Math topic中文

Gradient of curve

estimation of the gradient of a curve by drawing a tangent

Practice questions

1The equation of a curve is $y = x^2 e^{2x}$ . Obtain an expression for $\dfrac{dy}{dx}$ . Find the range of values of $x$ …
2It is given that $y = x\sin x + \cos^2\left(\tfrac{x}{2}\right).$ Obtain an expression for $\dfrac{dy}{dx}$ in the form…
3The equation of a curve is given by $y = \ln \sqrt{\dfrac{3x^3}{2x-1}}$ , where $x > \tfrac{1}{2}$ . Find the coordinates…
4The variables x and y are connected by the equation $y = 2x^3 - 21x^2 + 54x$ . Some corresponding values of x and y are g…
5The variables x and y are connected by the equation $y = x + \frac{5}{x^2} - 3$ Some corresponding values of x and y are…
6The table shows some values for $y = \frac{3}{10}x^3 - x + 1$ for $-3 \le x \le 3$ . | x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |…
7Complete the table of values for $y = 2x + \dfrac{20}{x} - 15$ . | x | 1 | 2.5 | 5 | 10 | 12.5 | 15 | 20 | |---|---|---|-…
8It is given that $f''(x) = e^{-\tfrac{1}{2}x} + \dfrac{5}{(5x-9)^2}$ . Given that the x-axis is a tangent to the curve $y = f(x)$ …
9The number of bacteria in a colony doubles every hour. The colony starts with: 50 bacteria. The table below shows the nu…
10Answer the whole of this question on a piece of graph paper. The variables x and y are related by the equation $y = x^3 - 3x^2 + 1$ …
11The table of values for $y = x + \dfrac{5}{x} - 7$ is given below. | x | 0.5 | 1 | 1.5 | 2 | 3 | 4 | 5 | 6 | 7 | |---|--…
12The diagram shows the speed-time graph of a particle. Find the speed of the particle when $t = 12$ s. Answer ...m/s Find…
13The variables x and y are connected by the equation $y = \frac{1}{3}x(11 - x^2). Some corresponding values of x and y, correct to 1 decimal places, are given in the following table. Calculate the value of p. Answer p = ... On the grid opposite, draw the graph of$ …
14The variables x and y are connected by the equation $y = 2x + \dfrac{6}{x} - 7$ . Some corresponding values of x and y ar…
15The variables x and y are connected by the equation $y = \frac{3}{2}x + \frac{5}{x} - 7$ . Some corresponding values of x…
16Let $y = 9x^3 + 5x^2 - 3x + 1$ . Complete the table for $y = 9x^3 + 5x^2 - 3x + 1$ . Give your answer correct to 1 decimal…
17The variables x and y are connected by the equation $y = x^3 - 3x + 1$ . Some corresponding values of x and y are given i…
18Complete the table of values for $y = 10 - \frac{x^2}{2} - \frac{4}{x}$ . Complete the table of values for $y = 10 - \frac{x^2}{2} - \frac{4}{x}$ …
19Complete the table of values for $y = 2x + \dfrac{9}{x} - 11$ . Values are given to 1 decimal place where appropriate. |…
20The table shows some values for $y = 4 - 2x - \dfrac{5}{x}$ for $0.5 \le x \le 5.5$ . Find the value of $p$ , correct to o…
21Answer (b), (c) and (d) Complete the table of values for y = $\dfrac{x^3}{5} - x^2 + 2$ . On the grid in the next page,…
22The diagram shows part of the curve $y = x^{\tfrac{3}{2}}$ and $y = -x^{\tfrac{3}{2}}$ . The tangent meets the curve $y = x^{\tfrac{3}{2}}$ …
23The variables x and y are connected by the equation $y = \frac{x^2}{3} + \frac{3}{x} - 4$ . Some corresponding values of…
24The variables x and y are connected by the equation $y = \frac{x^3}{2} - 5x - 2$ . Some corresponding values of x and y a…
25A ball was thrown up from the top of a cliff as shown below. The height of the ball, h metre, from the sea level is meas…
26A solid cylinder of height h cm and volume V cm^3 is cut from a solid sphere of radius 7 cm. The rim of each base of the…