Free Printable S1上下

1.

Given the $f\left(x\right)=x^{2\ }+bx+c$ , which of the following is correct for $g\left(x\right)$ ?

a)

$x^2+\left(b+2\right)x+\left(c+5\right)$

b)

$2x^2+\left(b-3\right)x+c$

c)

$x^2+\left(b-2\right)x+\left(c+3\right)$

d)

$2x^2+\left(b+3\right)x+\left(c-4\right)$

2.

Fig 1 shows the graph of $y=ax^2+bx+c$ .

Which of the following is true?

a)

$ab<0$

b)

$a>0$

c)

$b^2-4ac<0$

d)

$\frac{c}{a}>0$

3.

Find the domain of the $g\left(x\right)=\sqrt[]{\frac{x+3}{1-x}}$

a)

$\left[-3,1\right)$

b)

R \ {1}

c)

$\left(-3,1\right]$

d)

$\left\{x\le-3,\ x>1\right\}$

4.

Find the domain of $f\left(x\right)=\sqrt[]{\frac{x+1}{x-2}}$

a)

$\left\{x\le-1,\ x>2\right\}$

b)

R \ {2}

c)

$\left[\ 0\ ,\ \infty\right)$

d)

$\left\{-1\le x<2\right\}$

5.

a)

$x^2+10x+16$

b)

$x^{2\ }+10x+10$

c)

$x^2+8x+8$

d)

$x^2+8x+12$

6.

a)

$4x^{2\ }+34x+38$

b)

$4x^2+22x+22$

c)

$2x^{2\ }+11x+11$

d)

$2x^2+17x+19$

7.

Which of the following graphs is not correct ?

a)

b)

c)

d)

8.

a)

$k=-3,\ m>0$

b)

$k=-3,\ m<0$

c)

$k=3,\ m>0$

d)

$k=3,\ m<0$

9.

a)

8

b)

6

c)

10

d)

12

10.

When $x^3-4x^2+kx-1$ is divided by $x-2$ , the remainder is 1. Find the value of $k$ .

a)

5

b)

-5

c)

7

d)

-7

11.

Polynomial, $f\left(x\right)\$ , divided by (x+2) and (x-1) gives remainder of -19 and 2 respectively. What is the remainder for the $f\left(x\right)$

a)

7x-5

b)

5x-3

c)

3x-5

d)

5x-7

12.

$\frac{-3x^2+2}{x^{2\ }\left(x^2+1\right)}\equiv\ \frac{A}{x}+\frac{B}{x^2}+\frac{Cx+D}{x^2+1}$ .

$\left(A+B+C+D\right)=\ ?$

(a)

13.

Simplify $\frac{2x-y}{10x}-\frac{y}{2x}+\frac{2y-x}{15x}$

a)

$\frac{2x-7y}{15x}$

b)

$\frac{5x-6y}{15x}$

c)

$\frac{4x-9y}{15x}$

d)

$\frac{3x-4y}{15x}$

14.

Simplify

a)

$-\frac{1}{k}$

b)

$\frac{1}{k}$

c)

$\frac{1}{k+1}$

d)

$\frac{1}{k-1}$

15.

Simplify

a)

$\frac{\left(a-b\right)a^2}{y}$

b)

$\frac{a-b}{aby}$

c)

$\frac{aby}{a-b}$

d)

$\frac{\left(a-b\right)}{a^2y}$

16.

Simplify

a)

$\frac{t^2+4t+37}{2\left(t-3\right)\left(t+3\right)}$

b)

$\frac{t^2-3t+32}{3\left(t-3\right)\left(t+3\right)}$

c)

$\frac{t^2+5t-34}{2\left(t-3\right)\left(t+3\right)}$

d)

$\frac{t^2+2t+31}{3\left(t-3\right)\left(t+3\right)}$

17.

Simplify

a)

$a^{-\frac{2}{3}}b^{-\frac{1}{3}}$

b)

$a^{-\frac{1}{3}}b^{-\frac{2}{3}}$

c)

$a^{\frac{2}{3}}b^{-\frac{1}{3}}$

d)

$a^{\frac{2}{3}}b^{\frac{1}{3}}$

18.

If $\sin\left(\theta+18\degree\right)=\cos\ 60\degree$ ( $\left(0\degree<\theta<90\degree\right)$ , then value of $\cos\ 5\theta$ is?

a)

$\frac{1}{2}$

b)

$\frac{1}{4}$

c)

$\frac{\sqrt[]{2}}{2}$

d)

$1$

19.

Given $\alpha$ lies in the $3^{rd}\$ quadrant, $\cos\ \alpha\ =\ -\ \frac{5}{13}$ , then $\sin2\alpha\ =\ \ \left(\ \ \ \ \ \ \ \ \ \ \right)$

a)

$\frac{120}{169}$

b)

$-\frac{120}{169}$

c)

$\frac{12}{13}$

d)

$-\frac{12}{13}$

20.

Simplify $\cos\ \left(45\degree+x\right)-\cos\ \left(45\degree-x\right)$

a)

$-\ \sqrt[]{2}\sin\ x$

b)

$\sqrt[]{2}\sin x$

c)

$\sqrt[]{2}\cos\ x$

d)

$-\ \sqrt[]{2}\cos\ x$

21.

Simplify $\frac{\sin\ x}{1+\cos\ x}+\frac{\ 1+\cos\ x}{\sin x}$

a)

$\frac{2}{\sin\ x}$

b)

$1$

c)

$\frac{2}{\left(1+\cos\ x\right)}$

d)

$2$

22.

Find the length sides of the triangle, in which is valid for the size of angles A : B : C = 3 : 4 : 5 and the side lying opposite to the angle A is of a length $a=\ \sqrt[]{2}$ .

a)

$b=\sqrt[]{3},\ c\ =1.93$

b)

$b=\frac{\sqrt[]{5}}{2},\ c=\sqrt[]{3}$

c)

$b=\frac{\sqrt[]{3}}{2},\ c\ =\ \sqrt[]{3}$

d)

$b\ =\ \sqrt[]{3},\ \ c\ =\ \frac{\sqrt[]{3}}{2}$

23.

$5\ \tan^2x-5\sec^2x\ +1\ =\ ?$

a)

$-4$

b)

$-3$

c)

$-1$

d)

$-2\$

24.

If $\sec\ A\ +\ \tan\ A\ =x$ , then $\sec\ A\ =\ ?$

a)

$\frac{x^2+1}{2x}$

b)

$\frac{x^2-1}{2x}$

c)

$\frac{x^2+1}{x}$

d)

$\frac{x^2-1}{x}$

25.

Given $\Delta ABC,\$ $\sin\ A:\ \sin B:\ \sin C\ =\ 2\ :\ 3\ :\ 4$ . Find the value of $\cos\ C$ . (Hint: Cosine rules/余式定理)

a)

$-\frac{1}{4}$

b)

$\frac{1}{4}$

c)

$\frac{1}{2}$

d)

$-\frac{1}{2}$

26.

Given a,b,c are three sides of $\Delta ABC$ . If (b+c) : (c+a) : (a+b) = 6 : 7 : 8, find the value of $\cos\ A$ .

a)

$-\frac{1}{10}$

b)

$\frac{5}{9}$

c)

$-\frac{1}{5}$

d)

$-\frac{1}{2}$

27.

Find the area of the regular triangle.

a)

$\frac{\sqrt[]{3}}{4}a^2$

b)

$\frac{\sqrt[]{3}}{2}a^2$

c)

$\frac{\sqrt[]{3}}{4}a$

d)

$\frac{\sqrt[]{3}}{2}a$

28.

If $\sin\theta\ and\ \cos\ \theta$ are two roots of $4x^2+5x+k=0$ , find the value of $k$ .

a)

$\frac{9}{8}$

b)

$\frac{9}{4}$

c)

$-\frac{9}{4}$

d)

$-\frac{9}{8}$

29.

Given $\sin\ \theta+\cos\theta=\frac{\sqrt[]{2}}{2}$ , find the value of $\tan\ \theta+\cot\ \theta$

a)

$-4$

b)

$-2$

c)

$2$

d)

$4$

30.

Diagram 3 shows a sector LOM and an equilateral triangle JOK. It it given that $\angle LOM=130\degree$ and J is the midpoint of OL. Calculate the area of the shaded region in $cm^2$ . $\left[Use\ \pi=3.142\right]$

a)

$147.79$

b)

$159.54$

c)

$133.49$

d)

$139.65$

31.

Diagram 5 shows a sector POQ of a circle with the center O and the radius of r cm. It is given that the length of arc PQ is 18cm and the perimeter of the sector POQ is 48cm. Find $\theta$ in radians.

[ $use\ \pi=3.142$ ]

a)

1.2 rad

b)

1 rad

c)

0.8 rad

d)

0.6 rad

32.

Find the maximum value for the $f\left(x\right)\ =\sqrt[]{3}\sin x-\cos x$ .

a)

$2$

b)

$3$

c)

$4$

d)

$\frac{1}{2}$

33.

The shape ABCDOA, as shown in Figure 1., consists of a sector COD of a circle center O joined to a sector AOB of a different circle, also center O.

Given that arc length CD = 3cm,

$\angle COD=0.4\ radians$ and AOD is a straight line of length 12cm, find the area of shaded region $cm^2$

(a)

34.

The diagram shows a sector BAC of a circle with center A and radius 16cm. The angle BAC is 0.8 radians and the length AD is 7 cm.

Find the perimeter of the region BDC.

a)

34 cm

b)

35 cm

c)

36 cm

d)

38 cm

35.

Figure 1 shows ABD, a sector of a circle with center A and radius 7 cm. Given that the size of $\angle BAC$ is exactly 0.8 radians. The point D is the mid-point of AC. The region R, shown shaded in Figure 1, is bounded by CD, DB, and the arc BC.

Find the area of R, given your answer to 3 significant figures.

(a)

36.

The diagram shows a triangle ABC with A lying on the y-axis. The equation of the straight line ANB is y-x-1=0, and the equation of the straight line is y+3x-9=0. Find the ratio of AN : AB.

a)

1 : 3

b)

1 : 4

c)

1 : 2

d)

1: 1.5

e)

1: 2.5

37.

A(3,4),B(7,5),C(6,2) and D are the vertices of a parallelogram. Find the coordinates of D

a)

(2,1)

b)

(3,2)

c)

(0,0)

d)

(3,1)

e)

(1,0)

38.

Find the possible value of $k$ if the area of a triangle with vertices $A\left(3,2\right)$ $B\left(-1,6\right)$ and $C\left(k,5\right)$ is $8\ unit^2$ .

a)

-4, 4

b)

-3, 3

c)

-2, 2

d)

-1, 1

e)

-5, 5

39.

Given that A (2,8) , B (6,5), and C (8,9), find the distance, d from the point C to the line AB.

a)

$\frac{22}{5}$

b)

$\frac{11}{2}$

c)

$\frac{15}{4}$

d)

$\frac{17}{3}$

e)

$13$

40.

The solutions for the simultaneous equations are $y=m_1x\ ,\ y\ =\ m_2x$ .

Find the value of $m_1+m_2$

a)

$\frac{10}{7}$

b)

$\frac{2}{3}$

c)

$\frac{16}{21}$

d)

$\frac{8}{5}$

41.

A 点和B点的坐标分别为 $\left(1,-2\right)$ 和 $\left(3,m\right)$ 。

若P点 $\left(n,1\right)$ 外分AB成 $3:1$ ，则 m+n 为多少？

a)

$4$

b)

$-2$

c)

$-1$

d)

3

42.

Find the range (值域） for the fraction function

\frac{8x+1}{4x^{2\ }-4x}

a)

$\left(-\infty,-4\right]\ \cup\ \left[-1,+\infty\right)$

b)

$\left(-\infty,-2\right]\ \cup\ \left[1,+\infty\right)$

c)

$\left(-\infty,\ -1\right]\ \cup\ \left[2,+\infty\right)$

d)

$\left(-\infty,-3\right]\ \cup\ \left[2,+\infty\right)$

43.

Given a >0 ,b>0 ,c>0, x>0

find the least value of

x+x+\frac{8}{x^2}

.
a>0, b>0, c.0, x>0
求以上式子最小的值

a)

6

b)

3

c)

9

d)

12

44.

Given $\left(1,-3p\right)$ is the solution to the simultaneous equations $x^{2\ }-hy+6=10=hx-3y$ where $p\ and\ h\in Z^{\ +}\$ （正整数) . Find the value of $\left(p+h\right)$ .

a)

4

b)

2

c)

3

d)

5

45.

In the diagram, the area of the rectangle is greater than the area of the triangle. Set of possible is $\left\{x|\ x>a\right\}$ ,find the value of a.

如图所示，长方形的面积大于三角形。 $x$ 的可能集合是 $\left\{x|\ x<\frac{1}{a}\ ,\ x\ >\ a\right\}$ ，求 $a$ 的值。（整数）

(a)

46.

Find the value of $\sqrt[]{5\ \sqrt[]{5\ \sqrt[]{5\ \sqrt[]{5\cdot\cdot\cdot}}}}$

a)

$5$

b)

$\sqrt[]{5}$

c)

$\frac{1}{5}$

d)

$\sqrt[8]{5}$

47.

Find the infinite series $1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\cdot\cdot\cdot$

a)

$2$

b)

$\frac{1}{2}$

c)

$\frac{3}{2}$

d)

$1$

48.

Find the infinite series $\log_9\sqrt[]{3}+\log_9\sqrt[]{\ \sqrt[]{3}}+\log_9\ \sqrt[]{\sqrt[]{\sqrt[]{3}}}+\cdot\cdot\cdot$

a)

$\frac{1}{2}$

b)

$\frac{1}{3}$

c)

$\frac{1}{9}$

d)

$1$

49.

Simplify $\frac{1}{\log_x\left(xy\right)}+\frac{1}{\log_y\left(xy\right)}$

a)

$1$

b)

$1+\log_xy$

c)

$1+\log_yx$

d)

$\frac{\log_x\left(xy\right)}{\log_y\left(xy\right)}$

50.

Find the domain of function, $f\left(x\right)=\sqrt[]{\log_2\left(x^2+8x+8\right)}$

a)

$x\le-7\ or\ x\ge-1$

b)

$x<-7\ or\ x>-1$

c)

$x\le-4\ or\ x\ge-2$

d)

$-4\le x\le-2$

51.

(a)

52.

a)

-1

b)

0

c)

1

d)

2

53.

Express the curve $y=x^4-6x^3+4x^2+24x-32$ in the form of $y=\left(x+a\right)\left(x+b\right)\left(x+c\right)^2$ . Find the value of $a+b+c$ .

(a)

54.

When the polynomial $f\left(x\right)$ is divided by $\left(x-2\right)$ and by $\left(x+2\right)$ , the remainder is $5$ and $-11$ respectively. Find the remainder when the $f\left(x\right)$ is divided by $\left(x+2\right)\left(x-2\right)$

a)

$4x-3$

b)

$3x-2$

c)

$-2x+3$

d)

$4x+3$

55.

(a)

56.

Which of the following function describes the graph.

a)

$P\left(x\right)=\left(x-2\right)^2\left(x+2\right)^3$

b)

$P\left(x\right)=\left(x-2\right)^2\left(x+2\right)$

c)

$P\left(x\right)=\left(x-2\right)\left(x-1\right)\left(x+2\right)$

d)

$P\left(x\right)=\left(x-2\right)^2\left(x+2\right)^2$

57.

If $2x^4-x^3+ax^2+x+b\$ is divisible by $2x^2+x+1$ , then find the value of $a+b$ .

a)

6

b)

2

c)

4

d)

8

58.

Polynomial $f\left(x\right)$ divided by $x^2-5x+4$ and $x^2-5x+6$ , the remainder are $x+2$ and $3x+4$ respectively. Find the remainder if $f\left(x\right)$ is divided by $x^2-4x+3$ . （难度：高）

a)

$5x-2$

b)

$4x-3$

c)

$2x-1$

d)

$3x+4$

59.

(a)

S1上下

Total questions: 59

Worksheet time: 14hrs 33mins

Similar Resources on Wayground