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PSAT Test #1
Question 1: If a < 0, b < 0 and (a/b) < (b/a), which of the following inequalities must be true?
(a + b)(a - b) > 0
a + b > 0
a > b
a < b
ab < 0
Question 2: What set of numbers represents the union of sets A and B?
Set A {2, 15, 27, 33, 59, 65}
Set B {1, 3, 15, 59}
{15, 59}
{1, 2, 3, 27, 33, 65}
{1, 2, 3, 15, 15, 27, 33, 59, 59, 65}
{1, 2, 3, 15, 27, 33, 59, 65}
{1, 2, 3, 15, 20, 27, 33, 59, 65}
Question 3: Which of the following describes all values of a for which
|a + 3| > 6?
a < –9
a < –9 or a > 3
a > 3
a > –9 and a < 3
a = –9 or a = 3
Question 4: The square ABCD in the figure below is inscribed in circle C. What is the ratio between the area of the square ABCD and the area of the circle C?
2/¶
1/¶
¶
¶/2
4/¶
Question 5: If the area of a rectangle is 10 square inches and its perimeter is 14 inches, what are the lengths of its sides?
2 inches and 4 inches
2 inches and 5 inches
3 inches and 5 inches
3 inches and 4 inches
2 inches and 6 inches
Question 6: If a and b are positive integers such that a·b = 70, which of the following could be the sum a + b?
17
20
22
25
29
Question 7: Given the table below, which relation describes better the relation between x and y?
x
y
0
1
2
5
4
17
5
26
y = x + 5
y = x
^{2}
+ 1
y = 2x + 1
y = 3x - 1
y = x - 1
Question 8: The price of shirts in a store is $20 and the price of ties in the same store is $15. A customer buys 2 shirts and 3 ties during a sale when the price of shirts is discounted 15% and the price of ties is discounted 10%. How much did the customer save due to the sale?
$12
$7.5
$5
$10.5
$10
Question 9: If a◊b = a
^{1/b}
, what is (a◊b)◊(1/b)?
b
a
a
^{b}
ab
1/b
Question 10: The sides a, b, c of a right triangle satisfy the relation a
^{2}
+ b
^{2}
+ c
^{2}
= 18. What is the value of the hypotenuse c?
2
3
4
5
6