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Hits: 29 Question a. The polynomial f(x) is given by . i. Use the Factor Theorem to show that x+3 is a factor of f(x). ii. Express f(x) in the form , where p and q are integers. b. A curve has equation . i. Find . ii. Show that the x-coordinates of any stationary points of the curve satisfy the equation […]
Hits: 12 Question The quadratic equation has real roots. (a) Show that . (b) Find the possible values of k. Solution a. We are given the quadratic equation; For a quadratic equation , the expression for solution is; Where is called discriminant. If , the equation will have two distinct roots. If , the equation will have […]
Hits: 19 Question A curve has equation . The point P with coordinates (-1,6) lies on the curve. a. Find the equation of the tangent to the curve at the point P, giving your answer in the form . b. The point Q with coordinates (2,k) lies on the curve. i. Find the value of k. ii. Verify that […]
Hits: 12 Question a. i. Express in the form , where p and q are rational numbers. ii. Hence write down the minimum value of . b. The point A has coordinates (-3,5) and the point B has coordinates (x,3x+9). i. Show that . ii. Use your result from part (a)(ii) to find […]
Hits: 18 Question A circle C has the equation a. Write the equation of C in the form Where a, b and k are integers. b. Hence, for the circle C write down: i. the coordinates of its center; ii. its radius. c. i. Sketch the circle C. ii. Write down the coordinates of the point on C that […]
Hits: 12 Question a. i. Express in the form , where k is an integer. ii. Solve the equation giving your answer in its simplest form. b. Express in the form , where m is an integers. Solution a. […]
Hits: 12 Question The line AB has equation . a. The point with coordinates (p,p+2) lies on the line AB. Find the value of the constant p. b. Find the gradient of AB. c. The point A has coordinates (1,2). The point C(-5,k) is such that AC is perpendicular to AB. Find the value of k. d. The […]
