Math topic中文

Find unknown in formula

finding the value of an unknown quantity in a given formula

Practice questions

1A piece of wood which was 50 cm long, was in the shape of a uniform cylinder. A prism is cut out from the wood such that…
2y is inversely proportional to the square of x, $x > 0$ . If x is increased by 25%, find the percentage change in y. Answ…
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…
4 $y = \dfrac{x^3}{4} - 2x + 3$ . Complete the table of values for $y = \dfrac{x^3}{4} - 2x + 3$ . On the grid opposite, dra…
5Old MacDonald has a farm with a rock wall around it. The figure shows a portion of his farm where he plans to build two…
6It 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 $y = f(x)$ …
7The number of bacteria in a colony doubles every hour. The colony starts with: 50 bacteria. The table below shows the nu…
8The 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…
9The 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 | |---|--…
10One solution of the equation $(k+1)x^2 + kx = 15$ is $x = -3$ . (a) Find the value of $k$ . Answer k = ... (b) Find the se…
11The points A(0,2) and B(1,0) lie on the graph $y = x^2 + ax + b$ . Find the values of a and b. Answer a = ... b = ... C i…
12The illumination, $I$ units, of a bulb varies inversely as the square of the distance, $d$ metres. It is given that the…
13The Ideal Gas Law $PV = 8.3145\,nT$ relates pressure P (measured in Pascal), volume V (measured in metres^3), the number…
14Bernice invests $700 at a rate of r % per year compound interest, compounded every 3 months. At the end of 5 years the…
15The points P(2, 3) and Q(-1, -3) lie on the curve $y = ax^2 + bx + 2$ . Form and solve two simultaneous equations to find…
16The diagram shows a solid ornament in the shape of a cylinder with an upright cone cut out at one end and a hemisphere a…
17A chock is a block placed against a wheel or rounded object, to prevent it from moving. Jenny had to come up with a prot…
18The nth term of a sequence is given by $T_n = \frac{6n-5}{3n}$ . Use the formula to find $T_7$ , giving your answer as an…
19Solve the equation $2(x-5)=3x-1$ . Answer $x$ = ... Solve the inequality $7-4y>3(y+2)$ . Answer ... Given that $\dfrac{1}{p}-\dfrac{1}{2q}=\dfrac{1}{3r}$ …
20Matthew invests $20 000 into a fixed deposit at $r\%$ per month, compounded monthly. After 24 months he will be able to…
21The area of triangle $XYZ$ is 12.6 cm^2. $XY = 4.5$ cm and $YZ = 7.1$ cm. Find two possible values for $\angle XYZ$ . Giv…
22A model consists of a solid hemisphere attached to a solid cylinder as shown in diagram. The height of the cylinder is 2…
23The cumulative frequency curve shows the distribution of marks scored by 180 students in a Mathematics examination in 20…
24A vaccine was introduced to a virus in an experiment. The number, N, of virus t hours after being introduced to the vacc…
25If x is increased by 25%, find the percentage change in y. y = $\dfrac{k}{x^2}$ where k is a constant. Answer ... % Give…
26Express $\dfrac{-6x^3 - 9x^2 + x - 16}{(x^2 - 1)(2x^2 + 3)}$ in partial fractions.
27Given that $a = \sqrt{\frac{b^2+4ac}{2a}}$ , find the values of $b$ when $a = 4$ and $c = -1$ . Answer b = ... Simplify $\left(\dfrac{125p^6}{q^3}\right)^{-1/3}\times\left(\dfrac{3p^0}{\sqrt{q}}\right)^2$ …
28A number of regular n-sided polygons are placed together in a ring to form a regular N-sided polygon as shown in the dia…
29In the following graph, write down a possible value of n and the corresponding value of b for the equation. n = ... b =…
30The table below shows a flooring consisting of square tiles measuring 1 m^2 each. Each day similar tiles are added to th…
31A cylinder X has radius, $r$ cm and height $h$ cm. A hemisphere S is such that its radius is half of the radius of cylin…
32Given that one solution for the equation $\dfrac{1}{2x^{2} + kx} = \dfrac{1}{2}$ is $x = -2$ , find the value of k, a sec…
33Chris cycled from A to C in a certain part of a country. He travelled for 50 km from A, at a constant speed of $x$ km/h…
3420 female shoppers went to buy their groceries. The amount of time (in minutes) each female shopper spent is shown in th…
35 $x^2 - 10x + 27$ can be expressed in the form $(x + p)^2 + q$ . Find the value of $p$ and the value of $q$ . Answer $p =$ …
36The base areas of two geometrically similar cones are in the ratio of 9 : 49. If the volume of the bigger cone is 1200 c…
37The diagram shows a circle of radius 8 cm and centre O. The tangent to the circle at T meets OA produced at R and OB pro…
38已知二次函数的图象与 $y$ 轴的交点坐标为 $(0,a)$ ，与 $x$ 轴的交点坐标为 $(b,0)$ 和 $(-b,0)$ ，若 $a>0$ ，则函数解析式为 $(\quad)$ A. $y=\dfrac{a}{b^{2}}x^{2}+a$ …
39A piece of A0-sized paper has a total surface area of 1 m^2. The length and breadth of the A0-sized paper are x m and y…
40Given that $a^2 - \frac{6a}{b} + \frac{9}{b^2} = 0$ , find the value of $ab$ . Answer ab = ...