Question The diagram shows part of the curve and the line x = 1. The point A is the minimum point on the curve. i. Show that the x-coordinate of A satisfies the equation and find the exact value of at A. ii. Find, showing all necessary working, the volume obtained when the […]
Question The one-one function f is defined by for , where c is a constant. i. State the smallest possible value of c. In parts (ii) and (iii) the value of c is 4. ii. Find an expression for and state the domain of . iii. Solve the equation , giving your […]
Question The diagram shows a pyramid OABCD with a horizontal rectangular base OABC. The sides OA and AB have lengths of 8 units and 6 units respectively. The point E on OB is such that OE = 2 units. The point D of the pyramid is 7 units vertically above E. Unit vectors , and […]
Question a. i. Express in the form , where and are constants to be found. ii. Hence, or otherwise, and showing all necessary working, solve the equation For . b. The diagram shows the graphs of and for . The graphs intersect at the points A and B. […]
Question The coordinates of points A and B are (−3k – 1, k + 3) and (k + 3, 3k + 5) respectively, where k is a constant (k ≠ −1). i. Find and simplify the gradient of AB, showing that it is independent of k. ii. Find and simplify the equation of the perpendicular […]
Question The diagram shows a triangle OAB in which angle OAB = 90o and OA = 5 cm. The arc AC is part of a circle with centre O. The arc has length 6 cm and it meets OB at C. Find the area of the shaded region. Solution It is evident from the diagram […]
Question A curve with equation y = f(x) passes through the point A(3, 1) and crosses the y- axis at B. It is given that . Find the y-coordinate of B. Solution We are given that curve crosses y-axis at point B. The point at which curve (or line) intercepts y-axis, the value of . […]
Question The common ratio of a geometric progression is 0.99. Express the sum of the first 100 terms as a percentage of the sum to infinity, giving your answer correct to 2 significant figures. Solution We are given that common ration of a Geometric Progression is; Expression for Common Ratio () in a Geometric Progression […]
Question Find the coefficient of in the expansion of . Solution We are required to find the coefficient of in the expansion of . We are given expression as; Expression for the general term in the Binomial expansion of is: First rewrite the given expression in standard form. In the given case: Hence; Since […]
Question Express 3×2 − 12x + 7 in the form a(x + b)2 + c, where a, b and c are constants. Solution We have the expression; We use method of “completing square” to obtain the desired form. Next we complete the square for the terms which involve . We have the algebraic formula; For […]