Here is the Final UPCAT sample quiz for the subtest of Mathematics. You can also post your quiz score on our Facebook fanpage so that you will see how well you fared compared to the other quiz takers. Moreover, you might want to check out our Ultimate Guide to the UPCAT post after the quiz to learn more about the UPCAT [tips, coverage, facts, etc].
We will be updating this quiz regularly and will be adding math questions so that each quiz taker will be faced with a different quiz each time. If there are any corrections to the quiz or if you want to contribute your own solution set, please don’t hesitate to let us know in the comment section below. Keep in touch as we will be posting other quizzes about the other subsections of the UPCAT, ACET, USTET, etc.
Finally, Academic Clinic is a totally free education site for Filipino students. We also have posts on college scholarships, college survival, research about the top universities and colleges in the country, science high school admissions, etc. Please don’t forget to share this valuable resource with your friends and classmates by clicking the share button above. Goodluck on your UPCAT!^^
Advanced Math Quiz
Question 1 
A  The domain of f(x) are all real numbers except 0. 
B  The domain of f(x) are all real numbers.

C  The domain of f(x) are all real numbers except 3. 
D  The domain of f(x) are all real numbers except 3. 
Question 2 
43  33  24  51  36  31 
50  46  50  29  40  25 
38  35  31  35  42  50 
47  21  45  45  28  36 
58  62  37  55  52  49 
A  42 
B  40 
C  43 
D  41 
21 24 25 28 29 31 31 33 35 35 36 36 37 38 40 42 43 45 45 46 47 49 50 50 50 51 52 55 58 62
15th = 40
16th = 42
median = [N+1]/2 = [30+1]/2 = 31/2 = 15.5th score
x15 = 40
x16 = 42
[40+42]/2 = 41
Question 3 
A  II only 
B  III only 
C  I only 
D  I and II only 
Question 4 
A  6 
B  7 
C  9 
D  8 
sn = 127
a2 =2
n = ?
r=a2/a1 = 2/1 = 2
sum of nth terms in geometric progression:
sn = [a1(1r^n)]/ [1r]
127 = [1(12^n)]/(12)
127 = 12^n
2^7= 2^n
n=7 127 = 12n 1271 = 2n 27= 2n n = 7
Question 5 
A  3/8 
B  1/8 
C  1/7 
D  5/8 
Total number of boys = 5
Probability = 5/8
Question 6 
A  30 
B  12 
C  24 
D  10 
Question 7 
A  40 meters 
B  30 meters 
C  50 meters 
D  45 meters 
511 = 50
2,250 / 50 = 45 meters
Question 8 
A  36 
B  24 
C  12 
D  6 
Question 9 
A  cannot determine 
B  3 
C  1 
D  6 
Question 10 
A  all real numbers greater than 0 
B  all real numbers

C  all real numbers greater than or equal to 1/5 
D  all real numbers greater than 1/5 
y = \(\frac{2x^{2}1}{5}\)
5y = 2x^21
5y + 1 = 2x^2
\(\frac{5y+1}{2}=x^{2}\)
\(x = \sqrt{\frac{5y+1}{2}}\)
Range is defined as all possible values of y correspond to value of x. From the given equation \(\frac{5y+1}{2}\) must be greater than or equal to zero.
\(\frac{5y+1}{2} \geq 0\)
\(5y+1 \geq 0\)
\(\frac{5y}{5}\geq \frac{1}{5}\)
\(y \geq \frac{1}{5}\)
Therefore, range for given equation: all real numbers greater than or equal to 1/5 5y +1 Therefore, range for given equation: all real numbers greater than or equal to zero.
Question 11 
A  48 
B  32 
C  24 
D  70 
C = n!/[(nr)!r!]
n = 8 r = 4
8!/[(84!)4!
[4x2x7x6x5]/[4x3x2x1]
=2x7x5
C = 70
Question 12 
43  33  24  51  36  31 
50  46  50  29  40  25 
38  35  31  35  42  50 
47  21  45  45  28  36 
58  62  37  55  52  49 
A  46.4 
B  40.6 
C  40.8 
D  48.3 
sum = 1224
average: 1224/30 = 40.8
Question 13 
A  77 
B  51 
C  74 
D  55 
a7 = 20
a20 = 59
a7 = a1 +(71)d
a20 = a1 +(201)d
20 = a1+6d 59 = a1+19d
Solving by elimination, we can solve the value of d.
a1+19d = 59 a1+19d = 59
 a1+6d = 20 + a16d = 20
13d/13 = 39/13
d = 3
Solving for a1: Solving for a25:
20=a1+6(3) a25 = a1+24d
20 = a1+18 = 2 + 24(3)
a1 = 2018 = 2+72
a1 = 2 a25 = 74
Question 14 
X  0  1  2  3  4  5 
y  1  3  5  7  9  11 
A  y = 2x + 1 
B  y = 2x 
C  y = 2x – 1 
D  y = x 
=(31)/(10)
m=2
(yintercept) b=1
y=mx+b
y=2x+1
Question 15 
A  P50.00 
B  P54.00 
C  P58.00 
D  P40.00 
d = 4.00
an= 4 * 3 = 12wks
a12 = a1+(121)d
= 10.00 + (11) 4.00
= 10.00 + 44.00
= 54.00
Question 16 
A  1/3 
B  1 
C  2 
D  3 
r = a2/a1 = a3/a2 = a4/a3
r = 12/4 = 36/12 = 108/36
r = 3
Question 17 
A  \(y=\sqrt{x}\)

B  y = 9 – x 
C  \(y=\frac{5x3}{7}\)

D  y = 2x + 1 
\(y=\sqrt{x}\), is not a function because given a value of x say x=4, there corresponds two values for Y, 2 and 2
Question 18 
A  P69, 950.00 
B  P64, 100.00 
C  P69, 700.00 
D  P67, 200.00 
= 67,200 (starting annual salary)
n = 1 d = 250
a11 = a1+(111)d
= 67,200 +10 (250)
= 67,200 +2,500
= 69,700
Question 19 
A  [n+1]/2 
B  n/2  1 
C  n/2 + 1 
D  [n1]/2 
n1 = Odd number of house
[n1]/2 = Houses that are painted blue
Question 20 
A  2/3 
B  1/3 
C  3/4 
D  7/12 
= 8/12
= 2/3
Question 21 
A  20 
B  22 
C  21 
D  23 
an= 51 n = ?
an = a1+ (n1)d
51 = 6+(n1)(3)
51 = 6 +3n+3
51 = 9 + 3n
519 = 3n
60 = 3n
n = 20
Question 22 
43  33  24  51  36  31 
50  46  50  29  40  25 
38  35  31  35  42  50 
47  21  45  45  28  36 
58  62  37  55  52  49 
A  45 and 35 
B  50 and 45 
C  45 
D  50 
Question 23 
A  50 
B  120 
C  25 
D  100 
Question 24 
A  Frequency 
B  Array 
C  Discriminant 
D  Matrix 
Question 25 
A  256 
B  312 
C  82 
D  374 
Question 26 
43  33  24  51  36  31 
50  46  50  29  40  25 
38  35  31  35  42  50 
47  21  45  45  28  36 
58  62  37  55  52  49 
A  56 
B  40 
C  63 
D  41 
= 62 – 21 = 41
Question 27 
A  50 
B  45 
C  47 
D  49 
Question 28 
A  20.4 
B  22.8 
C  18.6 
D  21.5 
2nd Quiz = 6
3rd Quiz = 12
a1 = 3 r = 2
\(S_{n}= \frac{a_{1}(1r^{n})}{1r}= \frac{3(12^{5})}{12}\)
\(S_{n}= \frac{3(132)}{1r}= \frac{3(31)}{1}\)
\(S_{n}= \frac{93}{1} = 93\)
93/5 = 18.16
Question 29 
A  Decile 
B  tenths 
C  Quartile 
D  inter quartile 
Question 30 
A  23

B  24 
C  25 
D  26 
a1= 1
a6 = 1 + 5(2) = 9
sn = n/2(a1+a6)
s6 = 6/2(1+9)
= (3)8
= 24
Related posts:
 UPCAT Sample Questions: General Science
 UPCAT Sample Test: Basic Math
 UPCAT Sample Questions: Biology
 UPCAT Sample Exam: Chemistry
 UPCAT Review Questions: Algebra
 UPCAT Review Questions: Sample Trigonometry / Geometry Quiz
 UPCAT Review Questions: Sample Parts of Speech/General Grammar Rules Quiz
 UPCAT Sample Questions: Syntax and Mechanics
 UPCAT Reviewer / Sample Quiz: Diction and Vocabulary
 UPCAT Mock Test: Physics
 UPCAT Mock Exam: Reading Comprehension
OMG SANA MAKAPASA AKO. GOODLUCK SA MGA MAGUUPCAT AT SA MGA MAKAKASABAY KO SA NATIONAL INSTITUTE OF PHYSICS AUG 16 6:30 AM!!!!!
thanks
ang hirap pag english pinaguusapan
…i am really dumb…ahahahahahahaha
h! I’m Bea malapit na ang kaming mag take ng entrance exam sa UP, I hoe this website will help me kasi hnd na kami e rereview ng mga teachers namin…di ba mahirap?
sa sana sa ganitong paraan makaya ko ang exam….wish me luck and thank you 😉
i would like to check the answer in No. 13. I think the correct answer there is (n+1)/2. If there are odd no. of houses in a row say: A,B, C, D, E, F, G. First house is A painted with blue and B with yellow… so A, C, E and G are painted blue. 4 houses. So 7 + 1 = 8 /2 = 4…am i right?
yap . thought soo too
hahaha.. i just got 14 out of 30 with this exam .. i need to review more but its still good enough for first time taker :))
i’m only 15 years of age
i’m so glad that i’ll take that exam. !
out of .~*30 questions I only get 19
so kin’da freak di ba p0 .~
but i need more review para
pag’nag college na aco next year alam ko
na kung ano ang mga sagot.~
but don’t forget t0 pray bef0re y0u take the exam.
i hope that i will pass the exam. >>>
<3 i also need more inf0 para makapasa. ?
more strategies .:)
i’m only 15 years of age
i’m so glad that i’ll taked that exam. !
out of .~*30 questions I only get 19
so kin’da freak di ba p0 .~
but i need more review para
pag’nag college na aco next year alam ko
na kung ano ang mga sagot.~
but don’t forget t0 pray bef0re y0u take the exam.
i hope that i will pass the exam. >>>
<3 i also need more inf0 para makapasa. ?
more strategies .:)
HALF LANG NAKUHA KO
very easy but difficult for me!!!
wew!thanks..it’s not that difficult, actually..^.^
Pingback: UPCAT Review Questions
Pingback: UPCAT Review – Your Ultimate Guide
thanks a lot for this nosebleeding questions