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SOUTHVILLE 1 NATIONAL HIGH SCHOOL SENIOR HIGH SCHOOL DIAGNOSTIC TEST IN GENERAL MATHEMATICS Name Name:: ____ ______ ____ ___ _____ ______ ____ ____ ____ ____ ___ _____ ______ ____ ____ ____ ____ ____ ___ _____ _____ _ ________________________________ Teac eacer er:: ____ ______ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ___ _ _________________________ _____________________________________ ____________________ ________
Grad Gr ade e
&
Sect ection: ion:
Date Date::
I. Write the letter of the correct answer on the space provided. _________1. What What type of function function would would best represent represent the the situation stated stated below? “A user is charged P3 !onthly for a particular !obile plan which includes 1 free te"t !essages for all networ#s and 3!b of data usage. $essages in e"cess of 1 is charged P1 each.% a. li linear fu function b. po power fu function c. pi piece&wise fu function d. logarith!ic function _________'. What What is the value value of the function function f ( ( x )=2 x + 1 if x =1.5 ? a. ( b. 31 c. ') d. 3.* _________3. If If f ( ( x )=2 x + 7 and p ( x x )= x −3 + then what is a. '" , ) b. '" - 1( c. '" , 1
f ( ( p ( x ) ) ? d. '" - 1
_________(. $ar# started selling snac#s in the nearby school. In one day+ he spends P' for rent and P'* for each snac# ite! he prepares. is e"penses in a single day can be e"pressed as the function C ( x )=25 x + 200 + where " is the nu!ber of ite!s and /0" is his daily e"penses in pesos. ow !uch are his e"penses if he prepares 1 snac# ite!s? a. P' b. P'2 c. P3 d. P3* _________*. he he local barangay barangay received received a budget budget of P1+ to to provide provide !edical chec#ups for the children in the barangay. he a!ount is to be allotted a!ong all the children in the barangay. Write the e4uation representing the relationship of the allotted a!ount per child 0y versus the total nu!ber of children 0". 100000 a. y =100000 x b. y =100000 + x c. y =100000 − x d. y = x _________). Which Which of the following can can be classi5ed classi5ed as a rational rational e4uation? x + 1 = x2 a. f ( ( x )= x 2 + 2 x + 1 b. √ x c. x −2= 4 x − 2 x + 3 y = 2 _________2. What What is the value value of " in a. *6'
b. 36'
2 3 1 − = ? x 2 x 5 c. 7
d.
d. 26'
_________8. Which Which function function is represented represented by the graph graph given below9 below9 x − 2 a. y = x + 1 b.
y =
c.
y =
d.
y =
x −1 x + 1
x −2 x + 2 x x + 1
: e n $ a t h ; i a g n o s t i c e e s t _ : : / _ P a g e 1 < *
_________=. What is the do!ain of the function illustrated in ite! >8? a. (−∞, −2 ) ∪(−2, ∞ ) c. (− ∞, −2 ] ∪ ¿ b. (−∞ , 2 ) ∪ ( 2, ∞) d. (−∞, 2 ] ∪ ¿ _________1. Past records fro! a factory producing electronic co!ponents show that on average+ new e!ployees can asse!ble N(t) co!ponents per day after t days of 75 t , t ≥ 0 . What happens when t → ∞ ? training+ where N ( t )= t +5 a. N ( t ) → ∞ b. N ( t ) → 5 c. N ( t ) → 75 d. N ( t ) → 0 _________11. Which situation indicates a one&to&one function? a. pairing of an !e!ber to his or her nu!ber b. pairing a real nu!ber to its s4uare c. pairing a person to his or her citi@enship d. pairing a distance traveled along a given eepney route to the eepney fare _________1'. If p0" is the inverse of f0" where+ a. " - 1 d.
b. " - 3
f ( x )=3 x + 1 + then what is p0"? x + 3 c. 3
x − 1 3
_________13. Which of the following table of values represent the inverse of f ( x )= x + 5 ? a. b. & 1 ' " & & 1 ' & ' 1 ' 1 y 3 ( * ) 2 & 1 ' " & c.& d. 1 " ' & ' 1 ' 1 y & & & & & y & & & & & 3 ( * ) 2 _________1(. Which of the following state!ent is BCD 2 ) * ( 3 if p0" is the inverse of f0"? " a. he do!ain of p0" is the do!ain of f0". y 2 ) * ( 3 b. he do!ain of p0" is the range of f0". c. he range of p0" is the range of f0". d. he do!ain and range of p0" is the sa!e as that of f0". _________1*. /o!plete the state!ent below9 If we plot the inverse of a function+ we reEect the original function about the line ______________. a. y =2 x b. y =− x c. y =−2 x d. y = x _________1). Dngineers have deter!ined that the !a"i!u! force t in tons that a particular bridge can carry is related to the distance d in !eters between its 3 12.5 supports by the following function9 t ( d )= . What function shows how far the d supports should be? 12.5 12.5 12.5 a. d ( t )= 3 b. d ( t )= c. d ( t )= t √ t √ t d. d ( t )= 12.5 t
( )
_________12. Which of the following situations illustrate an e"ponential function? a. he population of bacteria doubles every three days. b. he nu!ber of students increases by * annually. c. he price of the house depreciates yearly. d. he a!ount to be paid for co!puter rentals is P' per hour.
: e n $ a t h ; i a g n o s t i c e s t _ : : / _ P a g e ' < *
_________18. Which of the following is an e"ponential ine4uality? a. 625 ≥ x 8 b. 625 ≥ 5 + x c. 625 ≥ 5 x +8 625 ≥ 5 x + 8 _________1=. What is " if a. 1
x −1 4 =16 ? b. '
c. 3
d.
d. (
_________'. Which of the following is BCD about the graph of y =2 x ? a. As " increases without bound+ the function approaches . b. As " decreases without bound+ the function approaches . c. As " increases without bound+ the function intersects . d. As " decreases without bound+ the function intersects . _________'1. Which of the following is FG a property of the e"ponential function of the for! x f ( x )=b ? a. he do!ain is the set of R . c. he range is the set of R . b. It is a one&to&one function. d. he y&intercept is 1.
()
1 _________''. Which of the following is BCD about the graph of g ( x ) =
a. Its y&intercept is 1. b. Its graph is increasing fro! left to right.
x
? 2 c. Its "&intercept is . d. Its asy!ptote is the y&a"is.
__________'3. A population starts with 1+ individuals and triples every 8 years. What is the population after 1 years? a. '*(= b. 3'* c. '=*8 d. 3=(8 __________'(. Which of the following is the logarith!ic for! of 53=125 ? a. log 5 125=3 b. log 3 125=5 c. log 5 3=125 d. log125 3 =5 __________'*. What is " in log x 16 =2 ? a. ' b. (
c. )
d. 8
__________'). uppose you have seats to a concert featuring your favorite !usical artist. Hind the appro"i!ate decibel level associated if a typical concerts sound intensity is 1&' W6!'. a. 1 dJ b. * dJ c. 1 dJ d. ' dJ __________'2. D"press a.
2 ln ( x y )
2 ln x −ln y as a single logarith!. 2 xy 2 x b. ln c. (¿) y ln ¿
( )
( ) 2
d.
ln
x y
__________'8. Which of the following logarith!ic function is the inverse of a. y = log x 2 b. y = log 2 x c. x =log x 2 d. y = log y 2 __________'=. Which of the following is BCD about the graph of
x
y =2
?
y = log 1 x ? 2
a. As " approaches @ero fro! the right+ the function increases without bound. b. As " approaches @ero fro! the left+ the function increases without bound. c. As " approaches @ero fro! the right+ the function approaches 1. d. As " approaches @ero fro! the left+ the function approaches 1.
: e n $ a t h ; i a g n o s t i c e s t _ : : / _ P a g e 3 < *
_________3. ow !uch interest is charged when P*+ is borrowed for = !onths at an annual si!ple interest rate of 1K? a. P3+ b. P=+* c. P*+* d. P3+2* _________31. What is the total a!ount of !oney in a savings account after t years at an interest rate r ? a. principal b. interest c. !aturity value d. ter! _________3'. At what si!ple interest rate per annu! will P'*+ accu!ulate to P33+ in * years? a. ).(K b. 1'K c. 2.'K d. *.*K _________33. ow !uch !oney should a student place in a ti!e deposit in a ban# that pays 1.1K co!pounded annually so that he will have P'+ after ) years? a. Around P1=+ b. Around P1*+ c. Around P1+ d. Around P13+ _________3(. Accu!ulate P1*+ for ' years at 1*K on co!pounded interest. a. P'+1'.* b. P'3+1*.2' c. P'+1'.'2 d. P'3+1'.* _________3*. ow !uch ti!e is needed for !oney to triple if invested at =K co!pounded se!i&annually? a. 1.* years b. ).* years c. 1*.* years d. 1'.* years _________3). Which of the following refers to a se4uence of pay!ents !ade at e4ual 05"ed intervals or periods of ti!e? a. annuity b. !ortgage c. a!orti@ation d. invest!ent _________32. Paolo borrowed P1+. e agrees to pay the principal plus interest by payingan e4ual a!ount of !oney each year for 3 years. What should be his annual pay!ent if interest is 8K co!pounded annually? a. P38+83.3* b. P('+3)2.'* c. P3*+3'2.* d. P3(+)32.* _________38. Hind the present value for the annual pay!ents of P1+ at the end of each ter! for 8 years with interest rate of )K co!pounded 4uarterly. a. P)+12).(' b. P=+=().( c. P)+13).( d. P2+2=(.*8 _________3=. What #ind of annuity does not begin until a given ti!e interval has passed? a. ordinary b. annual c. i!!ediate d. deferred _________(. D!!a availed of a cash loan that gave her an option to pay P1+ !onthly for 1 year. he 5rst pay!ent is due after ) !onths. ow !uch is the present value of the loan if the interest rate is 1'K converted !onthly? a. P3=+((1.1( b. P12+88.' c. P1+8=+*33.== d. P*2+=''.(1 _________(1. Which of the following is a for! of e4uity 5nancing or raising !oney by allowing investors to be part owners of the co!pany? a. bond b. stoc# c. savings d. loan _________('. Which is a for! of debt 5nancing or raising !oney by borrowing fro! investors? a. bond b. stoc# c. savings d. loan
: e n $ a t h ; i a g n o s t i c e s t _ : : / _ P a g e ( < *
_________(3. A certain corporation declared a 3K dividend on a stoc# with a par value of P*. $rs. Ligaya owns ' shares of stoc# with a par value of P*. ow !uch is the dividend she received? a. P* b. P'+* c. P' d. P3 _________((. Which of the following is FG a characteristic of bonds? a. A for! of debt 5nancing or raising !oney by borrowing fro! investors. b. Investors are guaranteed interest pay!ents and a return of their !oney at the !aturity date. c. Investors can earn if the security prices increase+ but they can lose !oney if the security prices decrease or worse if the co!pany goes ban#rupt. d. It can be appropriate for retirees 0because of the guaranteed 5"ed inco!e or for those who need the !oney soon. ________(*. What type of loan is illustrated by the situation below9 Boan has a co!puter shop. he owns ) co!puters. he decided to borrow so!e !oney fro! the ban# to buy 1 !ore co!puters. a. /onsu!er Loan b. Jusiness Loan c. Investors Loan d. ingle Loan ________(). $r. /atapang obtained a 1&year !ortgage for P1+'+. If his !onthly pay!ent is P3=+*+ how !uch is the total interest? a. P3(+ b. P8'+ c. P*(+ d. P(*+ ________(2. Which of the following is FG a proposition? a. Mose Bi@al is our Fational ero. b. '.* is an integer. c. Herdinand $agellan did not arrive in Philippines in 1*'1. d. !ile at your seat!ate. ________(8. D"press the proposition below in sy!bols. p9 Nictor has a date with Li@a. q: Manree is sleeping. r: Du!ir is eating. “Dither Nictor has a date with Li@a or Manree is sleeping or Du!ir is eating.% a. ( p ∨ q ) ∨ r b. ( p ∧ q ) ∨ r c. p ∨ ( q ∨ r ) d. ( p ∧ q ) ∨( p ∧ r ) ________(=. /o!plete the state!ent. “A proposition that is always true is called a tautology+ while a proposition that is always false is called a ____________________%. a. contradiction b. fallacy c. hoa" d. argu!ent ________*. Let p, q and r be propositions+ which of the following illustrates $odus Ponens in propositional for!? a. (( p → q ) ∧ p ) → q c. ( p →q ) ∧ ( p ) → q b.
( ( p →q ) ∧ ( q ) ) →
p
¿ d. ( p ∧ q ) → ( p ∧ q )
: e n $ a t h ; i a g n o s t i c e s t _ : : / _ P a g e * < *
