Sample exam 2
1. If xy = 2, then 2x3 y 3 is worth:
9. The lines described by the following equations y = 2x − 9
and 2y + x + 14 = 0
(A) share two disctinct points
(A) 64
(B) pass from the origin
(B) 16
(C) are parallel
(C) 128
(D) are perpendicular
(D) 8
2. What of the following expressions is TRUE for all x > 0?
10. If A = [−2, 4] ∪ (3, 5) and B = [0, 6] then A ∩ B is:
(A) [0, 5]
(A) log x2 = 2 log x
log x
√
(C) log x2 = log ( x)
(B) A
(D) log x2 = log 2x
(D) B
(B) log x2 =
1
2
(C) [0, 5)
3. What of the following equalities is TRUE for all a 6= ±b?
(A)
(B)
(C)
(D)
(a+b)(a−b)2
a2 −b2
2
(a+b)(a−b)
a2 −b2
(a+b)(a−b)
a2 −b2
2
(a+b)(a−b)
a2 −b2
2
=a−b
=a+b
=1
=
1
a−b
√
11. Find the set of solutions to 6 9x2 + 1 < 0
o
n p
p
(A) IR \ − 1/3, 1/3
np
o
p
(B)
1/3, − 1/3
n
p o
p
(C) x ∈ IR : − 1/3 < x < 1/3
(D) ∅
4. How many solutions does the equation |1 + x| = | − 3| admit?
12. The equation y 2 = 25 − x2 represents:
(A) a hyperbola
(A) 0
(B) a circle
(B) 1
(C) a parabola
(C) 2
(D) a straight line
(D) 4
5. Find the set of solutions to (x4 + 5)4 > 0
(A) IR
13. Given the sets A = {x ∈ IR | 2 ≤ x ≤ 5} and B = {x ∈
IR | 3 ≤ x ≤ 7}; what of the following is TRUE?
(A) A ∩ B = {3, 4, 5}
(B) ∅
(B) B \ A = {x ∈ IR | 2 ≤ x < 3}
(C) [−3, 3]
(C) A ∪ B = {x ∈ IR | 3 ≤ x ≤ 5}
(D) IR \ {−3, 3}
√ √
6. Given the sets A = {2, 3, π}, B = { 2, 5, 6}, C = {2, 3}
and D = {6}, then necessarily:
(D) A ∩ B = {x ∈ IR | 3 ≤ x ≤ 5}
14. The number 0.1234 belongs to the set of:
(A) natural numbers
(A) 4 ∈ C
(B) rational numbers
(B) C ⊂ A
(C) irrational numbers
(C) A = C
(D) integer numbers
(D) D ∩ B = B
15. The polynomial 2a3 b − 4a2 b + 2ab can be factorized as:
7. If log10 x = −1, then x is worth:
(A) 1
(A) 2ab(a − 1)2
(B) 1/10
(B) 2ab(a + 1)2
(C) 10
(C) 2ab(a3 + 1 + 2a2 )
(D) 20
(D) 2ab(a2 + 1 + 4a)
8. The set of solutions to
4z
z−5
=
20
z−5
is:
16. Find the set of solutions to x − 3 = 2x + 4
(A) z = 5
(A) {−7}
(B) z = 16
(B) {7}
(C) z 6= 5
(C) {− 71 }
(D) ∅
(D) ∅
17. Find the set of solutions to 2x2 + 7 < 4x
24. What of the following expressions corresponds to 4x2 − 9?
(A) x < 3
(A) (2x − 3)(2x + 3)
(B) (−∞, 4)
(B) (2x + 3)2
(C) IR
(C) (2x − 3)2
(D) ∅
(D) (2x)2 + 9
18. What of the following equations represents a line
parallel to the x-axis?
25. What of the following equations represents a circle with
radius 2 centered in P = (0, 1)?
(A) x2 + (y − 1)2 = 4
(A) x = −y + 10
(B) x2 + (y − 1)2 = 2
(B) y = x − 3
(C) x2 + y 2 = 22
(C) x = −π
(D) (x − 1)2 + y 2 = 4
(D) y = −20
19. Find S the set of solutions to
(
2x ≥ −3
x+2<0
√
26. The number 4/ 20 is equal to:
√
(A) 2/ 5
p
(B) 2/5
√
(C) 1/ 5
(D) 2/5
(A) S = [− 32 , 2)
27. Find the set of solutions to (1/3)x > 3
(B) S = (−∞, −2] ∪ ( 32 , +∞)
(C) S = IR
(A) x > −1
(D) S = ∅
(B) x < −1
(C) x < −1/3
2
20. Find the set of solutions to loge (x + 2) > 0
(A) −2 < x < 2 and x 6= 0
(D) x < −3
28. The slope of the line represented by 16x − 4y + 5 = 0 is
equal to:
(B) x 6= −2
(C) ∅
(A) −4
(D) IR
(B) 4
(C) 2
21. Given propositions P: “x is a multiple of 5” and Q:“x is a
multiple of 35”, then it is TRUE that:
(A) if P is TRUE then Q is TRUE
(D) 1/2
29. Find the set of solutions to (x2 + 1)/(x + 2) < 0
(B) if Q is TRUE then P is TRUE
(A) x < −2
(C) P is TRUE if and only if Q is FALSE
(B) x > 0
(D) all previous answers are not correct
(C) x > 2
(D) x ≤ 2
22. The equation y = (1 − x)2 represents:
30.
(A) a line with negative slope
(B) a line passing from P = (0, 1)
(C) a parabola passing from P = (0, 1)
(D) a circle with radius 1
2
3
+ ab , where b 6= 0, is equal to:
(B)
2a
3b
2(a+b)
3b
(C)
3a+2b
3b
(A)
(D) 2
23. Find the set of solutions to 3x
(A) x ≤ −2 and x ≥ 2
(B) ∅
(C) −2 ≤ x ≤ 2
(D) IR
2
−1
≥ 27