12th
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Mathematics

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Doni Saputra

4 years

Mathematics

12th -

University

Calculus

Doni Saputra

187
plays

12 questions

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1. Multiple Choice
5 minutes
1 pt
Find the gradient of the curve with equation
2x² − 4xy + 3y² = 3, at the point (2, 1).
2
3
4
5
2. Multiple Choice
5 minutes
1 pt
The equation of a curve is x²y + y² = 6x
the equation of the tangent to the curve at the point with coordinates (1, 2)
3x – 5y + 8 = 0
2x – 5y + 8 = 0
2x – 5y - 8 = 0
3x – 5y - 8 = 0
3. Multiple Choice
5 minutes
1 pt
A solid rectangular block has a square base of side x cm. The height of the block is h cm and the total surface area of the block is 96 cm^2.Find the stationary value of V
V = 84
V = 74
V = 64
V = 54
4. Multiple Choice
5 minutes
1 pt
The diagram shows the curve y = (x − 2)² and the line y + 2x = 7, which intersect at points A and B. Find the area of the shaded region.
$10\ \frac{5}{7}$
$10\ \frac{3}{4\ }$
$10\ \frac{1}{3\ }$
$10\ \frac{2}{3}$
5. Multiple Choice
5 minutes
1 pt
$\int_{ }^{ }\left(x^{3\ }+\frac{1}{x^3}\right)\ dx$
$\frac{x^{4\ }}{4}-\frac{x^{-2}}{2\ }+c$
$\frac{x^{4\ }}{4}+\frac{x^{-2}}{2}+c$
$\frac{x^4}{4}-\frac{x^2}{2\ }+c$
$\frac{-x^4}{4}+\frac{x^{2\ }}{2\ }+c$
6. Multiple Choice
5 minutes
1 pt
the equation of the curve $y=\frac{4}{3x-4}$
and P(2, 2) is a point on the curve. The equation of the tangent to the curve at P and the angle that this tangent makes with the x-axis respectively
y − 2 = −3(x − 2) and $108.4^o$
y − 2 = 3(x − 2) and $128.8^o$
y − 2 = −3(x + 2) and $78.3^o$
y + 2 = −3(x − 2) and $45^o$
7. Multiple Choice
5 minutes
1 pt
The diagram shows part of the curve $y=4\sqrt{x}-x$
The curve has a maximum point at M and meets the x-axis at O and A. Find the volume obtained when the shaded region is rotated through 360o about the x-axis, givingyour answer in terms of π
138.5π
137.5π
136.5π
135.5π
8. Multiple Choice
5 minutes
1 pt
The equation of a curve is $y=4\sqrt{x}+\frac{2}{\sqrt{x}}$
A point is moving along the curve in such a way that the x-coordinate is increasing at a constant rate of 0.12 units per second. Find the rate of change of the y-coordinate when x = 4
0.105
0.125
0.345
0.546
9. Multiple Choice
5 minutes
1 pt
The diagram shows part of the curve y = −x² + 8x − 10 which passes through the points A and B. The curve has a maximum point at A and the gradient of the line BA is 2. evaluate the area of the shaded region.
$9\ \frac{1}{3}$
$10\ \frac{1}{3}$
$11\ \frac{1}{3}$
$12\ \frac{1}{3}$
10. Multiple Choice
5 minutes
1 pt
A curve is such that $\frac{dy}{dx}=\frac{6}{x^2}$ and (􏰎2, 9)􏰏 is a point on the curve. Find the equation of the curve
$y=-6x^{-1}+12$
$y=6x^{-1}-12$
$y=-6x^{-2}+12$
$y=6x^{-2}+12$
11. Multiple Choice
5 minutes
1 pt
The straight line y = mx + 14 is a tangent to the curve $y=\frac{12}{x}+2$
at the point P. Find the value of the constant m and the coordinates of P
m = 3 and y = - 8
m = −3 and y = 8
m = 8 and y = - 3
m = −8 and y = 3
12. Multiple Choice
5 minutes
1 pt
The diagram shows the curve $y=\sqrt{1+4x}$
which intersects the x-axis at A and the y-axis at B. The normal to the curve at B meets the x-axis at C. the area of the shaded region
$\frac{6}{5}$
$\frac{5}{6}$
$\frac{6}{7}$
$\frac{7}{6}$
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