Thriving Scholars TMUA Full Mock Test 1 Paper 2
20 questions · 75 min · Difficulty 53 · by Thriving Scholars
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Questions in this paper
- Question 1A number is chosen at random from among the first 100 positive integers, and a positive integer divisor of that number is then chosen at…
- Question 2Let P(x) be the unique polynomial of minimal degree with the following properties: - P(x) has a leading coefficient 1, - 1 is a root of…
- Question 3How many three-digit positive integers N satisfy the following properties? - The number N is divisible by 7. - The number formed by…
- Question 4Let f(x)=3-2x. A differentiable function g satisfies g'(x)=f(x)f'(x)(x-3). For this question, take “g is increasing at x” to mean g'(x)≥0…
- Question 5Maureen is keeping track of the mean of her quiz scores this semester. If Maureen scores an 11 on the next quiz, her mean will increase by…
- Question 6What is the least value of n such that n! is a multiple of 2024?
- Question 7How many angles θ with 0≤θ≤2π satisfy log(sin(3θ))+log(cos(2θ))=0?
- Question 8On Halloween 31 children walked into the principal's office asking for candy. They can be classified into three types: Some always lie…
- Question 9Which expression is equal to |a-2-√((a-1)^2)| for a<0?
- Question 10What is the least possible value of (xy-1)^2+(x+y)^2 for real numbers x and y?
- Question 11In the following list of numbers, the integer n appears n times in the list for 1≤ n≤200. 1,2,2,3,3,3,4,4,4,4,…,200,200,…,200 What is the…
- Question 12What is the sum of all real numbers x for which |x^2-12x+34|=2?
- Question 13What is the value of 1+2+3-4+5+6+7-8+…+197+198+199-200?
- Question 14Four distinct real numbers a,b,c, and d are used to define four points A=(a,b), B=(b,c), C=(c,d), D=(d,a). The quadrilateral ABCD has all…
- Question 15Tom runs a small reptile education booth at the weekend market. He keeps notes on 13 snakes: 4 are purple and 5 are happy. From observing…
- Question 16Two transformations are said to commute if applying the first followed by the second gives the same result as applying the second followed…
- Question 17Positive real numbers a and b have the property that √(log a)+√(log b)+log√ a+log√ b=100 and all four terms on the left are positive…
- Question 18The equation x^2-4kx+y^2-4y+8=k^3-k is the equation of a circle
- Question 19A square of area 2 is inscribed in a square of area 3, creating four congruent triangles, as shown below. What is the ratio of the shorter…
- Question 20Define P(x)=(x-1^2)(x-2^2)…(x-100^2). How many integers n are there such that P(n)≤0?