James Chen TMUA Paper 1
20 questions · 75 min · Difficulty 35 · by James Chen
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Questions in this paper
- Question 1What is the gradient of the perpendicular bisector of the line segment connecting the points (-3,5) and (-1,9)?
- Question 2How many distinct real solutions does the equation x^8=2x^4+4 have?
- Question 3If π^2≈ g, π>0, then which estimate for ln(π) can be deduced?
- Question 4A circle in the x-y plane has radius r, perimeter P, and area A. Which of these statements is true?
- Question 5Let I(a)=∫_0^a 2x-3 d x. For what values of a are I(a) equal to -2?
- Question 6According to One Direction, you are beautiful iff you do not know you are beautiful. Also, if you flip your hair, One Direction will feel…
- Question 7What is the limit of ((x^2+5x+6)(x-1))/((x+3)(x^2-1)) as x→∞?
- Question 8The line y=x is tangent to the curve y=ax^2+5x+1 at the point with what x-coordinate?
- Question 9Evaluate Σ_(r=0)^∞(frac310^r+frac110^(r+1)+frac410^(r+2)).
- Question 10A coffee shop's 8 workers: Emily, Ethan, Olajide, Pranav, Rujul, Siddhant, Simon and Sabrina are all wearing T-shirts with the first of…
- Question 11Which function f(x) satisfies the equation √[4]abcd=f^(-1)(dfracf(a)+f(b)+f(c)+f(d)4), where f^(-1)(x) is the inverse function of f(x)?
- Question 12Which line in this false proof that 1=2 contains the first mistake? Let a&=b &&(1) a^2&=ab &&(2) a^2-b^2&=ab-b^2 &&(3) (a+b)(a-b)&=b(a-b)…
- Question 13The real numbers a,b are such that a>b. You are given that the function f(x) is defined over positive real x and is either always…
- Question 14I promise to do at least 5 STEP 1 questions, at least 3 STEP II questions, and at least 1 STEP III question next week. If I break my…
- Question 15Which of the following is a sketch of the graph y=(3-4sin x)^2?
- Question 16The 5 Backstreet Boys are asked if they want it that way. Their responses are as follows: Backstreet Boy A: “Exactly one of us wants it…
- Question 17A_n and B_n are an arithmetic sequence and a geometric sequence respectively, with first terms A_1 and B_1. You are given that A_2=B_3 and…
- Question 18For a given value of a, let f(x)=x^(x+a)^(x+2a)^(x+3a)^…. What is the value of f(0.3) when a=0.2? Note: a^b^(c^d)=a^(b^((c^d))), i.e. power…
- Question 19Let f(x) be the only degree 5 polynomial where the coefficient of x^5 is 1 and the following equations are true: f(1)&=5 f(2)&=4 f(3)&=3…
- Question 20How many distinct positive integer pairs, (a,b), with a>b, solve the equation: a^2=b^2+2025? Note: you are given that 2025=45^2=3^4×5^2.