Revision

(1) Find the range of x which satisfy the inequality (x 2)2 < x 2. [Ans: 2 < x < 3] (2) Given the functions f : x 2x - 3 and gf: x 2x , find the function g,.(3) Given the functions h : x 1 x and hg : x 1 3x2, find the function g. (4) The roots of the quadratic equation 2x2 + 8 = (k 3)x are real and different. Determine the range of values of k. (5) One of the roots of the equation 2x2 + 6x = 2k 1 is twice the other. Find the value of k and the roots of the equation. [Ans: x = -1 , x = -2 ; k = ](6) Given log3 x = p and log2 x = q. Find logx 36 in terms of m and n.(7) Solve the equation log2 (x + 5) = log2 (x 2) + 3.(8) Given that r cm is the radius of a sphere. Calculate the approximate change in its area when the radius increases from 8 cm to 8.002 cm. [Ans: 0.402](9) C is a point on the straight line that joins A(3, 6) and B(7, 1) such that 3AC = 2CB, find the coordinates of the point C. [Ans: C(1, 4)](10) The coordinates of the three vertices of a triangle are (1, 5), (2b, a) and (2a ,b). Given that a + b = 0 and the area of the triangle is 18 unit2. Find the value of a and of b. [Ans: a = 2 , b = 2; a = 2 , b = 2](11)

Diagram 14 shows a quadrilateral where is acute.

CBADDiagram 148.7 cm5.2 cm9.6 cm12.6 cm38.5o

Calculate

(a)(i) ABC, [Ans: 64.37 o]

(ii) ADC, Ans: (iii)the area, in cm2, of quadrilateral ABCD. Ans: 76.35

(b)A triangle ABC has the same measurements as those given for triangle ABC, that is, AC = 12.6 cm, CB = 8.7cm and CAB = 38.5o but is different in shape compared to triangle ABC. (i)Sketch the triangle ABC.(ii)Calculate the length, in cm, of AB. Ans: 6.098