Asher Falcon TMUA Paper 1
20 questions · 75 min · Difficulty 50 · by Asher Falcon
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Questions in this paper
- Question 1What is the value of √156+√156+√(156+…)?
- Question 2If f(sin(x))=0 has a solution at x=fracπ2, which of the following x could be a solution to 2f(2sin(x))=0?
- Question 3How many solutions are there to |sin(x^2)|-|cos(x^2)|=fracπ4 in the range 0≤ x≤π?
- Question 4What is the value of frac167+(11)/(67^2)+(111)/(67^3)+(1111)/(67^4)+…?
- Question 5The coefficient of x^3y^4z^3 in the expansion of (2x+4y^2+8z^3+128)^8 can be expressed in the form a·2^b. What is a+b?
- Question 6The function f(x) is defined as f(x)=4.dot3dot5x. What is the value, in its simplest form, of ∫_1^2 f(x) d x?
- Question 7Which of the following graphs shows e^frac1sin(x)?
- Question 8Which has the smallest value?
- Question 9What is the area of the region satisfied by the two inequalities 21+3y^2≤-3x(x+8), y≤-|x+4|?
- Question 10Let f(n) be defined as the total area of all the equilateral triangles starting with side length n and then being successively halved. What…
- Question 11What is the product of the two values of b which satisfy 2(log_a b)^2+fracln(b^(10))ln(a^2)-11=log_a(b^2)log_b(√ a)?
- Question 12ax^5+2x^5+bx^3+4x^2+5x+8 Given that the function above has a factor of (x^2+2), what is the value of 2a-b?
- Question 13Let F(x) be the smallest prime factor of x, for example F(9)=3 and F(125)=5. F(67^(2048)-1)=
- Question 14For which function is f(f(f(x)))>0 for all real x?
- Question 15What is the range of c for which √(x+4)=x+c has exactly two real solutions?
- Question 16What is the product of the real roots of the equation ln(x)^2bigl(ln(x^6)-7bigr)+ln(frace^(14)x^(12))=0?
- Question 17A function satisfies f(f(x))=9x-20. What is the possible positive value of f(9)?
- Question 18A student defines the function g(x)=x^2-3x+2, and then makes a new function: G(x)=fracg^(15)(x)g^(15)(x-1). What is G(5)?
- Question 19What is the last digit of 3^(123)·7^(456)+1?
- Question 20Find the total area of all bounded regions formed by the x-axis, the line x=1, and the curve y=3x|x+x^2|.