Math topic中文

Changing subject

changing the subject of a formula

Practice questions

1Hamid borrowed a sum of money for 3 years at an interest rate of 3.5% per annum simple interest to pay for his car. If t…
2By completing the square or otherwise, express $x$ in terms of $y$ given that $y = x^2 - 4x + 6$ . Answer x = ___ or ___…
3It is given that $y = x\sin x + \cos^2\left(\tfrac{x}{2}\right).$ Obtain an expression for $\dfrac{dy}{dx}$ in the form…
4In the diagram, AB is a tangent to the circle with centre O, ∠CAB = 58° and CDE is a straight line. Find, stating your r…
5已知方程 $2x+y-4=0$ ，用含 $x$ 的代数式表示 $y$ 为： $y=$ ___.
6The diagram shows a right circular cone cut from a solid steel sphere. Point O is the centre of the sphere with radius 1…
7Complete the table of values for $y = x - \frac{4}{x^2}$ . Values are given to one decimal place where appropriate. Compl…
8The variables x and y are connected by the equation $y = \frac{x^3}{5} - 2x + 1$ . Some corresponding values of x and y a…
9长方形的周长C厘米，长是α厘米，宽是（）厘米． A. C-2α B. （C-α）÷2 C. C÷2-α
10 $y = 12 - 6x^{3}$ Find $y$ when $x = -1$ . Answer ___ Rearrange the formula to make $x$ the subject. Answer ___
11In the diagram, the points P, Q and R have coordinates (9, -3), (6,1) and (18, -3) respectively. Find the length of PQ.…
12 $T = 2\pi\sqrt{\dfrac{L}{g}}$ Rearrange the formula to make g the subject. Answer g = ...
13把下列方程改写成用含 $x$ 的式子表示 $y$ 的形式： $(1)\dfrac{{3}}{{2}}x+{2}y={1}$ ； $(2)\dfrac{{1}}{{4}}x+\dfrac{{7}}{{4}}y={2}$ ； $(3)5x-3y=x+2y$ …
14Express $x^2-6x-2$ in the form $(x-a)^2 + b$ where $a$ and $b$ are constants. Answer ___ Hence, state the minimum value…
15Solve the inequality $\frac{3x+1}{3} < \frac{2-5x}{4}$ . Answer ... It is given that $a = \frac{2b-3c}{b+2c}$ . Find $a$ w…
16Old MacDonald has a farm with a rock wall around it. The figure shows a portion of his farm where he plans to build two…
17已知二元一次方程 $3x-2y+1=0$ ，用含 $x$ 的式子表示 $y$ ，则 $y=$ ___.
18The diagram shows a solid formed from a cone, a cylinder and a hemisphere. The cone has base radius $1.5x$ cm and height…
19In the parallelogram PQRS, QR = 12.7 cm and angle PQR = 50°. Show that the length of RS = 5.407 cm. Answer Hence or othe…
20The figure shows two rods PA and PB which are hinged at P. The rods slide such that P, A and B are on the same vertical…
21Complete the table of values for $y=\dfrac{2}{x^{2}}-2x. Values are given to one decimal place where appropriate. On the grid opposite, draw the graph of$ …
22Let $p = \frac{1}{2} \sqrt{\dfrac{x^2 - 3y}{x^2}}$ (a) Evaluate $p$ when $x = -12$ and $y = 4$ , giving your answer corre…
23The 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 | |---|--…
24Given $\dfrac{3x - y}{x + 2y} = \dfrac{1}{3}$ , find the ratio x : y. Answer x : y = ... Solve the inequality $\dfrac{2 - 3x}{3} < \dfrac{2x - 1}{6}$ …
25Simplify. $\dfrac{a^3}{3a^2}\times 27a^6$ Answer ... $\sqrt{\dfrac{4}{16x^3}}$ Answer ... $\dfrac{49^{2a}}{7^b}=343^{4c}$ …
26已知关于 $x$ ， $y$ 的二元一次方程组 $\begin{cases} & x+3y=4-a \\ & x-y=3a \end{cases}$ ，给出下列结论中正确的是 $()①$ 当这个方程组的解 $x$ ， $y$ 的值互为相反数…
27Express $x^2 + 6x + 10$ in the form $(x + p)^2 + q$ , where $p$ and $q$ are constants to be found. Answer ---------------…
28Factorise completely $m^2 - 2mn + n^2 - p^2$ . Answer ... Express as a single fraction in its simplest form $\dfrac{7}{2x-3} + \dfrac{x+1}{6-4x}$ …
29Sketch the graph of $y = 2\ln x$ . In order to solve the equation $x e^{2x} = \dfrac{1}{3x}$ , a suitable straight line ha…
30把方程 $2x+3y-1=0$ 改写成含 $x$ 的式子表示 $y$ 的形式为 $()$ A. $y= \dfrac {1}{3}(2x-1)$ B. $y= \dfrac {1}{3}(1-2x)$ C. $y=3(2x-1)$ …
31K is the point $(7, -8)$ and L is the point $(x, y).\n\nThe gradient of the line KL is$ \frac{2}{3} $.\n\nMaverick claims that it is possible to express$ …
32已知长方形的周长为 $40cm$ ，一边长 $y\:cm$ ，另一边长 $x\:cm$ ，则 $y$ 与 $x$ 的关系式为 ___.
33Factorise completely $x^4 - y^4$ . Answer ... Given that $x^2 - 2xy = 1 - y^2$ , express $y$ in terms of $x$ . Answer ... o…
34Simplify $\dfrac{25m^2-4}{4-4m-15m^2}$ . Given that $r = 3 - \sqrt{\dfrac{p^2}{4} - q}$ , evaluate $r$ when $p = -8$ and $q = 7$ …
35The diagram shows three points A(-16, 0), B(0, 12) and C(8, 2). A circle is drawn with centre C such that AB is a tangen…
36 $a = \frac{3 - b}{b + 4} + 2$ Find a when b = -6. Answer a = ... Rearrange the formula to make b the subject. Answer b =…
37Make b the subject of the formula $3b + 8d = 2ab + 5$ . Answer ...
38 $2c + b = \frac{b - c}{a}$ Rearrange the formula to make b the subject. Answer b = ...
39Write as a single fraction in the simplest form $\frac{3x}{2x^2-50}-\frac{1}{x-5}$ . $x = \sqrt[3]{\frac{25y}{7z+2}}$ Fin…
40Simplify $\displaystyle\frac{16a^6 b^2}{5} - \displaystyle\frac{8a^3}{25ab^3}$ . Answer ___ (i) Express $-4x + x^2 - 6$ i…
41Rearrange the formula $\dfrac{1}{a}-\dfrac{1}{2b}=\dfrac{1}{3c}$ to make $b$ the subject. Answer b = ...
42Factorise completely $5pr - 2ps - 5qr + 2qs$ . Given that $p \neq q$ , find the value of $\frac{r}{s}$ when $5pr - 2ps - 5qr + 2qs = 0$ …
43Simplify $\left(\dfrac{a^6 b^3}{8}\right)^{\tfrac{1}{3}}\times\dfrac{3b^{-1}}{a^2}$ . Answer ... Solve $\dfrac{2}{x-2}+\dfrac{3}{x+2}=0$ …
44方程3x+y=7，用x的代数式表示y，则y=___．
45 $b = \dfrac{a}{a-1} + \dfrac{2}{c}$ Find the value of $b$ when $a = 3$ and $c = 4$ . Answer b = ... Rearrange the formula…
46Solve the equation $2(x-5)=3x-1$ . Answer $x$ = ... Solve the inequality $7-4y>3(y+2)$ . Answer ... Given that $\dfrac{1}{p}-\dfrac{1}{2q}=\dfrac{1}{3r}$ …
47It is given that $\sqrt{3p^3 + 6r^2} = \frac{5r}{2}.$ Make r the subject of the equation.
48Let $y = 9x^3 + 5x^2 - 3x + 1$ . Complete the table for $y = 9x^3 + 5x^2 - 3x + 1$ . Give your answer correct to 1 decimal…
49The variables x and y are connected by the equation $y = x^3 - 3x + 1$ . Some corresponding values of x and y are given i…
50在方程 $7x-2y=8$ 中用含 $x$ 的代数式表示 $y=$ ___ ．
51方程2x+y=7的正整数解（） A. 有无数对 B. 只有一对 C. 只有三对 D. 以上都不对
52Given that $3v=\sqrt{25-x^2}$ , find the value of $v$ when $x=-3$ . make $x$ the subject of $3v=\sqrt{25-x^2}$ .
53已知甲、乙两地相距 $20$ 千米，汽车从甲地匀速行驶到乙地，则汽车行驶时间 $t($ 单位：时 $)$ 关于行驶速度 $v($ 单位：千米 $/$ 时 $)$ 的函数解析式是 $(\quad)$ A. $t=20v$ B. $t=\dfrac{20}{\upsilon}$ …
54P, Q, R and S are points on a triangular garden. S R Q is a straight line. It is given that $PQ = 55\ \text{m}$ , $RQ = 40\ \text{m}$ …
55A particle moves in a straight line so that t seconds after passing a fixed point O, its velocity, v m/s, is given by $v = t^2 + kt + 5$ …
56Given that $\frac{5a-3b}{2a} = \frac{4}{3}$ , find the value of $\frac{a}{b}$ . Answer ... Express $x^2 - 6x + 1$ in the f…
57It is given that $y=\dfrac{5x-2}{3x+1}$ . Find $y$ when $x=7$ . Answer $y$ = ... Express $x$ in terms of $y$ . Answer $x$ =…
58A number of regular n-sided polygons are placed together in a ring to form a regular N-sided polygon as shown in the dia…
59It is given that $p = \dfrac{q + r^2}{q - 5}$ . Find $p$ when $q = \dfrac{1}{5}$ and $r = -6$ . Answer p = ... Express $q$ …
60Simplify $\frac{1}{6x-4} - \frac{x+1}{3x^2-5x+2}$ . $\sqrt{2x^2 + x + z} = y$ Evaluate $y$ when $x = -\frac{1}{2}$ and $z = \frac{5}{2}$ …