I-1 : (a) = (b) = 12 (c) = (d)= 100% (e)=+ (f)=- I. (a)x r% =x1
+ r% = x(1 +r100) (b)x y = yxx 100% (c)x r% = x1 r% = x(1 r100)
(d)x y = xyx 100% (e) = 100% II. (a) = 100% (b) = 100% III. (a)=
(b) = 100% (c)= % (d)= (1 %) IV. P R% n A (a) I=P R% n = PRn100 A =
P + I =P + PRn100 =P(1 +Rn100) I-2 (b) A= P(1 + R%)n I = A P = P(1
+ R%)nP V. (a)P R% n =P(1 + R%)n (b)P R% n =P(1 R%)n V. = 4 (= 5%)
I. (a) l =2r 360 (b)A =r2 360 II. (a) =+2 = Ah (b) =2rh =2rh + 2r2
=r2h (c) =+ = 13Ah (d) =rl =rl +r2 = 13r2h (e) =4r2 = 43r3 III. (a)
X Y (b) C D I-3 IV. ABCACD=ab I. 33 44 55 66 II. 913 4 3 2 67 3 2 I
I. a + b + c = 180() a + b + c + d + e = 360() a = b, p = q () a =
b (, AB//CD) c = b (, AB//CD) b + d = 180 (, AB//CD) I-4 AB//CD (i)
a = b () iic = b () iiib + d = 180 () II. a + b + c = 180 d = a + b
III. ABC~XYZ (i)A =X,B =Y,C =Z; () (ii) ABXY=BCYZ=CAZX () A =X,B
=Y,C =Z, ABC~XYZ(A. A. A. ) ABXY=BCYZ=CAZX ABC~XYZ() I-5 ABXY=CAZXA
=X ABC~XYZ() IV. ABC XYZ (i)A =X,B =Y,C =Z; () (ii) AB = XY, BC =
YZ, CA = ZX. () AB = XY, BC = YZ, CA = ZX, ABC XYZ (SSS) AB = XY,
BC = YZ,B =Y, ABC XYZ (SAS) A =X,B =Y, AB = XY, ABC XYZ (ASA) A
=X,C =Z, AB = XY, ABC XYZ (AAS) AB = XY, BC = YZ,A =X= 90, ABC XYZ
(RHS) V. ABCD (a) AB = DC, AD=BC () (b)BAD=BCD,ABC=ADC () (c) AO =
OC, BO = OD () AB = DC, AD=BC ABCD () I-6 BAD=BCD,ABC=ADC , ABCD ()
AO = OC, BO = OD, ABCD () AB = DC, AB//DC , ABCD () VI. ACB = 90 c2
= a2 + b2() c2 = a2 + b2 ACB = 90() VII. AH=HB AK=KC HK = 12
BCHK//BC() AB//CD//EFAC=CE BD=DF () HK//BC AH=HB AK=KC () I-7 VIII.
a+b>c, b+c>a, c+a>b VIII. () I. a b (a)ab = a b (b)ab =ab
II. i = 1 a b (a)a i = i a = ai (b)ai + bi = (a + b)i (c)ai bi = (a
b)i (d)ai bi = ab (e) aibi=ab I. 2 + bx +c = 0a 0 = 242 II. = 24 2
+ bx +c = 0a 0 (a)> 0 (b)= 0 (c)< 0 III. + = ba; =ca x2 +x +
= 0 I. II. fxmx nf
m III. (a)f
m = 0mx nfx(b)mx nfxf
m = 0 I-8 I. m n a, b 0 m n m>0 II. MN ,a > 0, a 1k I. y x
y=kxk II. y x y =
xk III. (a)z x y z=kxyk (b)z x y z =
yk IV. (a)z x z = k1 + k2xk1k2 (b)z x y z = k1x +k2yk1k2
(a)a>b b>ca>c (b)a>ba+c>b+c (c)a>b
(i)c>0ac>bc; (i)c01a 0 I-9 I (a) A(x1, y1)B(x2, y2) (b) A(x1,
y1)B(x2, y2) (c) A(x1, y1)B(x2, y2) AB (d)m1, m2l1, l2 (i)l1//l2m1
= m2 (ii)l1l2m1m2 = 1 (e)l (x1, y1)(x2, y2)m (i): l (ii): l
(f)Ax+By+C=0 y=mx+c m c y- x-y=0 y-x=0 (g) AC:CB = m:n (h)
(i)(ii)(iii) y- I I. (a) ONABAN=NB () (b) AN=NBONAB () (c) CNAB
AN=NB CN O () I-10 (d) AB=CDOM=ON () (e) OM=ONAB=CD () II. (a) x=2y
() (b) AB APB = 90 () (c) APB = 90AB () (d) x=ya=b () III. (a)
(i)x=yAB
= CD
() (ii)AB
= CD
x=y() (b) (i)x=yAB = CD() (ii)AB = CDx=y() I-11 (c) (i)AB = CD
AB
= CD
() (ii)AB
= CD
AB = CD() (d) AB
: CD
=m:n () (e) AB
: CD
=x:y () IV. (a) A+C = 180 B+D = 180 () (b) x=y () (c) x=yA,B,C D
() (d) A+C = 180 B+D = 180 A,B,C D () (e) y=x A,B,C D (=) I-12 V.
(a) PQ T PQOT() (b) PQOT PQ T() (c) PA APB B (i) PA = PB (ii) x = y
(iii) m = n () (d) PQ T () (e) = = PTQ T () I I. (a) I-13 (b)(0
< < 360) r = x2 + y2 II. III. IV. I-14 II I. II. III. (a)
=
(b) f(x)+k(k>0)k f(x)-k(k>0)k f(x+k)(k>0)k
f(x-k)(k>0)k kf(x)(k>1)y-k kf(x)(0
