1. If f(x) = x2 – 3, where x is an integer, which of the following could be a value of f(x)?
A. I only
B. I and II only
C. II and III only
D. I and III only
E. I, II and III
Correct Answer: A
Choice I is correct because f(x) = 6 when x=3. Choice II is incorrect because to make f(x) = 0, x2 would have to be 3. But 3 is not the square of an integer. Choice III is incorrect because to make f(x) = 0, x2 would have to be –3 but squares cannot be negative. (The minimum value for x2 is zero; hence, the minimum value for f(x) = -3)
2. For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 200?
Correct Answer: C
1 < 4n + 7 < 200. n can be 0, or -1. n cannot be -2 or any other negative integer or the expression 4n + 7 will be less than1. The largest value for n will be an integer < (200 - 7) /4. 193/4 = 48.25, hence 48. The number of integers between -1 and 48 inclusive is 50