頁四第張六第日五初月四年西巴夏 WAH KIU YAT PO
A
報日僑華
二期星
日十二月五年九六九一番公年八十五國民中有教僑華
11. ABC is a triangle inscribed in a circle, centre 0. If ZA00=130°, ZE0C 150′′ and if O lies inside ➡ ABC, find ZACH.
Ane.
12. AB is a diameter of the circle APQRB. Find
LAPQ+/QRB.
Ans.
13. A variable triangle PQR is inscribed in a given
circle. If the angle QPR is of given size, what else can you say about APUR ?
·3(1-x)· 20
C
| 数中學會考試題預習
Ana.
數學科
(廿九 ) ·歐陽峪文。
MATHEMATICS (29)
14. ABCDEF is a hexagon circunscribing a circle,
can you say about AB+ CD + EF 7
what
Ans
LESSON 29: Exercise On Paper III
GEOMETRY
Attempt All questions in Section A and any FOUR question in Section B.
Section A
Credit will only be given for the correct answer. In 2.1 - 2.6, read carefully the given statements, and put a tick against the box onnasiting the statement which must always be trus.
In Q.7-0.22, put the answer in the space provided. Any workong may be done on the last few pages of the answer book but will not be marked.
The intersecting point of three medians of a triangle
is called "its
A) Circumcentre
B) Orthocentre
(C) Centroid
D) In-casa-
(E) Exmicen
2. In 4 ABC, if [A-90′′, then
(A) AC BC. > AB
B) AB AC > BC
C) BC AB AC
D) BO > AC > AB
E) None of the above is true
3. If ABCD is a parallelogram, then
(A) AC # BD
0000000 0000000000 00000 00000
B) AC L:BD
C) AC bisects LA, C and BD bisects (B & D
D) AC, BD bisect each other
E) AC. BD bisect each other at
If D is the orthocentre of ABC, what can you say -
about the orthocentre of ADBC ?
(A) Inside DEO –
(B)
Putside DBC
(C) lies on the perimeter of AABC
(D) Inside A ABC
(E) Outside AABC
If the sides of a triangle are 7 cm.,
(A) the triangle is acute-anglea
15. TEP TCQ are tangents to the circle ABC.
PBA 146 /QCA 128 find /BTC.
Ang.
16. In fig.
shown, find the unknown le
lengths.
Ans.
17. The radii of two circles are 2 cm. 5 cm. and the distance between their centres is 9 cm. Calculate to 3 figures, the length of an interior common. tangent.
Ana.
ABC is a triangle; three parallel lines AP, BQ, CR meet BC, CA, AB, produced if necessary at P Q, R resp. Find the value of
1 x x x 13
Ans
19. If I is the in-centre of a ABC and if AI cuts BC
at P, and if the lengths of BC, CA, AB are a, b, o units, find the ratio AI; IP in terms of a, b, G.
Ang.
20. From the figure sa shown, find the marked lengths.
Ans. X
J
21. From a pint Poutside a circle, two lines PAB, PCD
are drawn cutting the circle at A, B, C, D. Complete the relationar
ABPD A APC
PB BP PD M
Ana.(1)
(11)
construct, a square of area 7 sq.in. Then find b, measurement the approximate value of 4.7.
Section B
Measurement
Do any FOUR questions from this section. Start each new question on a new page.. All necessary working must be clearly shown. Marks will be deducted for poor presentation of material.
23. ABCD is a cyclic quadrilateral such that the tangent
at A to the circle is parallel to ED; AC cuts HD at
Prove that (a) AC bisects BCD,
(b) AB touches the circle CBE.
12 CA.
then
2k. ABCD is a quadrilateral; Y
AC, BD. Prove that
are the mid-points of
AB2+ BC2+ CD2+ DA2 = AC2+ BD2+ 4XY?
(B) the triangle is right-angled
...
(C) the triangle is obtuse-angled:
Quad, ABCD is formed by the external bisectors of
angles of any quadrilateral. Then
(A) ABCD 18 a parallelogram
(B) ABCD is a rectangle.
(C) ABCD is a cyclic quadrilateral
(D) ABCD is a quadrilateral
7. Find the number of sides of a polygon if the sum of it.
angles is three times that of an octagon.
25. AB, DC are the parallel sides of a trapezium ABCD; AG
cuts BD at K. If the line through K parallel to BA cuts AD at P, prove that A PBC= 2 AKAD.
26. In AABC, BAC #90° and AD is an altitude.
If t bisector of ABC meets AD, AC at L, X, prove that AL: LDCK: KA
27. In ABC, A is a right angle; 0 is the centre of the square BPC outside ABC. Prove that AO bisects, /BAC.
:
26. Given a point A between two given lines BC, DE,
construct points P, Q.on BC. DE respectively, such that AAPQ is equilateral.
KINTS & ANS. TO LESSON - 28
Ans.
Section
8. D is the mid-point of the side BC of AABC. IF AD-ED.
find the size of LDXC.
1. (A)
2. (D)
3. (C)
4. (E)
5. (A)
6. (Q)
7. (s)
8. (P)
9. (R)
11. (A)
10. (T)
Ans.
12. (C)
13. (A)
14. (D)
15. (E)
16. (Q)
17. (T)
18. (R)
19. (P)
20. (R)
9. ABCD is a square; ABX is an equilateral triangle
21. (A)
. 22. (D)
23. (B)
24. (D)
inside the square.
26. (R) 31. (A)
25. (A)
27. (a)
28. (T)
29. (S)
30. (P)
32. (B)
Ane.
10. D, E are points on the sidea AC, AB:resp., of ABC Buch that AD AG and AE AB. If the area of
ABC is 18 sq.in,, find the area of CDE
Ans.
36.(Q) 3?. (P)
33. (D) 38. (Q)
34. (A)
35. (E)
39.
(R)
40. (s)
Section B
43. (a)
2x 2n
=
2 x 2" x (23 - 1)
x 4
2 x 2" x 4
__3(1-x)
4(2-x)=3(1-x)
(or 1-2)
42. (a), 2x = 641 + x = -5 -4x=55+ 20 - 22
(5 +_ = 3 ) + (1 + 27)-(4+ _ _ 11 ) + ( 2+ _—_ )
+(x = 13) (x-13)(x-7)
2(x - 10) (x-130(2-7)
+
- 6)† (x - 14)
· (x=14)(x-6)
2(x - 10) (x-14)(x-6)
2(x-10) [(x-14)(x-6) - (x-13)(x-?)]
2(x-10) [ (x2-20x+84), (* -20x+91)]
10
10
(b) Let
BE then the equations become
12+ B2 = 4-
A
B
By substituting AB+ into the first equation, than we have
· ́`· (8+2)2+ B2= 4)
LNS. x=1, 9=2 or
43. (a) By the series.
log 2+ log 6+ log 18 + the lat term = log 2
2nd tera log 6
3rd tera log 18
B-2 or
Log 6- log 2 Log (log 3
log 18- log 6➡log (1) log 3
the series is an A.P. of which the common difference
log 3
Sun to 15 terms
b) Let a
d
[2a + (n-1)d]
* 15(10g 2+7 log 3) * 57:6
the 1st term of the A.P.
the common difference of the A.P. the 3rd term of the A, P. & +23
4th term of the A.P. = a +3d 7th term of the A.P. = a +6d'
they are consecutive terms of a G.
a+6da + 3d a+3d a+24 d(2a+3d) 0
Q (for d 0)
the following Earm of the G.P. = (a+60) (atéd);(art.r)
the 16th term of the A‚P. —
270
+15a=27d
44. Let x mph, the speed of the train
Original time taken to over 72 miles
Time taken at (6)mph. for 22 =12es
The time is shorten by 10 min.
Ans
•
72 x+6
br.
12
hr.
72 m
€ or x(x+6)=2160
The speed of the train is 45 mph.
5. The graph of 3 is a curve
x+3
While the graph of ywl-x 18 8 st. line. The quadratic equation whose roots are given by the intersections of the two graphs la
=1-
x + 3 3x2+x-6=()
The roots
1.26, -1.59
16. Let a, b, c, d be the four proportionals
such that
=
-10
And
•
a+d=13,
b+c=11
-2= 170
Ans. 3, 6, 5, 10.