Gresty Academy Paper 2
20 questions · 75 min · Difficulty 41 · by Gresty Academy
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Questions in this paper
- Question 1For integers a and b, if a^((√3+4))=5^((b+2√3)) then a+b=
- Question 2Which of the following circles is a counterexample to the statement > If a circle has radius greater than 5 then it crosses at least one of…
- Question 3In logic, how many of the following statements are necessary for x>2 to be true? - |x|>2 - |x|>2 and x>0 - x>0 - |x|=3 - |x|=3 and x>0 -…
- Question 4The number of real solutions to the equation x^2-ln(x)-4=0 is [Note: ln(x) is log_e x]
- Question 5The domain of the function f(x)=logbigl(x(x+1)(x+2)(x+3)bigr) is
- Question 6Which of the following functional equations does NOT represent reflective symmetry about the line x=a?
- Question 71000^2-999^2+998^2-997^2+&… &…+4^2-3^2+2^2-1^2=
- Question 8The result 21=3×7 can be used as a counterexample to how many of the following statements involving an integer p? - p+1 is always a…
- Question 9In logic, how many of the following statements are both necessary and sufficient for the conclusion y>4? - y^2>16 - y^3>64 - y>10 - y>0 -…
- Question 10Given that the sum of two positive real numbers x and y is 15, what is the maximum possible value of xy^2?
- Question 11Given that α and β are roots of 4x^2+7x-3=0 then dfrac2α-1 and dfrac2β-1 are roots of
- Question 12How many of the following statements are necessary for ∫_1^3 f(x) mathrm dx=0 to hold true? - f(x) 0 for some x∈[1,3] - f(x)≥0 for some…
- Question 13If the graph of y=f(x) translated 3 right and then reflected in the y-axis is identical to the graph of y=f(x) reflected in the y-axis and…
- Question 14The product of the roots of y=bigl|x^2+3|x|-4bigr| is
- Question 15Which of the following functions is a counterexample to the statement > If ∫_0^1 f(x) mathrm dx=0 > > then |f(x)|<2 for all x∈[0,1]
- Question 16If α is a root of x^3+x^2+x+1=0 then Σ_(n=0)^(1000)α^n=
- Question 17For which of the following functions is fracf(a)+f(b)2≤ f(fraca+b2) true for all real numbers a,b where a<b?
- Question 18Given that exactly one of the following is correct, which must it be?
- Question 19∫_(-2)^2 |x-1||x+1| mathrm dx=
- Question 20The length of the curve described by 2log_(10)(x+y)=log_(10)(1+2xy) is