Answers to Questions :

§ 1.2      \(\frac{41.3}{9.8  ×  0.8}\) =  \({5.3}\)

§ 1.4      \({ab^3}\) =  \({54}\) =>  \({2  ×  3^3}\) = \({54}\) => a = 2  and b = 3

§ 1.6  (1)  \({2.131313.....}\).= \(\frac{211}{9}\)        \({6.252525.......}\)  =  \(\frac{619}{99}\)

§ 1.6 (2 )                   LCM (8,12)= 24                                  HCF(8,12)=4

§ 1.6 (3)  y=3 x 10 -2 =28

§ 1.6 (4)  y=3 x (-7)-2 = -23

§ 2.3   2;    \(2 x^{\frac{-7}{4}}\) ; \(\frac{2}{x^2}\) ;  \(\frac{x^{\frac{5}{2}}}{5}\) ;  \(\frac{8x^{15}}{27}\)

\({2^5}\) =\({8}\)  ;  \({4^0}\) = \({1}\)  =  \(5^{-2}\) =  \(\frac{1}{25}\) ; \(8^{\frac{-2}{3}}\) =  \(\frac{1}{4}\) ;

\({32^x}\) = 2  =>  x = \(\frac{1}{5}\)

§ 2.4     9x² + 15y = 3(3x² +  5y)
3x(2x-4y) =  6x² – 12xy
(x+4)(x-7) = x² – 3x – 28
ax + bx + kay + kby = (a + b)(x + ky)
a² x² – b² y²  = (ax + by)(ax – by)
a² + 2ab + b² =  (a + b)²

ax² + bx + c = \(a(x +\frac{b}{2a} - \frac{\sqrt{b^2 - 4ac}}{2a})( x + \frac{b}{2a} + \frac{\sqrt{b^2 - 4ac}}{2a})\)

\(\frac{x^2 - 2x}{x^2 -x +6}\) = \(\frac{x}{x -3}\)

§2.7  (1) 9 × 5-2(7-4) = 39
(7-5)÷2 + (9-3)×4= \(\frac{5}{2}\)

(2)    w = \(\frac{y}{2x}\)

§ 3.7 (1)  octogon  = 1080° decagon = 1440°

(2) Octagon

(3) y = 110°

(4) y  = 125°
§ 4.6 (1)  Mode = 5 ;     Mean = 7.67 ;    Median = 5.5 ;
Range  =  11-2 = 9
Mean = 1.48 cm

§ 5.6  (1)  =   \(\frac{167}{72}\)

(2)  =  2.14

(3)  Auchan = £0.090 /h ;  Red dragon=£0.089/h

(4) = £ 8095.90
§ 5.7 (1) 12 rulers and 17 pencils

(2) Total  = £ 90.64
§ 6.7    x² + 3x + 2  =  (x+2)(x+1)

§ 7.7    A = a₁× a₂

§ 8.3  P(b)=0.8 => P(\(\bar{b}\) ) =1-0.8=0.2

§ 8.6 (1)  P(2∪5) = \(\frac{1}{3}\)

(2a) P(A∪B) = \(\frac{8}{15}\)

(2b) P(A∪B∪C) = \(\frac{29}{45}\)

(2c) 1-P(A∪B∪C) = \(\frac{16}{45}\)

(2d)1-P(A∪B) = \(\frac{7}{15}\)

(3) P(G|E) = P(E∩G)× P(E) = \(\frac{1}{15}\)

§9.6 p × q = 4 × 10⁴      \(\frac{p}{q}\) = 1.8 × 10⁸

§10.8 9.5 and 9.54 and 9.53

§ 11.7 (1) Arc  = rθ and Area  = \(\frac{1}{2}r^2θ\)

(2) Congruent (1 side and 3 angles)