5. Given that cos 60° = 0.5, what is the value of cos 240 °? 1 6. If sin ° = and cos ° = , calculate the value of tan °. 2 x x x 7. Simplify 2 (14) Functions, Polynomials & Graphs 1. Given that 10x + 18 = (x + find the values of and x2 a)2 b, a b. – – 3 2. Two functions are given below. = 4x, = 2x + 7 f(x) x2 g(x) – (a) If = show that 6x 7 = 0. 2 f(x) g(x), x2 – – (b) Hence find algebraically the values of for which = 2 x f(x) g(x). 3. Solve the equation 3x2 2x 10 = 0. – – Give your answer correct to 2 significant figures. 4 4. Find the range of values of such that the equation 2x + 3 = 0, 0, p px2 p – has no real roots. 4 5. The profit made by a publishing company of a magazine is calculated by the formula = 4x (140 where is the profit (in pounds) and is the selling y x), y x – price (in pence) of the magazine. The graph below represents the profit against the selling price y x. Find the maximum profit the company can make from the sale of the magazine. 4 6. The equation 6x + 8 = 0 can also be written as (x 2)(x 4) = 0. x2 – – – (a) Write down the roots of the equation 6x + 8 = 0. 1 x2 – Part of the graph of = 6x + 8 is shown below. y x2 –
5. Given that cos 60° = 0.5, what is the value of cos 240 °? 1 6. If sin x ° = and cos x ° = , calculate the value of tan x °. 2 7. Simplify 2 (14) Functions, Polynomials & Graphs 1. Given that x2 – 10x + 18 = (x – a)2 + b, find the values of a and b. 3 2. Two functions are given below. f(x) = x2 – 4x, g(x) = 2x + 7 (a) If f(x) = g(x), show that x2 – 6x – 7 = 0. 2 (b) Hence find algebraically the values of x for which f(x) = g(x). 2 3. Solve the equation 3x2 – 2x – 10 = 0. Give your answer correct to 2 significant figures. 4 4. Find the range of values of p such that the equation px2 – 2x + 3 = 0, p 0, has no real roots. 4 5. The profit made by a publishing company of a magazine is calculated by the formula y = 4x (140 – x), where y is the profit (in pounds) and x is the selling price (in pence) of the magazine. The graph below represents the profit y against the selling price x. Find the maximum profit the company can make from the sale of the magazine. 4 6. The equation x2 – 6x + 8 = 0 can also be written as (x – 2)(x – 4) = 0. (a) Write down the roots of the equation x2 – 6x + 8 = 0. 1 Part of the graph of y = x2 – 6x + 8 is shown below.
S4-N5-HW-Booklet.docx