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  2 and 17 
B  7 and 22 
C  12 and 27 
D  6 and 21 
Question 2 
A  (b + 1)(a + 1) 
B  (b – 1)(a – 1) 
C  (b + 1)(a – 1) 
D  (b – 1)(a + 1) 
Question 3 
A  60 
B  71 
C  108 
D  54 
Question 4 
A  4.5 
B  7 
C  5 
D  6 
Question 5 
A  20 
B  15 
C  25 
D  10 
Question 6 
A  \(9\sqrt{7}\) 
B  \(3\sqrt{7}\) 
C  \(5\sqrt{7}\) 
D  \(3\sqrt{7}\) 
Question 7 
A  \(2\pm 6\sqrt{2}\) 
B  \(2\pm 6\sqrt{2}\) 
C  \(4\pm 6\sqrt{2}\) 
D  \(4\pm 6\sqrt{2}\) 
Question 8 
A  20 
B  25 
C  24 
D  22 
Question 9 
A  \(\frac{12}{17}\) 
B  \(\frac{3}{2}\) 
C  \(\frac{15}{12}\) 
D  \(\frac{17}{12}\) 
Question 10 
A  PHP 5,253.13 
B  PHP 5,153.13 
C  PHP 5200.37 
D  PHP 5,000.53 
Question 11 
PIPE 
Rate 
Time 
Work 
A 
\(\frac{1}{8}\) 
\(x\) 
\(\frac{x}{8}\) 
B 
\(\frac{1}{6}\) 
\(x\) 
\(\frac{x}{6}\) 
C 
\(\frac{1}{4}\) 
\(x\) 
\(\frac{x}{4}\) 
A  24 minutes 
B  36 minutes 
C  1 hour 
D  12 minutes 
Question 12 
A  \(9x^{2}12x4\)

B  \(4x^{2}20x + 25\)

C  \(4x^{2}+10x + 25\)

D  \(x^{2}+10x + 36\)

Question 13 
A  \(x\ne 2\) 
B  \(x\le 2\) 
C  \(x=\Re \) 
D  \(x=0\) 
Question 14 
A  \((m+n)\) 
B  \({{(m+n)}^{2q}}\) 
C  \({{(m+n)}^{2q+1}}\) 
D  \(1\) 
Question 15 
A  \(\frac{2x+1}{x^{2}4}\)

B  \(\frac{2x7}{x^{2}+4}\)

C  \(\frac{2x+7}{x^{2}+4}\)

D  \(\frac{2x7}{x^{2}4}\)

Question 16 
A  4 
B  1 
C  3 
D  2 
Question 17 
A  11/7 
B  7/11 
C  11/7 
D  7/11 
Question 18 
RATE x TIME 
WORK 

Blacksmith A 
\(\frac{1}{7}\) 
x 
\(\frac{x}{7}\) 
Blacksmith B 
\(\frac{1}{8}\) 
x 
\(\frac{x}{8}\) 
A  3.33 days 
B  3.73 days 
C  4 days 
D  3.67 days 
Question 19 
A  250 cu. m. 
B  450 cu. m. 
C  750 cu. m. 
D  1000 cu. m. 
Question 20 
A  \(\frac{1}{cb}\) 
B  \(\frac{1}{c}\) 
C  \(\frac{1}{b}\) 
D  \(\frac{1}{bc}\) 
Question 21 
A  y = 4 – 2x 
B  y > 4 – 2x 
C  cannot be determined 
D  y < 4 – 2x 
Question 22 
A  Halved 
B  Quadrupled 
C  Tripled 
D  Doubled 
Question 23 
A  250 
B  224 
C  513 
D  548 
Question 24 
A  Inconsistent 
B  Complicated 
C  Dependent 
D  Consistent 
Question 25 
A  4 
B  9 
C  1 
D  0 
Question 26 
A  \(\frac{6}{5}\) 
B  \(\frac{5}{3}\) 
C  \(\frac{3}{5}\) 
D  \(\frac{5}{6}\) 
Question 27 
A  3 
B  1 
C  2 
D  4 
Question 28 
x 
2 
4 
6 
8 
y 
3 
6 
9 
12 
A  \(y=kx\) where \(x={}^{2}\!\!\diagup\!\!{}_{3}\;\) 
B  \(y=\frac{x}{k}\) where \(x={}^{3}\!\!\diagup\!\!{}_{2}\;\) 
C  \(y=\frac{x}{k}\) where \(k=1.33\) 
D  \(y=kx\) where \(x={}^{3}\!\!\diagup\!\!{}_{2}\;\) 
Question 29 
A  2 
B  1 
C  0 
D  1 
Question 30 
A  \(\frac{(1+\sqrt{3a})(\sqrt{a+2})}{a+2}\)

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

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

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

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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?