F.3 Chinese New Year

1.

1 point

AB and CD are two parallel line segments. E is a point on the plane such that
angle AEC is 50 degrees. angle BAE + angle DCE =

230 degrees

130 degrees

320 degrees

310 degrees

2.

1 point

$4c^2-(a-b)^2=$

$(2c+a-b)(2c-a+b)$

$(4c-a-b)(4c+a+b)$

$(2c-a-b)(2c-a+b)$

$(4c+a-b)(4c-a+b)$

3.

1 point

$\text{Factorize }x^3-3x^2+2x-6$

$(x-3)(x^2-2)$

$(x+3)(x^2+2)$

$(x-3)(x^2+2)$

$(x+3)(x^2-2)$

4.

1 point

ABCD is a square. E is a point on the edge BC such that angle BAE is 20 degrees. Find the measure of angle EDC correct to the nearest degree.

32 degrees

25 degrees

70 degrees

30 degrees

5.

1 point

Which of the following represents the statement 'The result of subtracting 10 from twice of m is less than 28'?

m-20<28

2m-10<28

10-2m<28

2m-20>28

6.

1 point

$\text{Solve }1-\frac{x-25}{2}>10.$

$x<7$

$x<-7$

$x>-7$

$x>7$

7.

1 point

$6x^2-17x+5=$

$(3x-1)(2x+5)$

$(3x-1)(2x-5)$

$(3x+1)(2x-5)$

$(6x-1)(x+5)$

8.

1 point

In an isosceles triangle ABC , AB = AC. D is a point on AC such that AD = BD = BC. Find the measure of angle BAC.

36 degrees

72 degrees

45 degrees

54 degrees

9.

1 point

$\text{Solve }21>x+12.$

$x<33$

$x<9$

$x>9$

$x>33$

10.

1 point

$\text{Which of the following is an exact value of }\pi?$

3.141592654

3.14

$\frac{22}{7}$

None of the above

11.

1 point

In triangle ABC , D is a point on BC such that triangle ACD is an equilateral triangle. If DA = DB = DC. Find the measure of angle BAC.

120 degrees

45 degrees

90 degrees

60 degrees

12.

1 point

In each of the following conditions, which of them must be a right-angled triangle?
(You may choose more than one answer)

AB=AC, angle ACB = 45 degrees

angle A : angle B : angle C = 1 : 4 : 5

AB=18 , BC = 80 , AC = 82

13.

1 point

$\text{If }\left\{\begin{matrix} x=2 & \\ y=t & \end{matrix}\right.\text{ is a solution of the equations }\left\{\begin{matrix} 4x-3y=s & \\ 2x-5y=19 & \end{matrix}\right.\\\text{Find the values of }s\text{ and }t.$

$s=17\text{ and }t=3$

$s=-3\text{ and }t=14$

$s=17\text{ and }t=-3$

$s=14\text{ and }t=-3$

14.

1 point

A rectangular frame is made from a wire so that the length is 5 cm longer than twice the width. If the perimeter of the frame is not longer than 70 cm, what is the maximum width?

8 cm

10 cm

9 cm

11 cm

15.

1 point

$\text{Simplify }\frac{1}{2(x-1)}-\frac{1}{4x}.$

$\frac{1+x}{4x(x-1)}$

$\frac{1}{2x(x-1)}$

$\frac{3-x}{4(x-1)}$

$\frac{1-x}{4(x-1)}$

16.

1 point

If (2r + s) : (3r + 4s) = 2 : 5 , find r : s.

16 : 13

3 : 4

13 : 16

4 : 3

17.

1 point

$\text{If }m>n\text{, which of the following must be true?}\\ \text{You may choose more than one answer.}$

$m-6>n-6$

$m+6>n+6$

$m^2>n^2$

$-3m<-3n$

$\frac{m}{2}>\frac{n}{2}$

$\frac{1}{m}>\frac{1}{n}$

18.

1 point

$\text{If }(x-A)(x+3)\equiv x^2+6x+B\text{, find the values of }A\text{ and }B.$

$A=-3,B=9$

$A=3,B=-9$

$A=9,B=-27$

$A=-3,B=-9$

19.

1 point

The greatest integral solution satisfying the inequality 2(3-x)>-4 is

4

6

9

5

20.

1 point

An athlete takes 2.5 hours to finish 42 km race. Find his running speed.

12.8 km/h

16.8 km/h

4.8 km/h

28 km/h

21.

1 point

In triangle ABC, AB = 13 cm , BC = 14 cm , AC = 15 cm. Find the area of triangle ABC.

97.5 cm square

105 cm square

91 cm square

84 cm square

22.

1 point

In a n-sides regular polygon, the interior angle is 3 times to its exterior angle.
Find the value of n.

6

8

12

4

23.

1 point

2 numbers are randomly drawn at the same time from five cards numbered 1,2,3,4 and 5 respectively. Find the probability that the sum of the numbers drawn is a multiple of 3.

3/10

9/20

9/25

2/5

24.

1 point

The measured length of a pencil is 9.2 cm , correct to the nearest 0.2 cm.
Find the lower limit of the pencil.

9.15 cm

9.1 cm

9.0 cm

9.05 cm

25.

1 point

Two fair dice are thrown. The probability of getting the same number is

1/6.

1/2.

5/6.

3/4.

26.

1 point

ABCD is a trapezium such that AD // BC.
The diagonals AC and BD intersects at E.
The area of △ABE = a cm square and the area of △CDE = b cm square.
Which of the following must true?

a>b

a=b

a

a=b+1

27.

1 point

Find the interior angle of a regular octagon.

135 degrees

108 degrees

150 degrees

120 degrees

28.

1 point

How many significant figures does the number 0.17020 have?

4

6

5

3

29.

1 point

Find the intersection of 3x+2y=12 and 9x-4y=6.

(x,y)=(4,0)

(x,y)=(0,3.5)

(x,y)=(1,4.5)

(x,y)=(2,3)

30.

1 point

If the length of a rectangle is increased by 10%, and its width is decreased by 10%, then the area of the rectangle will

be increased by 1%.

be decreased by 1%.

remain unchanged.

be increased by 2%.

31.

1 point

ABCD is a square. E is a point inside the square such that AEB is an equilateral triangle. Find the measure of angle CED.

100 degrees

135 degrees

150 degrees

120 degrees

32.

1 point

$\text{The degree of the polynomial }-xy^2z\text{ is}$

-1

4

3

2

33.

1 point

$\text{If }m>n>0\text{, which of the following must be true?}\\ \text{(You may choose more than one answer.)}$

$1-\frac{m}{4}<1-\frac{n}{4}$

$m^2>n^2$

$6-m>6-n$

$-3m<-3n$

$\frac{1}{m}<\frac{1}{n}$

34.

1 point

A box contains 2 red balls and 2 green balls. If 2 balls are drawn randomly from the box without replacement, the probability of getting 2 green ball is

1/4.

1/6.

1/2.

1/3.

35.

1 point

$8x^3-27y^3=$