Welcome to Academic Clinic’s sample Algebra exam for the UPCAT. Making the algebra quiz involved some coding for the special math characters involved so if the quiz doesn’t render well in your browser, please do let us know about it in the comments section. Please also let us know if there are any corrections for the quiz so that we can update it.
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Algebra Quiz
Question 1 
A  \(x=0\) 
B  \(x\le 2\) 
C  \(x=\Re \) 
D  \(x\ne 2\) 
Question 2 
x 
2 
4 
6 
8 
y 
3 
6 
9 
12 
A  \(y=\frac{x}{k}\) where \(x={}^{3}\!\!\diagup\!\!{}_{2}\;\) 
B  \(y=kx\) where \(x={}^{2}\!\!\diagup\!\!{}_{3}\;\) 
C  \(y=kx\) where \(x={}^{3}\!\!\diagup\!\!{}_{2}\;\) 
D  \(y=\frac{x}{k}\) where \(k=1.33\) 
Question 3 
A  20 
B  24 
C  25 
D  22 
Question 4 
A  750 cu. m. 
B  250 cu. m. 
C  1000 cu. m. 
D  450 cu. m. 
Question 5 
A  548 
B  513 
C  250 
D  224 
Question 6 
A  (2, 3) 
B  (3, 2) 
C  (3, 2) 
D  (2, 3) 
Question 7 
A  The graph is a parabola with vertex (3,25). 
B  The graph is a parabola opening upward. 
C  The graph is a parabola intersecting the xaxis n points at (2,0) and (8,0) 
D  The graph is a parabola with axis of symmetry \(x=1\) 
Question 8 
A  \(x+2\) 
B  \(x+1\) 
C  \(x2\) 
D  \(x1\) 
Question 9 
A  Ang graph ng dalawang linya ay parallel. 
B  Ang graph ay may iisang linya. 
C  Ang mga graph ng linya ay dumaraan sa mga point (0, 2) at (0, 3). 
D  Ang mga graph ng dalawang linya ay nagtatagpo sa point (2, 3). 
Question 10 
A  108 
B  71 
C  60 
D  54 
Question 11 
A  13 and 21 
B  23 and 11 
C  14 and 20 
D  10 and 24 
Question 12 
A  [d/h]2 
B  d/[h2] 
C  h2 
D  dh2 
Question 13 
A  45 
B  40 
C  30 
D  35 
Question 14 
A  \(\frac{(1+\sqrt{3a})(\sqrt{a+2})}{a+2}\)

B  \(\frac{1+\sqrt{3a}}{\sqrt{a+2}}\)

C  \(\frac{\sqrt{3a}}{\sqrt{a+2}}\)

D  \(\frac{1+\sqrt{3a}}{a+2}\)

Question 15 
A  7 
B  8 
C  6 
D  9 
Question 16 
RATE x TIME 
WORK 

Blacksmith A 
\(\frac{1}{7}\) 
x 
\(\frac{x}{7}\) 
Blacksmith B 
\(\frac{1}{8}\) 
x 
\(\frac{x}{8}\) 
A  3.67 days 
B  4 days 
C  3.73 days 
D  3.33 days 
Question 17 
A  d 
B  a 
C  b 
D  c 
Question 18 
A  Halved 
B  Tripled 
C  Quadrupled 
D  Doubled 
Question 19 
A  12.5% 
B  10.5% 
C  6.25% 
D  2.25% 
Question 20 
A  1 
B  2 
C  4 
D  3 
Question 21 
A  11% 
B  13% 
C  12% 
D  10% 
Question 22 
A  8 
B  5 
C  6 
D  7 
Question 23 
A  150000 
B  67500 
C  15000 
D  675000 
Question 24 
A  \(4\pm 6\sqrt{2}\) 
B  \(2\pm 6\sqrt{2}\) 
C  \(2\pm 6\sqrt{2}\) 
D  \(4\pm 6\sqrt{2}\) 
Question 25 
A  \(3x+y\le 9\) 
B  \(3xy\le 9\) 
C  \(3x+y<9[/latex] 
D  [latex]3x+y\ge 9\) 
Question 26 
A  7 
B  5 
C  4.5 
D  6 
Question 27 
A  1 min 
B  2 min 
C  3 min 
D  4 min 
Question 28 
A  \(x+4\) 
B  \(x2\) 
C  \({{\left( x2 \right)}^{2}}\) 
D  \(3x4\) 
Question 29 
A  30 
B  35 
C  25 
D  20 
Question 30 
A  13.33 
B  12.33 
C  11.33 
D  14.33 
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Question 2 should be 2q – 1 not 2q + 1
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Questions 7 and 21 seem wrong. Please check again. The question in number 7 says it will add 50L of the 1% Buttermilk. But in the equation, it says 50L(0.04) which is the 4% Buttermilk solution. Also, in number 21, the answer should be (m+n)^2q1 since the other m+n was under the division bar and should be subtracted.
mali po yung sagot sa Q 11. dapat po 4±3√2 kase √72=6√2 divided by 2=3√2
22 out of 25…. 5 questions did not display choices
Nasan na yung test?
28/30…..yehah….sayang..madadali pa ang namalian..pero ok na yan hehe
27/30
there’s something wrong with other key answers
Please check the answer in question number 5. The crossmultiplication is wrong. Thanks!
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yey
Tagalog na po ba test sa algebra?