Math topic中文

Gradient linear

the gradient of a linear graph as the ratio of the vertical change to the horizontal change (positive and negative gradients)

Practice questions

1The diagram (not drawn to scale) shows the speed-time graph of a vehicle. The vehicle starts from rest and accelerates u…
2The diagram below shows the speed-time graph of a bus journey. The bus accelerated from rest at 1.25 m/s^2 to a speed of…
3如果一次函数 $y=kx+1(k$ 是常数， $k\neq 0)$ 的图象过点 $(-1 , 0)$ ，那么 $y$ 的值随 $x$ 的增大而___ $($ 填“增大”或“减小” $)$ ．
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 diagram below shows the speed-time graph of a car's journey. For this journey, calculate the acceleration during the…
6The diagram shows the speed-time graph of two cars, A and B. Car A, starting from rest, accelerates uniformly for 2 seco…
7The diagram shows the speed-time graph of an object over a period of 40 seconds. Calculate the deceleration of the objec…
8The variables x and y are connected by the equation $y = x + \frac{5}{x^2} - 3$ Some corresponding values of x and y are…
9The variables x and y are connected by the equation $y = \frac{x^3}{5} - 2x + 1$ . Some corresponding values of x and y a…
10The 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 |…
11Complete the table of values for $y = 2x + \dfrac{20}{x} - 15$ . | x | 1 | 2.5 | 5 | 10 | 12.5 | 15 | 20 | |---|---|---|-…
12The diagram shows the speed-time graph of a motorcyclist. The shaded area represents the distance travelled. The distanc…
13It 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 $y = f(x)$ …
14The number of bacteria in a colony doubles every hour. The colony starts with: 50 bacteria. The table below shows the nu…
15Answer the whole of this question on a piece of graph paper. The variables x and y are related by the equation $y = x^3 - 3x^2 + 1$ …
16The 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 | |---|--…
17The diagram below shows the speed-time graph of a car which starts from rest. Calculate the speed of the car after 9 sec…
18已知 $f(x)=\left\{\begin{array}{l}-{{x}^{2}}\text{+}2ax,(x\leqslant 1)\\ (2a-1)x-3a+6,(x>1)\\\end{array}\right.$ ，若 $f(x)$ …
19Nurul took 2.5 hours to travel at a constant speed from Town A to B. On her journey back, she increased her constant spe…
20The diagram shows the speed-time graph of a particle. Find the speed of the particle when $t = 12$ s. Answer ...m/s Find…
21The variables x and y are connected by the equation $y = \frac{1}{3}x(11 - x^2). Some corresponding values of x and y, correct to 1 decimal places, are given in the following table. Calculate the value of p. Answer p = ... On the grid opposite, draw the graph of$ …
22The position vector of A is $\begin{pmatrix}3\\4\end{pmatrix}$ and the position vector of B is $\begin{pmatrix}7\\10\end{pmatrix}$ …
23The speed-time graph shows the journey that Lim makes during a three-hour journey. Find the acceleration at 0815. Answer…
24The variables x and y are connected by the equation $y = \frac{3}{2}x + \frac{5}{x} - 7$ . Some corresponding values of x…
25Let $y = 9x^3 + 5x^2 - 3x + 1$ . Complete the table for $y = 9x^3 + 5x^2 - 3x + 1$ . Give your answer correct to 1 decimal…
26The variables x and y are connected by the equation $y = x^3 - 3x + 1$ . Some corresponding values of x and y are given i…
27The diagram show the speed-time graph of a car's journey between two road junctions. The shaded area represents the dist…
28Complete the table of values for $y = 10 - \frac{x^2}{2} - \frac{4}{x}$ . Complete the table of values for $y = 10 - \frac{x^2}{2} - \frac{4}{x}$ …
29The table shows experimental values of two variables, x and y, which are connected by an equation of the form $y^{n} x^{k} = 10$ …
30下图由大、小两个正方形组成，已知小正方形的边长为 6，大正方形的边长为 8，三角形 $ABC$ 的面积是 ___.
31Complete the table of values for $y = 2x + \dfrac{9}{x} - 11$ . Values are given to 1 decimal place where appropriate. |…
32The 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…
33Answer (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,…
34The diagram shows the speed-time graph for Sriya's 100 metre race during her school's sports day. In the first 5 seconds…
35The variables x and y are connected by the equation $y = \frac{x^2}{3} + \frac{3}{x} - 4$ . Some corresponding values of…
36已知抛物线 $M$ ： $y^{2}=8x$ 的焦点为 $F$ ，过 $F$ 的直线交 $M$ 于 $A$ ， $B$ 两点，若 $S_{\triangle AOB}=4\sqrt{5}(O$ 为坐标原点 $)$ ，则该直线的斜率为 $(\quad)$ …
37The variables x and y are connected by the equation $y = \frac{x^3}{2} - 5x - 2$ . Some corresponding values of x and y a…
38A 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…
39The diagram shows the speed-time graph of a train for the first 62.5 seconds after entering a tunnel. Find the speed of…
40A 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…
41From the diagrams above, select one of them which best illustrates each of the following statements. $y = 4\pi x^3$ . The…