General Mathematics First Quarter Exam

(FIRST SEMESTER) SY: 2017-2018

I.

Read and understand each item carefully. Choose the leer of the best answer and write it on your answer sheets

1. Which of the following correspondence is a funcon? i. one to one ii. one to many   iii. many to one a. b. c. d.

i onl onlyy ii only only ii and and iii iii i and and iii iii

2. Which of the following is not a funcon? a. The rule that assigns the name of the school to each student. b. The rule that assigns to each person his/her surname. c. The rule that assigns to each person his/her mobile number d. The rule that assigns to each child his/her mother. 3. Which among the relaons is not a funcon? a. !"#$% # !"#&% # !&#"% !&#"% # !$#"% # !$#&%' b. !(2#$% # !"#$% # !2#$% # !&#$%' c. !(3#2% # !(2#$% # !(1#)% # !3#2%' d. !)#"% # !*#"% # !+#"% # !,#"%' &. Which of the following describes a funcon?

$. Which of the following graphs does not belong to the group?

iv . No

one

+. -n the funcon f!% 2# what is the 0alue of the funcon if "? a. " b. 1 c. 2 d. & *. i0en f!%  ,) ($"  1# what is f!1%? a. "  b. 1   c. &)   d. 1&) For numbers 8-11. If f(x) = x – 5 and (x) = !x " #$ what is%

). The sum of the two funcons f and g? a. 2 ( + b. 2  + c. & ( & d. &  & ,. The di4erence of the two funcons f and g? a. (& (+ b. & + c. (2 (+ d. 2  + 1". The product of the two funcons f and g? a. 32 ( 1&  $ b. 32   1& ( $ c. 32 ( 1& ( $ d. 3 ( 1&2  $ 11. The 5uoent of the two funcons f and g? a.  ( $6 3  1 b.

$ 3 ( 1 c. 66 $ ( 1 d.

$66 3

12. i0en g!%  3 and h!%  (3# what is ! g7 8 h%!%? a. , b. (, c. +

d.

(+

13. What is the composite funcon of !g 8 g%!1%? a. g!g!  %% b. g!g!1 %% c. g!g!(1%% d. g!(1!g%% 2

1&. What does the epression a. b. c. d.

 x −1   represent? f  ( x )=  x −3

raonal funcon raonal e5uaon raonal ine5uality raonal epression

1$. Which of the following ordered pairs is not a soluon to

f  ( x )= x + 4 ?

a. !"# &% b. (−5,−1 ) c. !2# +% d. !1# 2% 1+. What is the 0alue of  in the e5uaon $  $ ? a. 1 2 2 b. 2 c. 3 d. & 1*. What is the 0alue of  in the e5uaon  ( &  ? a. 2 3 b. & c. + d. ) 1). What is the symbol for the in0erse of a funcon? a. f -1 !% 1 b.  x f  1 c. f!%   x

d. ( f!% 1,. Which of the following is the test to determine if the graph is a onetoone funcon? a. 9lumb line test b. :iagonal line test c. ;ori
b. !2# "%# !$# 3%# !+# 1%' c.  "# 3# 1 ' d. 2# $# +' 22. What is a funcon that can be epressed mathemacally as f(x) b x? a. >inear funcon b. aonal funcon c.  @ponenal funcon d. -n0erse funcon 23. Which of the following is eponenal funcon? a. f!%  2 b. 22 ! $ 1%  $"" c. +2$ A $  ) d. f !%  23 2&. Which of the following maBes the asymptote of the graph of eponenal funcon y  a x # where a A 1? a.  ( ais b. y ( ais c. y   d. y  1 2$. What is the common point of all the graphs of logarithmic funcon? a. !"#"% b. !"#1% c. !1#"% d. !1#1% 2+. What is the single logarithm of C log  ( D log y ?

 √  xy

a.

log

b.

log

c.

log

d.

log

24

x  y

 √  y 3 √  x  √  x 4 √  y

( ) 3

 P Q log 2 2  R

2*. What is the epanded form of a.

log 2  P

3

4

?

+ log 2 Q 4 + log 2 R2

 b.

3log 2 P + 4 log 2 Q −2 log 2 R

c.

log 2 √  P + log 2 √ Q − log 2 √  R

d.

log 2 3 P + log 2 4 Q − log 2 2 R

3

4

2

2). Which among the following is a logarithmic funcon? a. log 2  & b. ln 2 A !ln %2  3 c. g!% log3  d. log2 +&  ) 2,. What is the logarithmic form of the eponenal e5uaon $ 3  12$?

a. log$ 3  12$ b. log$ 12$  3 c. log3 $  12$ d. log3 12$  $ 3". The decibel le0el of sound in a church is

−7

10

 waEs/m2. What is the corresponding sound intensity in

decibels? a. &" b. $" c. +" d. *"

II.

&i'en

f  ( x )=

2 x −1 2

 x −4

$ determine the 'alue of each of the followin roeres of the rah of the i'en raonal

 funcon.

a. y ( intercept

b. 0ercal asymptotes c. hori
III.

 *nswer the followin.(+ oints each)

1. :etermine the domain and range of each raonal funcon.  x a. f  ( x )= + 3 2 b.

2 f  ( x )=  x −3

2. Find the 0alue of  of each funcon. a. b.

 x + 2

=27 log 3 ( 3 x −2 )=2

3

3. Find the soluons of the following ine5ualies.

IV.

2 x + 1

 x

a.

2

b.

log 4 ( 3 x −5 )>1

≥2

,roblem -ol'in.(+ oints each)

1. G culture of 1$ bacteria in a petri dish doubles e0ery hour. ;ow many bacteria will there be aHer & hours? 2. G certain barrio in Ian >uis has a populaon of 1"# $"" that is increasing at the rate of &J each year. Find the populaon of that barrio aHer 3 years.