Hits: 117
Quadratics-2015
Hits: 117 Question The equation of a curve is i. Show that; ii. Find the x-coordinate of each stationary point of the curve in the interval . Give each answer correct to 3 significant figures. Solution i. We are required to show that; We are given; We utilize Quotient Rule to […]
Hits: 43 Question i. Find the quotient when is divided by , and show that the remainder is 39. ii. Hence, show that the equation has exactly one real root. Solution i. Hence quotient is and remainder is . ii. We are required to factorise; When a polynomial, , […]
Hits: 53 Question i. Find the quotient and remainder when is divided by . ii. It is given that, when is divided by , the remainder is ZERO. Find the values of the constants and . iii. When and have these values, show that there is exactly one real value of satisfying the […]
Hits: 94 Question i. Solve the equation . ii. Hence, using logarithms, 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; […]
Hits: 170 Question i. Solve the equation . ii. Hence, using logarithms, solve the equation , giving the answer correct to 3 significant figures. Solution SOLVING EQUATION: ALGEBRAICALLY i. Let, . We can write it as; We have to consider two separate cases; When When We have the […]
Hits: 370 Question i. Solve the equation . ii. Hence, using logarithms, 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; […]
Hits: 38 Question The equation , where p is a constant has no real roots. a. Show that p satisfies p2 – 6p +1 > 0 b. Hence, find the set of possible values of p. Solution a. We are given that; We are given that given equation has no real solutions of x (roots). For […]
Hits: 37 Question A curve has equation and a line has equation , where k is a constant. a. Show that the x-coordinate of any point of intersection of the curve and the line satisfies the equation b. Given that the line and the curve do not intersect:. i. Show […]
Hits: 33 Question a. Sketch the curve with equation . b. The polynomial is given by . i. Find the remainder when is divided by . ii. Use the Factor Theorem to show that is a factor of . iii. Express in the form , where B and c are integers. iv. Hence show that the equation has exactly one real root and state its […]
Hits: 24 Question a. Express in the form , where p and q are rational numbers. b. A curve has equation . i. Use the result from part (a) to write down the coordinates of the vertex of the curve. ii. State the equation of the line of symmetry of the curve. c. The curve with equation is translated by vector . Find the […]
Hits: 48 Question A circle with center C has the equation . a. Express this equation in the form b. i. State the coordinates of C. ii. Find the radius of the circle, giving your answer in the form . c. i. The point P with coordinates (4,k) lies on the circle. Find the possible values of k. […]
Hits: 803 Question The function is defined by for , where a is a constant. The function is defined for . i. Find the largest value of a for which the composite function can be formed. For the case where , ii. solve the equation , iii. find the set of values of which satisfy the inequality . Solution i. […]
Hits: 549 Question i. Express in the form , where a, b and c are constants. ii. The function, where , is defined for . Find and state, with a reason, whether is an increasing function, a decreasing function or neither. Solution i. We have the expression; We use method of “completing square” to obtain […]