Thriving Scholars TMUA Full Mock Test 1 Paper 1
20 questions · 75 min · Difficulty 40 · by Thriving Scholars
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Questions in this paper
- Question 1A square has centre (3,4) and one corner at (1,5). Another corner is at
- Question 2What is the value of ∫_0^1(e^x-x)(e^x+x)d x?
- Question 3A regular dodecagon is a 12-sided polygon with all sides the same length and all internal angles equal. If I construct a regular dodecagon…
- Question 4The positive number a satisfies ∫_0^a(√ x+x^2)d x=5 if
- Question 5Tangents to y=e^x are drawn at (p,e^p) and (q,e^q). These tangents cross the x-axis at a and b, respectively. It follows that, for all p…
- Question 6How many real solutions x are there to the equation x|x|+1=3|x|? [Note that |x| is equal to x if x≥0, and equal to -x otherwise.]
- Question 7If the expression (x+1+dfrac1x)^4 is fully expanded term-by-term and like terms are collected together, there is one term which is…
- Question 8The following five graphs are, in some order, plots of y=f(x), y=g(x), y=h(x), y=(df)/(dx) and y=(dg)/(dx); that is, three unknown…
- Question 9Let s_k denote the sum of the kth powers of the roots of the polynomial x^3-5x^2+8x-13. In particular, s_0=3, s_1=5, and s_2=9. Let a,b…
- Question 10In △ ABC with integer side lengths, cos A=(11)/(16), cos B=dfrac78, and cos C=-dfrac14. What is the least possible perimeter for △ ABC?
- Question 11Define binary operations and by a b=a^(log_7(b)) a b=a^(1/log_7(b)) for all real numbers a and b for which these expressions are defined…
- Question 12The graph of a differentiable function f is shown above. If h(x)=∫_0^xf(t)d t, which of the following is true?
- Question 13The graph of f', the derivative of a function f, consists of two line segments and a semicircle, as shown in the figure above. If f(2)=1…
- Question 14The function f is defined by f(x)=(x)/(x+2). What points (x,y) on the graph of f have the property that the line tangent to f at (x,y) has…
- Question 15A sequence of numbers is defined recursively by a_1=1, a_2=dfrac37, and a_n=fraca_(n-2)· a_(n-1)2a_(n-2)-a_(n-1) for all n≥3. Then a_(2019)…
- Question 16Let g be a function with first derivative given by g'(x)=∫_0^xe^(-t^2)d t. Which of the following must be true on the interval 0<x<2?
- Question 17Positive real numbers x≠1 and y≠1 satisfy log_2 x=log_y16 and xy=64. What is (log_2(x/y))^2?
- Question 18How many solutions does tan(2x)=cos(dfrac x2) have on the interval [0,2π]?
- Question 19What is the sum of all possible values of k for which the polynomials x^2-3x+2 and x^2-5x+k have a root in common?
- Question 20An even number of circles are nested, starting with a radius of 1 and increasing by 1 each time, all sharing a common point. The region…