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0 | 1 | What is the product of the real roots of the equation $x^{2}+4x+3=\sqrt{x^{2}+4x+5}\,$? | Not supported with pagination yet | -2 | Not supported with pagination yet | 1 | Not supported with pagination yet | 2 | Not supported with pagination yet | 4 | Not supported with pagination yet | 2 | Konkour_EN | en | konkour |
1 | 2 | The graph of the function \(y=\lvert 2x-6\rvert-\lvert x+4\rvert+x\) is decreasing on an interval. Which of the following is the formula of its inverse on that interval? | Not supported with pagination yet | \(y=-x+6,\; x<-4\) | Not supported with pagination yet | \(y=-x+5,\; x>2\) | Not supported with pagination yet | \(y=-\frac{1}{2}x+1,\; -4<x<3\) | Not supported with pagination yet | \(y=-\frac{1}{2}x+1,\; -4<x<10\) | Not supported with pagination yet | 4 | Konkour_EN | en | konkour |
2 | 3 | The function \(f(x)=x^{2}+2x+1\) is defined with domain \((-1,+\infty)\). How many intersection points do the graphs of \(f\) and \(f^{-1}\) have? | Not supported with pagination yet | 1 | Not supported with pagination yet | 2 | Not supported with pagination yet | 3 | Not supported with pagination yet | No intersection | Not supported with pagination yet | 4 | Konkour_EN | en | konkour |
3 | 4 | The solutions of the trigonometric equation \(\cot x+\tan x-4\cos 2x=0\) lie on the unit circle. The points corresponding to these solutions are the vertices of which polygon? | Not supported with pagination yet | Square | Not supported with pagination yet | Rectangle | Not supported with pagination yet | Triangle | Not supported with pagination yet | Quadrilateral with non-right angles | Not supported with pagination yet | 1 | Konkour_EN | en | konkour |
4 | 5 | How does the graph of the function \(f(x)=\frac{-x-1}{x-\lvert x\rvert}\) behave around its vertical asymptote? | Not supported with pagination yet | 3 | Konkour_EN | en | konkour | ||||||||
5 | 6 | The sum of the slopes of the left-hand and right-hand tangents of the graph of the function \(f(x)=\lfloor x\rfloor x+x^{2}\) at \(x=0\) is which of the following? (Here \(\lfloor\ \rfloor\) denotes the greatest-integer (floor) function.) | Not supported with pagination yet | 1 | Not supported with pagination yet | -1 | Not supported with pagination yet | 0 | Not supported with pagination yet | \(\frac{1}{2}\) | Not supported with pagination yet | 2 | Konkour_EN | en | konkour |
6 | 7 | What is the maximum value of the function \(f(x)=-\lvert x\rvert \cos x\) on the interval \([-1,1]\)? | Not supported with pagination yet | 0 | Not supported with pagination yet | \(\frac{1}{2}\) | Not supported with pagination yet | \(\cos 1\) | Not supported with pagination yet | 1 | Not supported with pagination yet | 1 | Konkour_EN | en | konkour |
7 | 8 | If the solution set of the inequality \(\sqrt{3x+4} > 2\lvert x-1\rvert - x\) is the interval \((a,b)\), what is the midpoint of this interval? | Not supported with pagination yet | \(\frac{5}{2}\) | Not supported with pagination yet | 3 | Not supported with pagination yet | \(\frac{7}{2}\) | Not supported with pagination yet | 4 | Not supported with pagination yet | 3 | Konkour_EN | en | konkour |
8 | 9 | What is the sum of the solutions of the trigonometric equation \(\sin 4x=\sin^{4}x-\cos^{4}x\) in the interval \([0,\pi]\)? | Not supported with pagination yet | \(\frac{7\pi}{4}\) | Not supported with pagination yet | \(\frac{9\pi}{4}\) | Not supported with pagination yet | \(\frac{5\pi}{2}\) | Not supported with pagination yet | \(\frac{11\pi}{3}\) | Not supported with pagination yet | 3 | Konkour_EN | en | konkour |
9 | 10 | What is the limit of the expression \(\lfloor \sin\left(x-\frac{\pi}{3}\right)\rfloor \cos 3x + \lfloor \tan^{2}x \rfloor\) as \(x \to \frac{\pi}{3}\)? (Here \(\lfloor\ \rfloor\) denotes the greatest-integer (floor) function.) | Not supported with pagination yet | 1 | Not supported with pagination yet | 2 | Not supported with pagination yet | 3 | Not supported with pagination yet | The limit does not exist. | Not supported with pagination yet | 3 | Konkour_EN | en | konkour |
10 | 11 | How many points of discontinuity does the function \(f(x)=\lfloor x^{2}\rfloor\) have on the interval \([-1,2]\)? (Here \(\lfloor\ \rfloor\) denotes the greatest-integer (floor) function.) | Not supported with pagination yet | 3 | Not supported with pagination yet | 4 | Not supported with pagination yet | 5 | Not supported with pagination yet | 6 | Not supported with pagination yet | 3 | Konkour_EN | en | konkour |
11 | 12 | How many asymptotes does the function \(y=\frac{1}{\sqrt{x^{3}-4x^{2}}}\) have? | Not supported with pagination yet | 2 | Not supported with pagination yet | 3 | Not supported with pagination yet | 1 | Not supported with pagination yet | 0 | Not supported with pagination yet | 1 | Konkour_EN | en | konkour |
12 | 13 | What is the x-coordinate of the inflection point of the function \(y=(5-x)\sqrt[3]{x^{2}}\)? | Not supported with pagination yet | -1 | Not supported with pagination yet | 0 | Not supported with pagination yet | 1 | Not supported with pagination yet | 2 | Not supported with pagination yet | 1 | Konkour_EN | en | konkour |
13 | 14 | For which values of \(a\) does the quadratic equation \(x^{2}-2(a-2)x+14-a=0\) have two positive roots? | Not supported with pagination yet | \(-2<a<2\) | Not supported with pagination yet | \(2<a<5\) | Not supported with pagination yet | \(2<a<14\) | Not supported with pagination yet | \(5<a<14\) | Not supported with pagination yet | 4 | Konkour_EN | en | konkour |
14 | 15 | If \(f(x)=\frac{1+x^{2}}{1-x^{2}}\) and \(g(x)=\sqrt{x-x^{2}}\), what is the domain of \(g\circ f\)? | Not supported with pagination yet | [0, 1) | Not supported with pagination yet | \(\{0\}\) | Not supported with pagination yet | (-1, 1) | Not supported with pagination yet | \(R\setminus\{1,-1\}\) | Not supported with pagination yet | 2 | Konkour_EN | en | konkour |
15 | 16 | The graphs of the two functions \(y=\left(\frac{\sqrt{3}}{3}\right)^{2x}\) and \(y=3^{x}+\frac{8}{3}\) intersect at a point \(A\). What is the distance from \(A\) to the point \((-1,1)\)? | Not supported with pagination yet | 1 | Not supported with pagination yet | \(\sqrt{2}\) | Not supported with pagination yet | 2 | Not supported with pagination yet | \(\sqrt{5}\) | Not supported with pagination yet | 3 | Konkour_EN | en | konkour |
16 | 17 | How many points attain the minimum value of the function \(y=2\sin\!\left(\frac{\pi}{3}-2\pi x\right)\) on the interval \([-1,1]\)? | Not supported with pagination yet | 1 | Not supported with pagination yet | 2 | Not supported with pagination yet | 3 | Not supported with pagination yet | 4 | Not supported with pagination yet | 2 | Konkour_EN | en | konkour |
17 | 18 | For the function \(f(x)=\cos^{2}x-2\cos x\) with \(x\in[0,2\pi]\), on which interval is the graph decreasing and concave down? | Not supported with pagination yet | \(\left(\frac{\pi}{2},\frac{2\pi}{3}\right)\) | Not supported with pagination yet | \(\left(\pi,\frac{4\pi}{3}\right)\) | Not supported with pagination yet | \(\left(\frac{2\pi}{3},\pi\right)\) | Not supported with pagination yet | \(\left(\frac{4\pi}{3},\frac{3\pi}{2}\right)\) | Not supported with pagination yet | 2 | Konkour_EN | en | konkour |
18 | 19 | Let $y = -5x^2 + ax - 8$. If the largest interval on which the graph of this function is increasing is $(-\infty, 2.5)$, find the $y$-coordinate (ordinate) of the vertex of the parabola. | Not supported with pagination yet | 13.75 | Not supported with pagination yet | 14.25 | Not supported with pagination yet | 23.25 | Not supported with pagination yet | 24.75 | Not supported with pagination yet | 3 | Konkour_EN | en | konkour |
19 | 20 | For how many integer values of \(m\) are both roots of the equation \(2x^{2}+7x+m=0\) greater than \(-3\)? | Not supported with pagination yet | 4 | Not supported with pagination yet | 3 | Not supported with pagination yet | 1 | Not supported with pagination yet | 0 | Not supported with pagination yet | 2 | Konkour_EN | en | konkour |
20 | 21 | In the figure given, what is the length of the diagonal of the shaded square? | \(2.5\sqrt{2}\) | Not supported with pagination yet | \(3.5\sqrt{2}\) | Not supported with pagination yet | \(\frac{9}{2\sqrt{2}}\) | Not supported with pagination yet | \(\frac{9}{\sqrt{2}}\) | Not supported with pagination yet | 3 | Konkour_EN | en | konkour | |
21 | 22 | How many points of intersection does the graph of \(f(x)=\sqrt{\,1-\sqrt{1+x}\,}\) have with its inverse function? | Not supported with pagination yet | 4 | Not supported with pagination yet | 3 | Not supported with pagination yet | 2 | Not supported with pagination yet | 1 | Not supported with pagination yet | 4 | Konkour_EN | en | konkour |
22 | 23 | Which is the graph of the function $y = -\lvert x - 1 \rvert + 2$? | Not supported with pagination yet | 3 | Konkour_EN | en | konkour | ||||||||
23 | 24 | How many critical points does the function $y = \lvert f(x) \rvert$ have, where $f(x) = x(\lvert x \rvert + 3)$? | Not supported with pagination yet | 5 | Not supported with pagination yet | 3 | Not supported with pagination yet | 1 | Not supported with pagination yet | 0 | Not supported with pagination yet | 3 | Konkour_EN | en | konkour |
24 | 25 | The function $y = a + 2^{\,b - x}$ is given. Find the value of $b - \log_2 (6)$. | 1 | Not supported with pagination yet | 2 | Not supported with pagination yet | -1 | Not supported with pagination yet | -2 | Not supported with pagination yet | 3 | Konkour_EN | en | konkour | |
25 | 26 | How many distinct real roots does the equation $(x^2 - 2x)^2 - (x^2 - 2x) = 2$ have? | Not supported with pagination yet | 1 | Not supported with pagination yet | 2 | Not supported with pagination yet | 3 | Not supported with pagination yet | 4 | Not supported with pagination yet | 3 | Konkour_EN | en | konkour |
26 | 27 | What is the area of the region bounded by the graphs of $y = |x|$ and $y = 5 - |x - 1|$? | Not supported with pagination yet | 8 | Not supported with pagination yet | 9 | Not supported with pagination yet | 10 | Not supported with pagination yet | 12 | Not supported with pagination yet | 4 | Konkour_EN | en | konkour |
27 | 28 | If $f(x)=x+|x|$ and $g(x)=|x+1|+1,$ then the range of $\left(\frac{f}{g}\right)(x)$ is which of the following? | Not supported with pagination yet | \([0, 1)\) | Not supported with pagination yet | \([0, 2)\) | Not supported with pagination yet | \([0, +\infty)\) | Not supported with pagination yet | \([1, +\infty)\) | Not supported with pagination yet | 2 | Konkour_EN | en | konkour |
28 | 29 | All solutions of the equation $\sqrt{\sin x}=\sqrt{\cos x}$ are which of the following? | Not supported with pagination yet | $2k\pi+\frac{\pi}{4}$ | Not supported with pagination yet | $k\pi+\frac{\pi}{4}$ | Not supported with pagination yet | $2k\pi$ | Not supported with pagination yet | $\frac{k \pi}{2}+\frac{\pi}{4}$ | Not supported with pagination yet | 1 | Konkour_EN | en | konkour |
29 | 30 | If the graph of the function f is as shown, which of the following is the graph of $y = \frac{2 x}{f(x)}$ near $x = a$? | 1 | Konkour_EN | en | konkour | |||||||||
30 | 31 | If the graph of the function $y=f(x)$ is as shown, which of the following is the graph of $y=f^{'}(x)$? | 2 | Konkour_EN | en | konkour | |||||||||
31 | 32 | How many relative extrema does the function $y=\sqrt[3]{x^3-4x^2}$ have? | Not supported with pagination yet | 0 | Not supported with pagination yet | 1 | Not supported with pagination yet | 2 | Not supported with pagination yet | 3 | Not supported with pagination yet | 3 | Konkour_EN | en | konkour |
32 | 33 | The graph of the function $y=-x^{2}+2x+5$ is first translated 3 units in the positive $x$-direction and then 2 units in the negative $y$-direction; for which interval is the new graph above the bisector of the first quadrant? | Not supported with pagination yet | (3, 4) | Not supported with pagination yet | (2, 5) | Not supported with pagination yet | (3, 5) | Not supported with pagination yet | (2, 6) | Not supported with pagination yet | 1 | Konkour_EN | en | konkour |
33 | 34 | Which of the following is the sum of the solutions of the trigonometric equation $\sin^3 x+\cos^3 x=1-\frac{1}{2}\sin 2x$ on the interval $[0,2\pi]$? | Not supported with pagination yet | $\frac{5\pi}{2}$ | Not supported with pagination yet | $\frac{7\pi}{2}$ | Not supported with pagination yet | $2\pi$ | Not supported with pagination yet | $3\pi$ | Not supported with pagination yet | 1 | Konkour_EN | en | konkour |
34 | 35 | What is the distance of the absolute minimum point of the function $f(x)=\frac{x^2+2x}{(x-1)^2}$ from its vertical asymptote? | Not supported with pagination yet | 1 | Not supported with pagination yet | 4/3 | Not supported with pagination yet | 3/2 | Not supported with pagination yet | 2 | Not supported with pagination yet | 3 | Konkour_EN | en | konkour |
35 | 36 | What is the area of the region bounded by the graphs of the two functions $y=\frac{1}{2}x+2$ and $y=\sqrt{x^{2}-4x+4}$? | Not supported with pagination yet | 8 | Not supported with pagination yet | 9 | Not supported with pagination yet | 10 | Not supported with pagination yet | 12 | Not supported with pagination yet | 4 | Konkour_EN | en | konkour |
36 | 37 | Which line is the axis of symmetry between the original graph of $f(x)=\sqrt{x}$ and the graph obtained by reflecting it across the $y$-axis and then shifting it 4 units to the right? | Not supported with pagination yet | x = 1 | Not supported with pagination yet | x = 1.5 | Not supported with pagination yet | x = 2 | Not supported with pagination yet | x = 2.5 | Not supported with pagination yet | 3 | Konkour_EN | en | konkour |
37 | 38 | Which of the following is the sum of the solutions of the trigonometric equation $\tan(3x)\tan(x)=1$ on the interval $[\pi,2\pi]$? | Not supported with pagination yet | $5\pi$ | Not supported with pagination yet | $6\pi$ | Not supported with pagination yet | $\frac{9\pi}{2}$ | Not supported with pagination yet | $\frac{11\pi}{2}$ | Not supported with pagination yet | 2 | Konkour_EN | en | konkour |
38 | 39 | If $\tan\!\left(\frac{\alpha}{2}\right)=\frac{1}{4}$, then which of the following is the value of $\frac{\tan(\alpha)-\sin(\alpha)}{\sin(\alpha)-\cos(\alpha)}$? | Not supported with pagination yet | $-\frac{91}{105}$ | Not supported with pagination yet | $-\frac{16}{105}$ | Not supported with pagination yet | $\frac{16}{105}$ | Not supported with pagination yet | $\frac{91}{105}$ | Not supported with pagination yet | 2 | Konkour_EN | en | konkour |
39 | 40 | Which of the following is the maximum element of the solution set $A$ of the trigonometric equation $(1+\cos(2\alpha))(1+\cos(4\alpha))(1+\cos(8\alpha))=\frac{1}{8}$ on the interval $[0,\pi]$? | Not supported with pagination yet | $\frac{5}{7}\pi$ | Not supported with pagination yet | $\frac{6}{7}\pi$ | Not supported with pagination yet | $\frac{7}{9}\pi$ | Not supported with pagination yet | $\frac{8}{9}\pi$ | Not supported with pagination yet | 4 | Konkour_EN | en | konkour |
40 | 41 | Suppose the range of the function $f(x)=2^{\sqrt[3]{9\cos^2(x)-1}}-2^{\sqrt[3]{1-9\cos^2(x)}}$ is the interval $[a,b]$; what is the value of $b-a$? | Not supported with pagination yet | $\frac{9}{4}$ | Not supported with pagination yet | $\frac{15}{4}$ | Not supported with pagination yet | $\frac{9}{2}$ | Not supported with pagination yet | $\frac{21}{4}$ | Not supported with pagination yet | 4 | Konkour_EN | en | konkour |
41 | 42 | Consider the intervals on which the function $f(x)=\frac{x^{4}}{x^{3}-8}$ is strictly decreasing; which of the following is the minimum length of these intervals? | Not supported with pagination yet | 2 | Not supported with pagination yet | $\sqrt[3]{4}-1$ | Not supported with pagination yet | $2\sqrt[3]{4}$ | Not supported with pagination yet | $2(\sqrt[3]{4}-1)$ | Not supported with pagination yet | 4 | Konkour_EN | en | konkour |
42 | 43 | The function $f(x)=x^{2}\sqrt{x^{2}}$ is decreasing on an interval; which of the following is the formula for the inverse function on that interval? | Not supported with pagination yet | $-\sqrt{x^{3}},\ x\le 0$ | Not supported with pagination yet | $-\sqrt[3]{x},\ x\le 0$ | Not supported with pagination yet | $-\sqrt{x^{3}},\ x\ge 0$ | Not supported with pagination yet | $-\sqrt[3]{x},\ x\ge 0$ | Not supported with pagination yet | 4 | Konkour_EN | en | konkour |
43 | 44 | Which of the following is the sum of the solutions of the trigonometric equation $\sin x+\sqrt{3}\cos x=\sqrt{2}$ on the interval $[-\pi,2\pi]$? | Not supported with pagination yet | $\frac{\pi}{3}$ | Not supported with pagination yet | $\frac{7\pi}{3}$ | Not supported with pagination yet | $\frac{9\pi}{4}$ | Not supported with pagination yet | $\frac{11\pi}{6}$ | Not supported with pagination yet | 3 | Konkour_EN | en | konkour |
44 | 45 | At the point of intersection of the graphs $f(x)=\sin x+\frac{1}{2}\cos x$ and $g(x)=\frac{3}{2}\sin x$ on the interval $[0,\pi]$, a tangent line to the graph of $f(x)$ is drawn; at which point does this line intersect the $x$-axis? | Not supported with pagination yet | $\frac{\pi}{4}-1$ | Not supported with pagination yet | $\frac{\pi}{4}-3$ | Not supported with pagination yet | $\frac{\pi}{4}+\frac{1}{8}$ | Not supported with pagination yet | $\frac{\pi}{4}+\frac{3}{8}$ | Not supported with pagination yet | 2 | Konkour_EN | en | konkour |
45 | 46 | A parabola passes through the points $(1,a)$ and $(-2,a)$, is tangent to the line $y+3=0$, and passes through all four quadrants; if the distance from its intersection point with the $y$-axis to the origin is 2 units, then $a$ is which of the following? | Not supported with pagination yet | 20 | Not supported with pagination yet | -20 | Not supported with pagination yet | -6 | Not supported with pagination yet | 6 | Not supported with pagination yet | 4 | Konkour_EN | en | konkour |
46 | 47 | The function $y=\left|2x+2\right|-\left|\frac{x}{2}-2\right|$ is decreasing on an interval; which of the following is the formula for its inverse function on that interval? | Not supported with pagination yet | $-\frac{2}{3}x-\frac{8}{3},\ x\ge -\frac{5}{2}$ | Not supported with pagination yet | $-\frac{2}{3}x+\frac{8}{3},\ x\ge -\frac{5}{2}$ | Not supported with pagination yet | $-\frac{2}{3}x-\frac{8}{3},\ x\ge -\frac{3}{2}$ | Not supported with pagination yet | $-\frac{2}{3}x+\frac{8}{3},\ x\ge -\frac{3}{2}$ | Not supported with pagination yet | 1 | Konkour_EN | en | konkour |
47 | 48 | How many solutions does the equation $\sin x \cos x + \frac{1}{2}\sin^{2}x = \frac{1}{2}\cos^{2}x$ have on the interval $[-\pi,\pi]$? | Not supported with pagination yet | 3 | Not supported with pagination yet | 4 | Not supported with pagination yet | 6 | Not supported with pagination yet | 8 | Not supported with pagination yet | 2 | Konkour_EN | en | konkour |
48 | 49 | At the intersection point of the graphs $f(x)=-\sqrt[3]{x}$ and $g(x)=\sqrt[3]{x^2}-2$ in the second quadrant of the coordinate plane, a tangent line to $g(x)$ is drawn; what is the distance from the line's point of intersection with the $y$-axis to the origin? | Not supported with pagination yet | (1)\; $\frac{5}{3}$ | Not supported with pagination yet | (2)\; $\frac{4}{3}$ | Not supported with pagination yet | (3)\; $\frac{2}{3}$ | Not supported with pagination yet | (4)\; $\frac{1}{3}$ | Not supported with pagination yet | 3 | Konkour_EN | en | konkour |
49 | 50 | The point $A(-1,2)$ is a relative minimum of the function $y=ax^{2}+b|x|$; what is the value of $ab$? | Not supported with pagination yet | 1 | Not supported with pagination yet | $\frac{8}{9}$ | Not supported with pagination yet | $-\frac{1}{4}$ | Not supported with pagination yet | -8 | Not supported with pagination yet | 4 | Konkour_EN | en | konkour |
50 | 51 | For how many integer values of $x$ does the graph of $y=\frac{2}{x^{2}-3x+2}$ lie between the two horizontal lines $y=0$ and $y=-2$? | Not supported with pagination yet | 1 | Not supported with pagination yet | 3 | Not supported with pagination yet | 4 | Not supported with pagination yet | 0 | Not supported with pagination yet | 4 | Konkour_EN | en | konkour |
51 | 52 | Let $f(x)=\log(2x-5)$ and $g(x)=x+\sqrt{2x-4}$. If $y=g^{-1}(f^{-1}(x))$, then at which point does the graph intersect the $y$-axis? | Not supported with pagination yet | $4-\sqrt{2}$ | Not supported with pagination yet | $4-\sqrt{3}$ | Not supported with pagination yet | $4+\sqrt{2}$ | Not supported with pagination yet | $4+\sqrt{3}$ | Not supported with pagination yet | 2 | Konkour_EN | en | konkour |
52 | 53 | How many real solutions does the equation $x\sin x - 1 = 0$ have on the interval $[-\pi,\pi]$? | Not supported with pagination yet | 2 | Not supported with pagination yet | 4 | Not supported with pagination yet | 5 | Not supported with pagination yet | 6 | Not supported with pagination yet | 2 | Konkour_EN | en | konkour |
53 | 54 | On the interval $(a,b)$, the graph of $y=\sqrt{x+3}$ lies above the graph of $f(x)=|x-1|-2$; what is the maximum value of $b-a$? | Not supported with pagination yet | 6 | Not supported with pagination yet | 7 | Not supported with pagination yet | 8 | Not supported with pagination yet | 9 | Not supported with pagination yet | 3 | Konkour_EN | en | konkour |
54 | 55 | If $f(x)=\sqrt{2x - x^{2}}$, which of the following is the domain of $f(3-x)$? | Not supported with pagination yet | [0, 2] | Not supported with pagination yet | [0, 3] | Not supported with pagination yet | [1, 2] | Not supported with pagination yet | [1, 3] | Not supported with pagination yet | 4 | Konkour_EN | en | konkour |
55 | 56 | The critical points on the graph of $f(x)=(x-1)\left|x^{2}+x-2\right|$ form the three vertices of a triangle; what is the area of this triangle? | Not supported with pagination yet | 4 | Not supported with pagination yet | 4.5 | Not supported with pagination yet | 6 | Not supported with pagination yet | 8 | Not supported with pagination yet | 3 | Konkour_EN | en | konkour |
56 | 57 | For which values of $m$ does the graph of $y=(m+2)x^{2}+3x+1-m$ intersect the $x$-axis at two points on opposite sides of the origin? | Not supported with pagination yet | $m > 1 \text{ or } m < -2$ | Not supported with pagination yet | $-2 < m < 1$ | Not supported with pagination yet | Only $m < -2$ | Not supported with pagination yet | Only $m > 1$ | Not supported with pagination yet | 1 | Konkour_EN | en | konkour |
57 | 58 | If the solution set of the inequality $|x^2 - 2| < |x + 1| - 1$ is the interval $(a, b)$, what is the midpoint of this interval? | Not supported with pagination yet | 0.5 | Not supported with pagination yet | 1 | Not supported with pagination yet | 1.5 | Not supported with pagination yet | 2 | Not supported with pagination yet | 3 | Konkour_EN | en | konkour |
58 | 59 | The graph of the function $y = x(x^2 - 3x + 3) - 2$ is which of the following? | Not supported with pagination yet | 2 | Konkour_EN | en | konkour | ||||||||
59 | 60 | Given the functions $f(x) = x - \sqrt{2x}$ and $g(x) = \sqrt{2x} + x$, the graph of the function $y = (f . g)(x)$ does not pass through which quadrant(s)? | Not supported with pagination yet | Only the second quadrant | Not supported with pagination yet | Only the third quadrant | Not supported with pagination yet | The second and third quadrants | Not supported with pagination yet | The first and third quadrants | Not supported with pagination yet | 3 | Konkour_EN | en | konkour |
60 | 61 | If $f(x) = \sqrt{2 - x}$ and $g(x) = \log\left(x^2 - 15x\right)$, what is the domain of the function $f \circ g$? | Not supported with pagination yet | $(0,5]\cup[20,25)$ | Not supported with pagination yet | $[-5,0)\cup(15,20]$ | Not supported with pagination yet | (15, 20] | Not supported with pagination yet | [-5, 0) | Not supported with pagination yet | 2 | Konkour_EN | en | konkour |
61 | 62 | The sum of the solutions of the trigonometric equation $\sin\left(x+\frac{\pi}{8}\right)+\cos\left(x-\frac{3\pi}{8}\right)=1$ over the interval $[0,2\pi]$ is equal to which of the following? | Not supported with pagination yet | $\frac{3\pi}{4}$ | Not supported with pagination yet | $\frac{5\pi}{4}$ | Not supported with pagination yet | $\frac{3\pi}{2}$ | Not supported with pagination yet | $\frac{7\pi}{4}$ | Not supported with pagination yet | 1 | Konkour_EN | en | konkour |
62 | 63 | The limit of the expression $\sin\left(\frac{x}{2}\right)\lfloor\cos\left(\frac{x}{2}\right)\rfloor-\cos x\lfloor\sin(2x)\rfloor$ as $x \to \pi$ is which of the following? (Here \(\lfloor\ \rfloor\) denotes the greatest-integer (floor) function.) | Not supported with pagination yet | -1 | Not supported with pagination yet | 0 | Not supported with pagination yet | 1 | Not supported with pagination yet | The limit does not exist. | Not supported with pagination yet | 1 | Konkour_EN | en | konkour |
63 | 64 | How many asymptotes does the function $y=\frac{x}{x-\lfloor x\rfloor\ -1}$ have on the interval $(-1,3]$? (Here \(\lfloor\ \rfloor\) denotes the greatest-integer (floor) function.) | Not supported with pagination yet | 2 | Not supported with pagination yet | 3 | Not supported with pagination yet | 4 | Not supported with pagination yet | 5 | Not supported with pagination yet | 2 | Konkour_EN | en | konkour |
64 | 65 | What is the $x$-coordinate of the relative maximum point of the function $y = (x-1)^2 \sqrt[3]{x^2}$? | Not supported with pagination yet | $\frac{1}{4}$ | Not supported with pagination yet | $\frac{1}{3}$ | Not supported with pagination yet | $\frac{1}{2}$ | Not supported with pagination yet | $\frac{2}{3}$ | Not supported with pagination yet | 1 | Konkour_EN | en | konkour |
65 | 66 | For which values of \(a\) is the graph of the function \(y=(1-a)x^{2}+2\sqrt{6}\,x-a\) always above the \(x\)-axis? | Not supported with pagination yet | \(a<1\) | Not supported with pagination yet | \(a<-2\) | Not supported with pagination yet | \(a>3\) | Not supported with pagination yet | \(-2<a<1\) | Not supported with pagination yet | 2 | Konkour_EN | en | konkour |
66 | 68 | The graphs of the two functions \(f(x)=4^{x}\) and \(g(x)=\left(\frac{1}{2}\right)^{2x}+\frac{3}{2}\) intersect at a point \(A\). What is the distance between \(A\) and the point \(\left(-\frac{1}{2},\,1\right)\)? | Not supported with pagination yet | 1 | Not supported with pagination yet | \(\sqrt{2}\) | Not supported with pagination yet | 2 | Not supported with pagination yet | \(\sqrt{5}\) | Not supported with pagination yet | 2 | Konkour_EN | en | konkour |
67 | 69 | How many solutions does the equation \(1+\cos x=\sin x+\sin 2x\) have in the interval \([0,2\pi]\)? | Not supported with pagination yet | 2 | Not supported with pagination yet | 3 | Not supported with pagination yet | 4 | Not supported with pagination yet | 0 | Not supported with pagination yet | 3 | Konkour_EN | en | konkour |
68 | 70 | Evaluate \(\lim_{x\to 0^{+}} \frac{1-\cos\sqrt{x}}{x}\). | Not supported with pagination yet | -1 | Not supported with pagination yet | \(-\frac{1}{2}\) | Not supported with pagination yet | \(\frac{1}{2}\) | Not supported with pagination yet | 1 | Not supported with pagination yet | 3 | Konkour_EN | en | konkour |
69 | 71 | In the graph of the function \(y=\frac{-2x^{2}+3x+5}{x^{2}-2x+1}\), what is the distance between the intersection point of its two asymptotes and the point \((-2,-6)\)? | Not supported with pagination yet | 5 | Not supported with pagination yet | \(2\sqrt{5}\) | Not supported with pagination yet | \(5\sqrt{2}\) | Not supported with pagination yet | \(\sqrt{5}\) | Not supported with pagination yet | 1 | Konkour_EN | en | konkour |
70 | 72 | What is the maximum value of the function \(y=\frac{x^{3}}{3}-\frac{x^{2}}{2}-2x+1\) on the interval \([-2,2]\)? | Not supported with pagination yet | 2 | Not supported with pagination yet | \(\frac{1}{3}\) | Not supported with pagination yet | \(-\frac{7}{3}\) | Not supported with pagination yet | \(\frac{13}{6}\) | Not supported with pagination yet | 4 | Konkour_EN | en | konkour |
71 | 73 | For the function \(f(x)=\sin^{2}x-2\sin x\) on the interval \(x\in[0,2\pi]\), in which interval is \(f\) increasing and its concavity downward? | Not supported with pagination yet | \(\left(\frac{7\pi}{6},\frac{3\pi}{2}\right)\) | Not supported with pagination yet | \(\left(\frac{3\pi}{2},\frac{11\pi}{6}\right)\) | Not supported with pagination yet | \(\left(\frac{\pi}{2},\frac{5\pi}{6}\right)\) | Not supported with pagination yet | \(\left(\frac{\pi}{2},\frac{7\pi}{6}\right)\) | Not supported with pagination yet | 1 | Konkour_EN | en | konkour |
72 | 74 | If \(x=4\) is one of the solutions of the equation \(x+a=\sqrt{5x-x^{2}}\), then what is its other solution? | Not supported with pagination yet | \(\frac{1}{2}\) | Not supported with pagination yet | 2 | Not supported with pagination yet | 3 | Not supported with pagination yet | There is no other solution. | Not supported with pagination yet | 4 | Konkour_EN | en | konkour |
73 | 75 | For which values of \(a\) does the graph of the function \(f(x)=ax^{2}+(a+3)x-1\) intersect the \(x\)-axis at two points with negative \(x\)-coordinates? | Not supported with pagination yet | \(a<-9\) | Not supported with pagination yet | \(a<-3\) | Not supported with pagination yet | \(a>-1\) | Not supported with pagination yet | \(-3<a<0\) | Not supported with pagination yet | 1 | Konkour_EN | en | konkour |
74 | 76 | If \(f(x)=2-|x+1|\) and \(g(x)=x+|x|\), then the range of \(\left(\frac{f}{g}\right)(x)\) is which? | Not supported with pagination yet | \((-\infty,\frac{1}{2})\) | Not supported with pagination yet | \((-1,+\infty)\) | Not supported with pagination yet | \((-\frac{1}{2},+\infty)\) | Not supported with pagination yet | \((0,+\infty)\) | Not supported with pagination yet | 3 | Konkour_EN | en | konkour |
75 | 77 | In the given figure, the graph shown is that of \(f(x)\). What is the domain of the implicit function \(y=\sqrt{(x+1)f(x)}\)? | \([-3,2]\) | Not supported with pagination yet | \([-1,+\infty)\) | Not supported with pagination yet | \((-\infty,-1]\) | Not supported with pagination yet | \(\mathbb{R}\setminus(-3,2)\) | Not supported with pagination yet | 4 | Konkour_EN | en | konkour | |
76 | 78 | Two functions \(f(x)=\frac{x+1}{x+\sqrt{x}}\) and \(g(x)=\frac{1-x}{x-\sqrt{x}}\) are defined. How many asymptotes does the graph of \((f+g)(x)\) have? | Not supported with pagination yet | 0 | Not supported with pagination yet | 1 | Not supported with pagination yet | 2 | Not supported with pagination yet | 3 | Not supported with pagination yet | 2 | Konkour_EN | en | konkour |
77 | 79 | How many relative extremum points does the function \(y=\frac{|x|}{1+x^{2}}\) have? | Not supported with pagination yet | 2 | Not supported with pagination yet | 3 | Not supported with pagination yet | 1 | Not supported with pagination yet | 4 | Not supported with pagination yet | 2 | Konkour_EN | en | konkour |
78 | 80 | For which values of \(m\) is the parabola with equation \(y=(1-m)x^{2}+2(m-3)x-1\) always below the \(x\)-axis? | Not supported with pagination yet | \(1<m<5\) | Not supported with pagination yet | \(2<m<5\) | Not supported with pagination yet | \(2<m<4\) | Not supported with pagination yet | \(2<m<6\) | Not supported with pagination yet | 2 | Konkour_EN | en | konkour |
79 | 81 | The graph of the function \(y = x^2 - x - 3\) is shifted \(2\) units toward the negative \(x\)-direction, and then \(9\) units toward the negative \(y\)-direction. In which interval is the new graph below the \(x\)-axis? | Not supported with pagination yet | (-5, 2) | Not supported with pagination yet | (-5, 3) | Not supported with pagination yet | (-2, 3) | Not supported with pagination yet | (-2, 5) | Not supported with pagination yet | 1 | Konkour_EN | en | konkour |
80 | 82 | What is the sum of the solutions of the equation \(\lvert 2x-1\rvert+\lvert x+2\rvert=3\)? | Not supported with pagination yet | \(-\frac{2}{3}\) | Not supported with pagination yet | \(\frac{2}{3}\) | Not supported with pagination yet | 1 | Not supported with pagination yet | \(\frac{4}{3}\) | Not supported with pagination yet | 2 | Konkour_EN | en | konkour |
81 | 83 | Evaluate \(\lim_{x\to 1^{+}} \frac{\sin^{2}(\pi x)}{\lfloor x\rfloor + \cos(\pi x)}\) (Here \(\lfloor\ \rfloor\) denotes the greatest-integer (floor) function.). | Not supported with pagination yet | 1 | Not supported with pagination yet | 2 | Not supported with pagination yet | \(\pi\) | Not supported with pagination yet | \(2\pi\) | Not supported with pagination yet | 2 | Konkour_EN | en | konkour |
82 | 84 | What is the period of the function \(f(x)=\tan(\pi x)-\cot(\pi x)\)? | Not supported with pagination yet | \(\frac{1}{2}\) | Not supported with pagination yet | 1 | Not supported with pagination yet | 2 | Not supported with pagination yet | \(\pi\) | Not supported with pagination yet | 1 | Konkour_EN | en | konkour |
83 | 85 | What is the sum of the solutions of the trigonometric equation \(\sin^{4}x+\cos^{4}x=\frac{1}{2}\) on the interval \([0,2\pi]\)? | Not supported with pagination yet | \(\frac{5\pi}{2}\) | Not supported with pagination yet | \(3\pi\) | Not supported with pagination yet | \(\frac{7\pi}{2}\) | Not supported with pagination yet | \(4\pi\) | Not supported with pagination yet | 4 | Konkour_EN | en | konkour |
84 | 86 | The graph of the function \(y=\frac{2x^{2}-x-2}{x^{2}+2x}\), relative to its horizontal asymptote, has which behavior at infinity? | Not supported with pagination yet | 1 | Konkour_EN | en | konkour | ||||||||
85 | 87 | At how many points is the function \(f(x)=\frac{\lvert x^{3}-2x\rvert}{x}\) not differentiable? | Not supported with pagination yet | 1 | Not supported with pagination yet | 2 | Not supported with pagination yet | 3 | Not supported with pagination yet | 4 | Not supported with pagination yet | 3 | Konkour_EN | en | konkour |
86 | 88 | What is the distance of the relative maximum point of the function \(f(x)=\frac{2x-x^{2}}{(x+1)^{2}}\) from its horizontal asymptote? | Not supported with pagination yet | \(\frac{2}{3}\) | Not supported with pagination yet | 1 | Not supported with pagination yet | \(\frac{4}{3}\) | Not supported with pagination yet | \(\frac{3}{2}\) | Not supported with pagination yet | 3 | Konkour_EN | en | konkour |
87 | 89 | The graphs of the two functions \(y=\lvert x-2\rvert+\lvert x+1\rvert\) and \(y=x+7\) intersect at two points \(A\) and \(B\). What is the length of the segment \(\overline{AB}\)? | Not supported with pagination yet | \(8\sqrt{2}\) | Not supported with pagination yet | 12 | Not supported with pagination yet | 13 | Not supported with pagination yet | \(10\sqrt{2}\) | Not supported with pagination yet | 4 | Konkour_EN | en | konkour |
88 | 90 | First, we draw the graph of the function \(f(x)=(x-1)^{2}\) reflected about the origin. Then we shift the resulting curve upward by 4 units. What are the \(x\)-coordinates of the intersection points of the final curve with the original curve? | Not supported with pagination yet | 0, 2 | Not supported with pagination yet | -1, 1 | Not supported with pagination yet | -1, 2 | Not supported with pagination yet | -2, 1 | Not supported with pagination yet | 2 | Konkour_EN | en | konkour |
89 | 91 | The solutions of the trigonometric equation \(\sin\!\left(x+\frac{\pi}{6}\right)+\cos\!\left(x+\frac{\pi}{3}\right)=\cos2x\) are which of the following? | Not supported with pagination yet | \(x=\frac{2k\pi}{3},\ k\in\mathbb{Z}\) | Not supported with pagination yet | \(x=\frac{k\pi}{3},\ k\in\mathbb{Z}\) | Not supported with pagination yet | \(x=2k\pi\pm\frac{\pi}{3},\ k\in\mathbb{Z}\) | Not supported with pagination yet | \(x=k\pi\pm\frac{\pi}{3},\ k\in\mathbb{Z}\) | Not supported with pagination yet | 1 | Konkour_EN | en | konkour |
90 | 92 | Evaluate \(\lim_{x\to 0^-}\frac{\sqrt{2+3x}-\sqrt{2-x}}{\sqrt{1-\cos x}}\). | Not supported with pagination yet | -2 | Not supported with pagination yet | \(-\sqrt{2}\) | Not supported with pagination yet | \(\sqrt{2}\) | Not supported with pagination yet | 2 | Not supported with pagination yet | 1 | Konkour_EN | en | konkour |
91 | 93 | What is the sum of the solutions of the equation \(\log_{2}(4^{x}+15)=x+3\)? | Not supported with pagination yet | 8 | Not supported with pagination yet | 15 | Not supported with pagination yet | \(\log_{2}15\) | Not supported with pagination yet | \(\log_{4}15\) | Not supported with pagination yet | 3 | Konkour_EN | en | konkour |
92 | 94 | How many solutions does the equation \(\sqrt{x+\sqrt{-x^{3}+4x^{2}+25x-100}}+\sqrt{x^{2}+\sqrt{-x^{2}+6x-8}}=x+2\) have? | Not supported with pagination yet | 3 | Not supported with pagination yet | 2 | Not supported with pagination yet | 1 | Not supported with pagination yet | 0 | Not supported with pagination yet | 3 | Konkour_EN | en | konkour |
93 | 95 | What is the sum of the solutions of the trigonometric equation \(2\sin(x)\cos(2x)+\sin(x)=1\) on the interval \([0,2\pi]\)? | Not supported with pagination yet | \(2\pi\) | Not supported with pagination yet | \(\frac{5\pi}{2}\) | Not supported with pagination yet | \(3\pi\) | Not supported with pagination yet | \(\frac{7\pi}{2}\) | Not supported with pagination yet | 2 | Konkour_EN | en | konkour |
94 | 96 | At the intersection point of the graph of \(f(x)=\sqrt{x}+2\) and its inverse \(f^{-1}\), we draw two tangent lines: one to \(f\) and one to \(f^{-1}\). If \(\alpha\) is the acute angle between these two tangent lines, what is the value of \(\sin(2\alpha)\)? | Not supported with pagination yet | \(\frac{7}{15}\) | Not supported with pagination yet | \(\frac{8}{15}\) | Not supported with pagination yet | \(\frac{225}{289}\) | Not supported with pagination yet | \(\frac{240}{289}\) | Not supported with pagination yet | 4 | Konkour_EN | en | konkour |
95 | 97 | Which set of real numbers is the interval on which the function \(f(x)=3\sqrt[3]{x}+\lvert x\rvert\) is increasing? | Not supported with pagination yet | \([-1,\infty)\) | Not supported with pagination yet | \((-\infty,\infty)\) | Not supported with pagination yet | \([-1,0)\cup(0,\infty)\) | Not supported with pagination yet | \([-3\sqrt{3},0]\) | Not supported with pagination yet | 1 | Konkour_EN | en | konkour |
96 | 98 | How many intervals are there on which the function \(f(x)=\frac{x^{4}-3}{x^{2}-2}\), with \(x\in(-2,2)\), is strictly decreasing? | Not supported with pagination yet | 2 | Not supported with pagination yet | 3 | Not supported with pagination yet | 4 | Not supported with pagination yet | 5 | Not supported with pagination yet | 3 | Konkour_EN | en | konkour |
97 | 99 | Suppose \(A\) and \(B\) are the local minima, and \(C\) and \(D\) are the inflection points, of the function \(f(x)=x^{4}-6x^{2}+5\). What is the angle between the segments \(\overline{AB}\) and \(\overline{CD}\)? | Not supported with pagination yet | \(0^\circ\) | Not supported with pagination yet | \(30^\circ\) | Not supported with pagination yet | \(45^\circ\) | Not supported with pagination yet | \(60^\circ\) | Not supported with pagination yet | 1 | Konkour_EN | en | konkour |
98 | 100 | A function with formula \(y=\sqrt{(x+1)^{2}}-\lvert 3x-6\rvert\) is decreasing on some interval. Which of the following is the formula of the inverse function on that interval? | Not supported with pagination yet | \(y=-\frac{1}{2}x-7,\; x\ge 2\) | Not supported with pagination yet | \(y=-\frac{1}{2}x+\frac{7}{2},\; x\le 3\) | Not supported with pagination yet | \(y=-2x+14,\; x\le 3\) | Not supported with pagination yet | \(y=-2x-\frac{14}{3},\; x\ge 2\) | Not supported with pagination yet | 2 | Konkour_EN | en | konkour |
99 | 101 | The graphs of the two functions \(y=\lvert x+2\rvert+\lvert x-1\rvert\) and \(3y+x=17\) intersect at two points \(A\) and \(B\). What is the length of the segment \(\overline{AB}\)? | Not supported with pagination yet | \(2\sqrt{10}\) | Not supported with pagination yet | \(4\sqrt{5}\) | Not supported with pagination yet | \(2\sqrt{2}\) | Not supported with pagination yet | \(4\sqrt{3}\) | Not supported with pagination yet | 1 | Konkour_EN | en | konkour |
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VAMPS: Visual-Assisted Mathematical Problem Solving Benchmark
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