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Hits: 115 Question The first term of an arithmetic sequence is 30 and the common difference is –1.5. a. Find the value of the 25th term. The rth term of the sequence is 0. b. Find the value of r. The sum of the first n terms of the sequence is Sn. c. Find the largest positive […]
Hits: 26 Question The curve C has equation y=(x + 3)(x −1)2 . a. Sketch C showing clearly the coordinates of the points where the curve meets the coordinate axes. b. Show that the equation of C can be written in the form y = x3 + x2 − 5x + k, where k is a […]
Hits: 19 Question The curve C has equation y = f(x), x > 0, and . Given that the point P(4,1) lies on C, a. find f(x) and simplify your answer. b. Find an equation of the normal to C at the point P(4, 1). Solution a. We are required to find f(x), when; We are also […]
Hits: 141 Question The equation x2 + kx + 8 =k has no real solutions for x. a. Show that k satisfies k2 + 4k – 32 >0. b. Hence find the set of possible values of k. Solution a. We are given; We are given that given equation has no real roots. For a […]
Hits: 16 Question A sequence is given by: x1=1, xn+1=xn(p+ xn), where p is a constant (p≠0) . a. Find x2 in terms of p. b. Show that x3=1+3p+2p2. Given that x3=1, c. find the value of p, d. (d) write down the value of x2008 . Solution a. We are given the sequence […]
Hits: 33 Question Figure 1 shows a sketch of the curve with equation y= f(x). The curve crosses the x-axis at the points (1, 0) and (4, 0). The maximum point on the curve is (2, 5). In separate diagrams sketch the curves with the following equations. On each diagram show clearly the coordinates of the maximum point […]
Hits: 34 Question a. Write in the form where p and q are constants. Given that , x > 0, b. find , simplifying the coefficient of each term. Solution a. We are given; b. We are given; We are required to find; Therefore; Rule for differentiation of is: As demonstrated in (a); Therefore; Rule for differentiation […]
Hits: 17 Question The point A(–6, 4) and the point B (8, –3) lie on the line L. a. Find an equation for L in the form ax + by + c = 0, where a, b and c are integers. b. Find the distance AB, giving your answer in the form , where k is an integer.` […]
Hits: 7 Question Simplify Giving your answer in the form , where a and b are integers. Solution We are given; If we need a rational number in the denominator of a fraction, we need to follow procedure of “denominator rationalization” as given below. ü If the denominator is of the form then multiply both numerator and denominator by […]
Hits: 10 Question a. Find the value of . b. Simplify . Solution a. b.
Hits: 9 Question Find Solution We are required to find; Rule for integration of is: Rule for integration of is: Rule for integration of is: