Unattributed TMUA Mock Set B Paper 1
20 questions · 75 min · Difficulty 37 · by Unattributed
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Questions in this paper
- Question 1Find ∫_1^2(3x+frac1x)^2 dx.
- Question 2The equation of a curve C is given by y=dfracx^2-2√(x). Find the gradient of C at the point (2,√2).
- Question 3The coefficient of x^3 in the expansion of (2√ p+3x)^5 is 8640. What is the value of p?
- Question 4R is the sum to infinity of the geometric progression 1,√(0.3),0.3,0.3√(0.3),…. S is the sum to infinity of the geometric progression…
- Question 5P is the area of the region bounded by the curve y=5x-x^2 and the x-axis. Q is the area of the region between the curve y=5x-x^2 and the…
- Question 6Find the sum of the real roots of the equation 49^x-7^(x+1)+12=0.
- Question 7Which of the following graphs is the image of the inverse function of y=(1-x)/(x) (x≠0)?
- Question 8The function f is given by f(x)=2x^3+px^2+qx+6, where p and q are real constants. When f(x) is divided by (x+1), the remainder is 12. When…
- Question 9The curve C has equation y=x^3-7x-6. Find the equation of the tangent to C at the point where C cuts the positive x-axis.
- Question 10There is a rectangle ABCD. We fold the lower right corner of the rectangular paper ABCD so that the vertex of the corner falls on the side…
- Question 11The simultaneous equations 3x^2-xy=4, 2x-y=p, where p is a real constant, have two distinct real solutions for x. What is the complete set…
- Question 12For an arithmetic sequence a_n, a_1+a_2+…+a_(100)+a_(101)=0. Which of the following is correct?
- Question 13Curve C has an equation (x-1)^2+(y-2)^2=5. Line L intersects curve C at A and B. Line L: y=x. Find the distance AB.
- Question 14The quadratic function f(x)=x^2+2ax+2b has two distinct roots x_1 and x_2. If -1<x_1<1<x_2<2, then which of the following is the range of…
- Question 15Which of the following is the image of the derivative function of f(x)=xsin x+cos x?
- Question 16For the equation sin x=dfrac x2, use a graphical method or otherwise to find the total number of real solutions.
- Question 17We define the slope of the tangent for the function f(x)=ln x at x=n (n is an integer) as a_n. Then what is the value of…
- Question 18The equation (|sin x|)/(x)=k (k>0) has exactly two different real solutions θ,φ (with θ>φ). Which of the following statements is correct?
- Question 19Suppose that x_1,x_2 are two different roots of f(x)=x^2+mx+√(1+m^2)=0. There is a line passing through the points A(x_1,x_1^2) and…
- Question 20The graph of y=f(x) intersects the x-axis at exactly two distinct points. Consider the graphs of the following: - I. y=f(x)+2 - II…