Math topic中文

Area rectilinear

area of rectilinear figure

Practice questions

1The normal to the curve $y = 2\tan 3x - 1$ at point $P\left(\frac{\pi}{3}, -1\right)$ crosses the $y$ -axis at point $A$ …
2The point $P$ lies on the curve $y = \ln\left(\frac{x+1}{x-1}\right)$ for $x > 1$ . The normal to the curve at $P$ is par…
3The figure shows part of the curve $y = g(x)$ . $(2, 8)$ and $(6, 1)$ are two points on the curve. Given that $\int_{2}^{6} y \text{ } dx = 32$ …
4The diagram shows part of the curve $y = 3e^{-\frac{1}{2}x} - 6$ which crosses the $x$ -axis at $P$ and the $y$ -axis at $Q$ …
5The triangle ABC is such that its area is $\dfrac{16 + 7\sqrt{10}}{2}\ \text{cm}^2$ , the length of AB is $(3\sqrt{2} + \sqrt{5})\ \text{cm}$ …
6一个三角形和一个平行四边形面积相等，底也相等．如果平行四边形的高是18厘米，三角形的高就是厘米．
7The diagram shows a chocolate bar in the form of a triangular prism and the cross-section of the chocolate bar is an iso…
8一个等腰直角三角形的腰长8厘米，这个三角形的面积是平方厘米．
9The diagram shows part of the curve $y = \sqrt{3x + 4}$ . The line $AB$ is tangent to the curve at $A$ . The points $B$ an…
10The diagram shows two triangles DAB and DBC. It is given that BD = 5 m and BC = 2 m. Angle DAB = angle DBC = angle DEC =…
11The diagram shows part of the curve $y = (1 - x)(x - 4)$ and two lines $l_1$ and $l_2$ . The lines $l_1$ and $l_2$ are ta…
12一个平行四边形的底和高都是1.6m，它的面积是 m 2 ，和它等底等高的三角形的面积是 m 2 。
13The diagram below shows the graph of $y = \frac{1}{2x+1}$ and the tangent to the curve where the curve intersects the $y$ …
14 $ABCD$ is a rectangle which fits inside a semicircle of radius 8 cm and centre $O$ . It is given that $AB = x$ cm and $BC = y$ …
15有一堆圆木堆成梯形，最上面一层有 $6$ 根，最下面一层有 $10$ 根，一共堆了 $5$ 层，这堆圆木共有 ___ 根．
16The diagram shows part of the curve $y = \frac{1}{\left(\frac{3}{4}x - 5\right)^2} + 1$ . $P$ is the point on the curve w…
17Solutions to this question by accurate drawing will not be accepted. In the trapezium $OABC$ , the point $A$ has coor…
18已知椭圆 $\dfrac {x^{2}}{a^{2}}+ \dfrac {y^{2}}{b^{2}}=1(a > b > 0)$ ， $F_{1}$ 和 $F_{2}$ 是椭圆的左、右焦点，过 $F_{1}$ 的直线交椭圆于 $A(x_{1},y_{1})$ …
19已知抛物线 $y=ax^{2}$ 经过点 $A(2,1).(1)$ 求此抛物线的表达式 $;(2)$ 写出抛物线上点 $A$ 关于 $y$ 轴的对称点 $B$ 的坐标 $;(3)$ 求 $\triangle OAB$ 的面积 $;(4)$ …
20A rhombus PQRS is drawn on a square grid. Draw square RSTU on the grid such that RSTU does not overlap with PQRS. Using…
21Solutions to this question by accurate drawing will not be accepted. The diagram, which is not drawn to scale, shows…
22Solutions to this question by accurate drawing will not be accepted. The diagram shows a trapezium $ABCD$ in which $AB$ …
23Solutions to this question by accurate drawing will not be accepted. The diagram shows an isosceles triangle PQR in whic…
24The equation of a circle is $x^2 + y^2 + 2x - 8y - 8 = 0$ . Find the coordinates of the centre, $C$ and the radius of the…
25In the diagram, $OPQR$ is a trapezium with $OP$ parallel to $RQ$ and $OP$ perpendicular to $PQ$ . The point $P$ has coord…
26直线 $y=2x$ 与圆 $C:(x-2{)}^{2}+(y+1{)}^{2}=14$ 交于 $A$ ， $B$ 两点，则 ${\rm\triangle}ACB$ 的面积等于 $(\quad).$ A. $\dfrac{3\sqrt[]{5}}{2}$ …
27The diagram shows part of the curve $y = 4 - e^{-2x}$ which crosses the axes at $A$ and at $B$ . Find the coordinates of…
28The diagram below shows an isosceles triangle $ABC$ , where $AB = AC = 2\text{ cm}$ , and a square $BCDE$ . $M$ is the midp…
29 $ABCD$ is a parallelogram. Point $A$ lies on the $y$ -axis and coordinates of $D$ is $(6, -1)$ . $AC$ is a horizontal line…
30The diagram shows a prism in which the cross-section is a trapezium $ABCD$ . $AB = 4x\text{ cm}$ , $BC = DC = AD = 2x\text{ cm}$ …
31已知双曲线 $C$ ： $\dfrac{x^{2}}{a^{2}}-\dfrac{y^{2}}{b^{2}}=1(a>0,b>0)$ 的左、右焦点分别为 $F_{1}$ ， $F_{2}$ ，点 $M$ 在双曲线 $C$ 上，点 $I$ 为…
32The diagram shows part of the curve $y = \sqrt{4x + 5}$ . The normal of the curve at $P$ meets the $x$ -axis at $T$ . The $x$ …
33A parallelogram ABCD is drawn on a square grid inside a box. By joining dots on the grid with straight lines, draw squar…
34一个梯形的下底是28分米，比上底的2倍多2分米，又是高的2倍，它的面积是．
35The graph shows part of the curve $y = -3(2x-4)^{-1/3}$ . The point $P(-2,\ 1.5)$ lies on the curve and the normal to the…
36一个平行四边形的底是10dm，高是4dm，一个三角形的面积与这个平行四边形的面积相等，底是8dm，这个三角形这条底边上的高是___。
37The diagram shows part of the curve $y = \sqrt{2x + 4}$ , meeting the $x$ -axis at the point $A$ and the $y$ -axis at the p…
38梯形上下底不变，高扩大2倍，这个梯形的面积就．
39The diagram shows part of the curve $y = 2 \sin 2x + 1$ . $P$ is the maximum point of the curve and $Q$ is the point on t…
40Solutions to this question by accurate drawing will NOT be accepted. The figure shows a right-angled triangle $ABC$ ,…
41The diagram shows a quadrilateral $ABCD$ with vertices $A(-4, -3)$ , $B(6, 1)$ , $C(3, 5)$ and $D(-2, 3)$ . $M$ which lies…
42一个三角形的高是 $18$ 厘米，底是高的一半，它的面积是 ___平方厘米，与它等底等高的平行四边形的面积是 ___平方厘米。
43The diagram shows a trapezium with vertices A(6, 8), B, C and D. The sides AB and DC are parallel and angle ABC is $90^\circ$ …
44The diagram shows points $A(5, 0)$ , $B(a, 3a)$ and $C(-2, 6)$ such that the line $AB$ is perpendicular to the line $BC$ .…
45The diagram shows a glass window $ABCDEF$ , consisting of a rectangle $ABEF$ of height $3x\text{ cm}$ and width $y\text{ cm}$ …
46Solutions to this question by accurate drawing will not be accepted. $ABCD$ is a trapezium where $AD$ is parallel to…
47直线 $y=-x$ 与直线 $y=x+2$ 与 $x$ 轴围成的三角形的面积为___.
48The diagram shows part of the curve $y = 27 + \frac{8}{(x-2)^3}$ which crosses the axes at points $A$ and $B$ . Explain w…
49The diagram shows part of the curve $y = 2\sin\frac{x}{2}$ , where $A$ lies on the curve. The $x$ -coordinate of $A$ is $\frac{4\pi}{3}$ …
50In the diagram below, the line $OP$ makes an angle of $\alpha^\circ$ with the positive $x$ -axis such that $\tan \alpha = 0.2$ …
51Solutions to this question by accurate drawing will not be accepted. $OABC$ is a trapezium with right angle $OAB$ . T…
52A parallelogram ABCD is drawn on a square grid inside a box. By joining dots on the grid with straight lines, draw squar…
53一个梯形上底长6厘米，下底长9厘米，高厘米，面积是45平方厘米．
54The diagram shows the curve $y = \cos x + \sin x$ for $0 \le x \le \pi$ . The curve meets the $y$ -axis at the point $A$ a…
55The diagram shows part of the curve $y = \frac{15}{(0.5x+1)}$ and a straight line $y = 1.25x - 10$ . The straight line in…
56设函数 $f(x)=ax+ \dfrac {b}{x}$ ，曲线 $y=f(x)$ 在点 $M( \sqrt {3},f( \sqrt {3}))$ 处的切线方程为 $2x-3y+2 \sqrt {3}=0$ ． $($ Ⅰ $)$ 求 $f(x)$ …
57The diagram (not drawn to scale) shows a quadrilateral $ABCD$ such that $AB = BC$ and angle $BCD = 90^\circ$ . The point…
58The diagram shows part of the curve $y = \frac{7}{6x + 1}$ intersecting the $y$ -axis at $A(0, 7)$ . The tangent to the cu…
59一个平行四边形的面积比与它等底等高的三角形的面积大24平方厘米，这个三角形的面积是平方厘米，平行四边形的面积是平方厘米．
60已知 ${\rm Rt}\triangle ABC$ 的两条直角边的长度恰好是一元二次方程 $x^{2}-12x+32=0$ 的两个实数根，那么 $\triangle ABC$ 的面积为 $(\quad)$ A. $16$ B. $32$ …