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Hits: 30 Question a. i. Express in the form , where and . ii. Hence find the smallest positive value of satisfying the equation b. Solve the equation for , showing all necessary working and giving the answers correct to 2 decimal places. Solution i. We are given the expression; We […]
Hits: 37 Question The diagram shows the curve with parametric equations , for 0 ≤ t ≤ 2. At the point P on the curve, the y-coordinate is 1. i. Show that the value of t at the point P satisfies the equation . ii. Use the iterative formula with t1 […]
Hits: 34 Question i. Find the quotient and remainder when is divided by . ii. Hence find the exact value of giving the answer in the form where k and a are constants. Solution i. Hence quotient is and remainder is . ii. We are required to solve; When a […]
Hits: 43 Question a. Find the exact value of Show all necessary working. b. Use the trapezium rule with two intervals to find an approximation to Solution a. We are required to show; We know that , therefore; Rule for integration of is: Rule for integration of is: Rule for integration of is: Rule […]
Hits: 36 Question Find the exact coordinates of the stationary point of the curve with equation Solution We are required to find the exact coordinates of the stationary point of the curve. A stationary point on the curve is the point where gradient of the curve is equal to zero; Therefore, we find the […]
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: 43 Question The polynomial is defined by where and are constants. Given that is a factor of , express in terms of . Solution We are given that; We are also given that is a factor of . When a polynomial, , is divided by , and is factor of , then the remainder […]