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)
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