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UPCAT REVIEWER
ANSWER KEY AND SOLUTION TO



UPCAT MATHEMATICS REVIEWER
(60 ITEMS)




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,ANSWER KEY
1 D 13 C 25 D 37 D 49 B
2 C 14 C 26 C 38 A 50 C
3 A 15 D 27 BONUS 39 D 51 D
4 B 16 C 28 B 40 B 52 B
5 C 17 D 29 B 41 C 53 C
6 B 18 D 30 A 42 D 54 C
7 B 19 C 31 A 43 C 55 D
8 D 20 A 32 A 44 C 56 A
9 B 21 D 33 D 45 C 57 C
10 C 22 C 34 A 46 D 58 B
11 A 23 B 35 A 47 A 59 A
12 D 24 C 36 C 48 A 60 D



SOLUTION
1. Amanda wants to buy a graphing calculator that is already on sale for P4200.
The sale price is 30% below the original price. If she is able to get an additional
15% off for being a student, how much money was saved from the original price?

(A) P1,890.00 (B) P1,170.00 (C) P2,000.00 (D) P2,430.00

Solution:


100%-30%

To get the original price divide P4200 by 0.7 the result is P6,000.00.

100%-15%

Amanda paid P4200 x 0.85 which is equal to P3,570.00

Amanda saved P6,000 – P3,570.00 = P2,430.00.


Answer: D

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,2. Let r and s be the roots of the quadratic equation
x  2 x  3  x  3x  1  x  1x  2   0.
1 1 1
Evaluate:   .
r  1s  1 r  2s  2 r  3s  3
(A) 1 4 (B) 3 (C) 811 4
17 (D) 15
Solution :
If we simplify the quadratic equation, the result is
Recall:
x 2  5 x  6  x 2  2 x  3  x 2  x  2  0.
3 x 2  8 x  1  0. If r and s are the roots of
rs 8 and rs  1 . ax 2  bx  c  0 then
3 3
1 1 1 b
Simplify   sum of roots = r  s 
r  1s  1 r  2s  2 r  3s  3 a
1 1 1
 
rs  r  s   1 rs  2r  s   4 rs  3r  s   9 product of roots = rs 
c
a
1 1 1
  
1 8 1 8 1 8
 1  2   4  3   9
3 3 3 3 3  3
1 1 1 1 3 1 8
      
1 8
 1
1 8 1 8 4  11 4 11
 2   4  3   9
3 3 3 3 3  3


Answer : C




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, 3. Solve for x: 25 30  6 5
x 3 5
    
(A) 3 (B) 4 (C) 6 (D) 8

Solution:

    
25 30 x  63 55
 5 5  6   6 5 
2 x x 3 5
divide both sides by 5
2



 5  6  6 5 
x x 3 3


 30 x  303
 x3

Answer: A




4. The x-intercepts of a parabola are 2 and 4, and the y-intercept is 8. If the
parabola passes through the point (a,8), what is the value of a?




0,8 a,8


2,0 4,0




A) 5 (B) 6 (C) 7 (D) 8


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