Here is the Final UPCAT sample quiz for the subtest of Mathematics. As always, please be reminded that there is no timer for this quiz so you will have to monitor your own pace. 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].
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Advanced Math Quiz
Question 1

X  0  1  2  3  4  5 
y  1  3  5  7  9  11 
y = 2x – 1


y = x


y = 2x + 1


y = 2x

=(31)/(10)
m=2
(yintercept) b=1
y=mx+b
y=2x+1
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 
45


50 and 45


45 and 35


50

Question 3

50


25


100


120

Question 4

I only


III only


I and II only


II only

Question 5

50


47


45


49

Question 6

1


cannot determine


6


3

Question 7

[n1]/2


[n+1]/2


n/2 + 1


n/2  1

n1 = Odd number of house
[n1]/2 = Houses that are painted blue
Question 8

5/8


1/7


3/8


1/8

Total number of boys = 5
Probability = 5/8
Question 9

10


24


30


12

Question 10

36


24


12


6

Question 11

P69, 950.00


P64, 100.00


P67, 200.00


P69, 700.00

= 67,200 (starting annual salary)
n = 1 d = 250
a11 = a1+(111)d
= 67,200 +10 (250)
= 67,200 +2,500
= 69,700
Question 12

26


25


23


24

a1= 1
a6 = 1 + 5(2) = 9
sn = n/2(a1+a6)
s6 = 6/2(1+9)
= (3)8
= 24
Question 13

22


20


21


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 14

74


51


55


77

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 15

2/3


3/4


7/12


1/3

= 8/12
= 2/3
Question 16

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 
42


43


40


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 17

48


32


70


24

C = n!/[(nr)!r!]
n = 8 r = 4
8!/[(84!)4!
[4x2x7x6x5]/[4x3x2x1]
=2x7x5
C = 70
Question 18

7


8


6


9

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 19

2


1/3


3


1

r = a2/a1 = a3/a2 = a4/a3
r = 12/4 = 36/12 = 108/36
r = 3
Question 20

all real numbers greater than 1/5


all real numbers greater than 0


all real numbers


all real numbers greater than or equal to 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 21

inter quartile


Decile


Quartile


tenths

Question 22

The domain of f(x) are all real numbers except 3.


The domain of f(x) are all real numbers except 3.


The domain of f(x) are all real numbers.


The domain of f(x) are all real numbers except 0.

Question 23

\(y=\sqrt{x}\)


y = 2x + 1


y = 9 – x


\(y=\frac{5x3}{7}\)

\(y=\sqrt{x}\), is not a function because given a value of x say x=4, there corresponds two values for Y, 2 and 2
Question 24

18.6


20.4


22.8


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 25

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 
40.8


46.4


48.3


40.6

sum = 1224
average: 1224/30 = 40.8
Question 26

Matrix


Frequency


Discriminant


Array

Question 27

45 meters


30 meters


40 meters


50 meters

511 = 50
2,250 / 50 = 45 meters
Question 28

P54.00


P40.00


P58.00


P50.00

d = 4.00
an= 4 * 3 = 12wks
a12 = a1+(121)d
= 10.00 + (11) 4.00
= 10.00 + 44.00
= 54.00
Question 29

312


374


82


256

Question 30

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 
56


41


40


63

= 62 – 21 = 41
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thanks a lot for this nosebleeding questions