Five Points Each. Total 150 Points. Choose the best answer from (A) – (D). 1. Compute
3 – (–3) – [24 – 2 × (–3)] ÷ 3.
(A) 10
(B) 12
(C) –4
(D) –8
2. Which of the following pairs are relatively prime? (A) 65, 91
(B) 51, 119 (C) 38, 119 (D) 57, 95 7 3. The expression − 9 x is a simplified version of which one of the following 8 expressions? 7 7 7 7 (A) − 9 + + x (B) ( −9 + ) × x (C) − 9 + × x (D) − (9 + ) × x 8 8 8 8 4. The value for
is 45 when x=1 and y=2.
ax+by
y=1, what is the value for
(A) 24
(B) 23
If
ax+by = 21 when x=2 and
b–a ?
(C) 22
(D) 21
5. Which one of the following equations implies x and y are inversely proportional to each other? (A) 6 xy + 11 = 0
(B)
y x
= –4
1 f ( x ) = − x + 3 and g ( x ) = 2( 2 is b = ?
6. If
(A) 1 7. If
(B) 2 4
(C) 3
−
(D) 8 x + 3 y – 13 = 0
3) + 4 have the same value at x = b, what
(D) 4
3
a = 3 , b = 4 , and c = 3×4, which one of the following statements is correct?
(A) a = b = c 8. Compute (A)
(C) 3 x – 7 y = 0
23 7
(B) a = b > c 2 6 4 (− )2 + 5 × ( − ) . 3 7 45 27 30 (B) (C) 7 7
(C) b > a > c
(D)
(D) a > b > c
33 7
9. Consider a 2–digit number P. If the digit 5 is appended to the right of the units digit of P, which one of the following expressions represents this new number? (A) 10P + 5
(B) P + 5
(C) P + 50
(D) 5P 2015 Final
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2
2
10. If a = 0.988, then the point ( a –a, a +a) is located in which quadrant of a standard coordinate axis system? (A) I
(B) II
(C) III
(D) IV
11. Suppose that the ages of a father and son are in the proportion Six years from now, their ages will be in the proportion
9 : 4 today.
2 : 1. What is the
father's age today? (A) 36
(B) 45
(C) 54
(D) 63
12. Which one of the following represents the solution of the inequality
2 x – 1 > 7
> 16 – 3 x? (A)
(B)
(C)
(D)
13. On a number line, points A and B represent the values a and b, respectively, such that a < b and |a – b| = 9.
If point A is moved to the right by 3 units and we call
this new location C, then what is the distance between B and C? (A) 3 14. Let
(B) 6
(C) 9
(D) 12
a = 6×98×63, b = 12×16×147, and c = 42×14×35. Which one of the
following expressions is true? (A) a > b > c
(B) c > b > a
(C) a > c > b
15. If x = 4 is the solution for the equation
(D) b > c > a
ax + 1 = 2(3 x – 1) + 7, find the value
for a. (A) –7 16. If
(B) –2
(C) 7
(D) 4
3x – 2y + 7 = x + 4y – 7 = 5x + 2y + 1, then its solution (x, y) is located in
which quadrant of a standard coordinate axis system? (A) I
(B) II
17. Suppose
(C) III
a : b : c = 5 : 6 : 7
(D) IV and
LCM[a, b, c] = 420. Find 2 a + b + c.
(LCM = Least Common Multiple) (A) 46
(B) 43
(C) 36
(D) 18
18. Suppose the point P( x+7, 2 x+2) belongs to the Fourth Quadrant. What then is the range of values for x? (A) –7 < x 2
2015 Final
(B) –7 < x < –5
(C) –7 < x < –1
(D) –5 < x < –1
19. If the number 543210 can be expressed in scientific notation as
c
a×b , which
one of the following expressions is correct? (A) a = 5
(B) b = 5
(C) c = 5
(D) a + b + c = 15
20. The figure on the right is a factorization tree that represents the process of finding prime factors of a number. Find P + Q + R. (A) 38
(B) 46
(C) 54
(D) 62
21. If there are four Sundays in August of a certain year and the sum of the dates of the month of these four Sundays is 66, then what day of the week is August 1? (A) Monday (B) Tuesday (C) Wednesday (D) Thursday 10 x × 10 y = 106 22. If y , then what is the value for x×y? x 4 ÷2 =8 (A) –7 23. Suppose is
(B) 6
(C) 9
a : c = 3 : 2
(D) 5 b : c = 4 : 5
and
and
a + b + c = 99.
What then
(a+9) : (c–3)?
(A) 18 : 11
(B) 2 : 1
(C) 11 : 9
24. Let f(x) = ax + b and g(x) = –bx + a . (A) 17 25. Compute (A) 20
(B) 27 4
3
(C) 8 2
2
(D) 3 : 2 If f (9) = g(–4) and f (–3) = –1, find g(–3).
(D) 1 4
3
|2 – 2 – 2 | + |2 – 2 –2 |. (B) 24
(C) 28
(D) 32
26. As shown in the figure on the right, A and B are both rectangles and a, b, and c are all whole numbers greater than 1. If Area(A) = Area(B), which one of the following numbers cannot be the value of a (A) 57
(B) 67
(C) 77
(D) 87
27. George's father told George, "You were only a 3 year old baby when I was your current age." Then George said, "Don't forget that when I am your age now, you will be an 81 year old man." How old is George now? (A) 27
(B) 29
(C) 31
(D) 33 2015 Final
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28. It is given that the line L: y = 2 x – a (a>0) intersects the x– and y– axes to enclose a triangle of area 5 square units. Find the area of the triangle that is enclosed by the straight line M: y = x – 2a and the two axes. (A) 10
(B) 20
(C) 30
(D) 40
29. If the proportion of the bases of two parallelograms is 3 : 2 and the proportion of their areas is 5 : 3, find the proportion of their heights. (A) 9 : 10
(B) 10 : 9 (C) 5 : 2 (D) 2 : 5 1 1 − ( x > 0). Find f (1) + f (2) + … + f (10). 30. Let f ( x ) = x + 1 1 9 10 (A) − (B) − (C) –1 (D) − 110 10 11
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2015 Final
