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Hits: 18 Question The function f is defined by for . i. Express in the form of . ii. Hence find the set of values of for which , giving your answer in exact form. Solution i. We have the expression; We use method of “completing square” to obtain the desired form. We complete […]
Hits: 41 Question The curve C1 has equation y = x2− 4x + 7. The curve C2 has equation y2 = 4x + k, where k is a constant. The tangent to C1 at the point where x = 3 is also the tangent to C2 at the point P. Find the value of k […]
Hits: 137 Question The function f is defined by for . i. Express in the form of where and are constants. ii. State the greatest value of . The function g is defined by for . iii. Find the value of for which . Solution i. We have the expression; […]
Hits: 102 Question The line , where is a constant, is a tangent to the curve at the point on the curve. i.Find the value of . ii.Find the coordinates of . Solution i. We are given equation of the line as; We are given equation of the curve as; It is given that line […]
Hits: 76 Question i. Express in the form of . The function f is defined by for , where is constant. ii. State the largest value of for which is a decreasing function. The value of is now given to be 1. iii. Find an expression for and state the domain of . […]
Hits: 34 Question Two vectors, and , are such that and Where is a constant. i. Find the values of for which is perpendicular to . ii. Find the angle between and when q = 0. Solution i. We are given that; If and & , then and are perpendicular. Therefore, if […]
Hits: 100 Question i. Solve the equation ii. Hence, using logarithms, solve the equation giving the answer correct to 3 significant figures. Solution SOLVING EQUALITION: PIECEWISE i. Let, . We have to consider both moduli separately and it leads to following cases; OR We have the equation; We have to consider […]
Hits: 123 Question The polynomial is defined by where and are constants. It is given that is a factor of and that remainder is 27 when is divided by . i. Find the values of a and b. ii. Hence factorise completely. iii. State the number of roots of the equation p(2y) […]
Hits: 110 Question i. Solve the inequality . ii. Hence find the greatest integer satisfying the inequality Solution SOLVING INEQUALITY: PIECEWISE i. Let, . We can write it as; We have to consider both moduli separately and it leads to following cases; When If then above four intervals translate to […]
Hits: 50 Question The polynomial is defined by where is a constant. It is given that is a factor of i. Find the value of a . ii. Using this value of a, factorise completely. iii. Hence solve the equation , giving the answer correct to 2 significant figures. Solution i. […]
Hits: 76 Question i. Solve the inequality . ii. Hence find the largest integer n satisfying the inequality . Solution SOLVING INEQUALITY: PIECEWISE i. Let, . We can write it as; We have to consider both moduli separately and it leads to following cases; When If then above four intervals translate […]
Hits: 28 Question The polynomial is defined by where is a constant. It is given that is a factor of . i. Find the value of . ii. Using this value of a, factorise completely. iii. Hence solve the equation , giving the answer correct to 2 significant figures. Solution i. […]
Hits: 30 Question i. Solve the inequality . ii. Hence find the largest integer n satisfying the inequality . Solution SOLVING INEQUALITY: PIECEWISE i. Let, . We can write it as; We have to consider both moduli separately and it leads to following cases; When If then above four intervals translate […]
Hits: 41 Question i. Solve the equation . ii. Hence solve the equation , giving the answer correct to 3 significant figures. Solution i. SOLVING EQUATION: PIECEWISE Let, . We have to consider both moduli separately and it leads to following cases; OR We have the equation; We have to consider both […]
Hits: 88 Question i. Solve the equation . ii. Hence solve the equation , giving the answer correct to 3 significant figures. Solution i. SOLVING EQUATION: PIECEWISE Let, . We have to consider both moduli separately and it leads to following cases; OR We have the equation; We have to consider both […]
Hits: 326 Question i. Find the quotient when is divided by , and show that the remainder is 5. ii. Show that the equation has exactly one real root. Solution i. Hence quotient is and remainder is . ii. We are required to show that following equation has exactly […]
Hits: 57 Question Given that satisfies the equation find the value of Solution SOLVING EQUALITION: PIECEWISE Let, . We have to consider both moduli separately and it leads to following cases; OR We have the equation; We have to consider both moduli separately and it leads to following cases; This cannot be solved. Hence, the […]