝒏 𝟏° × 𝐥𝐨𝐠 𝒕𝒂𝒏 𝟐° × 𝐥𝐨𝐠 𝒕𝒂𝒏 𝟑° × … … … × 𝐥𝐨𝐠 𝒕𝒂𝒏 𝟕𝟑° = ⋯ … … …
a) 1
b) 3
c) zero
d) none of the previous
(17) 𝐥𝐨𝐠 𝒕𝒂𝒏 𝟏° × 𝐥𝐨𝐠 𝒕𝒂𝒏 𝟐° × 𝐥𝐨𝐠 𝒕𝒂𝒏 𝟑° × … … … × 𝐥𝐨𝐠 𝒕𝒂𝒏 𝟖𝟗° = ⋯ … … …
a) 1
b) 3
c) zero
d) none of the previous
2
Algebra
SECONDARY TWO
(18) Which of the following arrows represent a function from X to Y?
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THREE
(19) If the function 𝒇 is even over [ a , b ] , then b = …….
a) a
b) -a
c) 2a
d) 𝒂𝟑
(20) if 𝒇 is an odd function, 𝒇(𝟏) = 𝟐, then which of the following points lies on the
curve?
a) (-1,2)
b) (-1,-2)
c) (1,-2)
d) (-1,0)
(21) If 𝒇, 𝒈 are two functions where 𝒇(𝒙) = 𝒙𝟑 , 𝒈(𝒙) = 𝒙 + 𝟐 , 𝒕𝒉𝒆𝒏 (𝒈 ∘ 𝒇)(𝒙) is …..
function
a) one-to-one
b) odd
c) even
d) linear
(22) If 𝒇(𝒙) = 𝟕 , then the range of the function is ……….
a) R
b) 𝑹+
c) {7}
d) R – {7}
0
when 𝒙 ≤ 𝟎
(23) 46) The range of the function 𝒇: 𝒇(𝒙) =
a) {1}
b) {0}
1
d) {0,1}
c) R
is ………..
when 𝒙 > 𝟏
(24) If 𝐥𝐨𝐠 𝟑 𝟓 = 𝒂 , then 𝐥𝐨𝐠 𝟏𝟓 𝟓 =…….
a- 𝒂𝟐
b- 𝟑𝒂 c-
𝟏
𝒂+𝟑
d-
𝒂
𝒂+𝟏
(25) If 𝐥𝐨𝐠 𝟏 𝒇(𝒙) = 𝒙 , then 𝟖𝒇(𝟐) + 𝒇(−𝟑) + 𝒇(𝟎) =……..
𝟐
a-
𝟏
𝟏𝟔
b-
𝟏
𝟖
c- 11 d- 22
(26) If 𝟓𝒙−𝟏 = 𝟒𝒙−𝟏 , then 𝒙 =………
a- 5
b- 1
c- -1 d- 0
3
Algebra
SECONDARY TWO
(27) Which of the functions that are defined by the following rules represents an
THREE
exponential decay function?
𝟏 −𝒙
a- 𝒇(𝒙) = 𝟐𝒙 b- 𝒇(𝒙) = ( )
𝟑
𝟐 𝒙
c- 𝒇(𝒙) = 𝟑𝒙 d-𝒇(𝒙) = ( )
𝟑
𝒂 𝒙
(28) If the function 𝒇: 𝒇(𝒙) = ( ) is an increasing
exponential function , then…….
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𝟑
a- 𝒂 > 𝟎 b- 𝒂 > 𝟏
c- 𝒂 > 𝟑 d- 𝒂 < 𝟑
(29) The curve of the function 𝒇: 𝒇(𝒙) = 𝟑𝒙+𝟏 intersects the 𝒚 − 𝒂𝒙𝒊𝒔 at the point………
a- (𝟎, 𝟏) b- (𝟏, 𝟎) c- (𝟓, 𝟏) d- (𝟏, 𝟓)
(30) The area between the curves of the functions 𝒇: 𝒇(𝒙) = |𝒙 + 𝟐| − 𝟐 = 𝟎 and
𝒈: 𝒈(𝒙) = 𝟎 equals ………. Square units.
a- 2 b- 3 c- 4 d- 5
𝟏 𝒙
(31) If the straight line 𝒚 = 𝟖 cuts the two curves 𝒚 = 𝟐𝒙 , 𝒚 = ( ) at the two points
𝟐
A,B respectively, then the length of AB = ………… length unit.
(a) 2
(b) 3
(c) 4
(d) 6
(32) If 𝒇(𝒙) =
(a)
𝟗𝒙
𝟗𝒙 +𝟑
, then 𝒇(𝒙) + 𝒇(𝟏 − 𝒙) =………………
𝟐
(b)
𝟗𝒙 +𝟑
𝟗𝒙 +𝟑
(c)
𝟐
𝟏
(d) 1
𝟑
(33) 𝑰𝒇 𝐥𝐨𝐠 𝒙 = 𝒛 + 𝐥𝐨𝐠 𝒚 , 𝒕𝒉𝒆𝒏 𝒙 = … … ….
(a) 𝒚 × 𝟏𝟎𝒛
(34)
𝟏
𝟏+𝐥𝐨𝐠 𝒃 𝒂+ 𝐥𝐨𝐠 𝒃 𝒄
(a)𝐥𝐨𝐠 𝒂 𝒃𝒄
+
(b)
𝒛
𝒚
(c) 𝒛 − (𝟏𝟎)𝒚
𝟏
𝟏+𝐥𝐨𝐠 𝒄 𝒂+ 𝐥𝐨𝐠 𝒄 𝒃
(b) 𝐥𝐨𝐠 𝒃 𝒂𝒄
+
𝟏
𝟏+𝐥𝐨𝐠 𝒂 𝒃+ 𝐥𝐨𝐠 𝒂 𝒄
(c) 𝐥𝐨𝐠 𝒄 𝒂𝒃
𝟏
(d) × (𝟏𝟎)𝒛
𝒚
= … … ..
(d) 1
(35) The sum of the roots of the equation: (𝟐𝟓)𝒙 − 𝟏𝟐 × (𝟓)𝒙 + 𝟐𝟕 = 𝟎
(a) 𝐥𝐨𝐠 𝟓 𝟏𝟐
(b) 12
(c) 𝐥𝐨𝐠 𝟓 𝟐𝟕
(d) 27
𝒄
(36) 𝒇 𝒂 > 𝒃 > 𝒄 > 𝟏, 𝒕𝒉𝒆𝒏 𝐥𝐨𝐠 𝒄 𝐥𝐨𝐠 𝒃 𝐥𝐨𝐠 𝒂 𝒂𝒃
(a) Zero
(b) 1
(c) 2
(d) abc
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SECONDARY TWO
Algebra
THREE
Model Answer:
1) c
2) c
3) 1) b , 2) b , 3) c
4) b
5) c
6) b
7) d
8) c
9) d
10) c
11) b
12) a
13) b
14) c
15) a
16) c
17) c
18) b
19) b
20) b
21) a
22) c
23) d
24) d
25) c
26) x=1
27) d
28) c
29) d
30) c
31) d
32) d
33) a
34) b
35) c
36) b
THREE
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