The cross-sectional profile of a custom-designed skate ramp is modeled by the curve C1C_1C1 with equation y=f(x)y = f(x)y=f(x), where f(x)=(6−x)(2x+5)2f(x) = (6 - x)(2x + 5)^2f(x)=(6−x)(2x+5)2 and xxx represents horizontal distance from a sensor in meters.
Sketch C1C_1C1 showing the coordinates of any point where the curve touches or crosses the coordinate axes.
Hence or otherwise, (i) find the values of xxx for which f(3x)=0f(3x) = 0f(3x)=0. (ii) find the value of the constant kkk such that the curve with equation y=f(x)+ky = f(x) + ky=f(x)+k passes through the origin.
A second curve C2C_2C2 has equation y=g(x)y = g(x)y=g(x), where g(x)=f(x−2)g(x) = f(x - 2)g(x)=f(x−2).
(c) (i) Find, in simplest form, g(x)g(x)g(x). You may leave your answer in a factorised form. (ii) Hence, or otherwise, find the yyy-intercept of curve C2C_2C2.
532 exam-style questions on AQA A Level Maths 1.5 B: Algebra and functions, covering 1.5.1 Laws of indices, 1.5.2 Surds, 1.5.3 Quadratic functions, 1.5.4 Simultaneous equations, 1.5.5 Linear and quadratic inequalities, 1.5.6 Polynomials and rational expressions, 1.5.7 Graphs of functions and proportion, 1.5.8 Composite and inverse functions (A-level only), 1.5.9 Transformations of graphs, 1.5.10 Partial fractions (A-level only), and 1.5.11 Functions in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.