Welcome to Academic Clinic’s sample Geometry and Trigonometry exam for the UPCAT. We do not have a timer for this quiz so you will have to time yourself and check if the time you’ve spent on answering the quiz is well within the time limit of the UPCAT.
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Geometry / Trigonometry Quiz
Question 1

6


4


8


10

Question 2

60


cannot be determined


30


45

Question 3

III


II


I


IV

Question 4

\(\frac{7\Pi }{6}\)


\(\frac{3\Pi }{4}\)


\(\frac{5\Pi }{4}\)


\(\frac{9\Pi }{4}\)

5 * \frac{\Pi radians}{4}
\(\frac{5}{4} \Pi radians \)
Question 5

The area will increase twice.


The area will remain the same.


The area will increase 4 times.


The area will increase 8 times.

Question 6

III only


I only


II only


I and II only

Question 7

105


85


115


95

Question 8

24


30


40


42

Question 9

The area of the rectangle is 1 / 2 times that of the square.


The area of the rectangle is 1 / 4 times that of the square.


The area of the square is 1 / 4 times that of the rectangle.


The area of the square is 1 / 2 times that of the rectangle.

Question 10

\(300^{\circ}\)


\(360^{\circ}\)


\(280^{\circ}\)


\(330^{\circ}\)

Question 11

BA


AC


cannot be determined


BC

Question 12

15/2


17/4


23/7


11/3

Question 13

4/5


5/3


3/4


4/3

Question 14

100


169


81


144

Question 15

9


11


7


5

Question 16

\(\csc \Theta\)


\(\cot \Theta\)


\(\sec \Theta\)


\(\cos \Theta\)

Question 17

III only


II only


I and II only


I only

Question 18

64


36


72


81

Question 19

120


140


160


100

Question 20

2


1


3


4

Question 21

6


4.5


3


2.75

Question 22

24 cm


15 cm


21 cm


18 cm

Question 23

40


22/3


22


44

Question 24

3/5


4/5


5/3


3/4

Question 25

\(\frac{\sqrt{5}}{2}\)


\(\frac{3}{\sqrt{5}}\)


\(\frac{\sqrt{5}}{3}\)


\(\frac{2}{\sqrt{5}}\)

Question 26

18


22


20


16

Question 27

\(\frac{20\sqrt{3}}{3}\)


\(\frac{\sqrt{3}}{20}\)


\(\frac{\sqrt{3}}{3}\)


\(\frac{2\sqrt{3}}{3}\)

Question 28

60


40


90


30

Question 29

13


11


12


10

Question 30

\(4+2\sqrt{3}\)


\(4\sqrt{2}\)


\(4+2\sqrt{2}\)


\(4\sqrt{3}\)

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^ Martin Morelos is correct. The answer is 3, which is not in the options. Good job on the sample quiz, nonetheless.
Your explanation for Question 12 is inaccurate, which is why the real answer is not in the options.
“TP = 2x+1 RP =y+5 SP = 43y QP = x5 TP = RP SP = QP diagonals of a parallelogram bisect each other. Substituting and Equating 1. 2x+1 = y+5 2. 43y = x5 using equation 2: x = 93y substituting to equation 2: 2(93y) = y+5 186y = y+5 7y = 11 y = 11/7 x = 93 (11 / 7) = (8 33) / 7 = (5633) / 7 x = 23/7″
When you substituted to equation 2: 2x+ 1 = y+5; you forgot to add the one.
This was an inaccuracy: 2(93y) = y+5.
Furthermore, “186y = y+5; 7y = 11″
when you transposed the 5 to the side of 18 and combine, you should get 13, not 11.
My answer for this question is 3.