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1.2 Algebra and Functions

1.2 Algebra and Functions

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Question 203

The altitude hhh of a surveying drone, measured in decameters relative to a reference level, is modeled by the function y=f(x)y = \mathrm{f}(x)y=f(x), where xxx represents the horizontal displacement from a base station. The graph of this function, curve CCC, is characterized by the following properties:

  • It has a single maximum turning point at (5,12.5)(5, 12.5)(5,12.5).
  • It intersects the coordinate axes at exactly two points: (0,7.5)(0, 7.5)(0,7.5) and (15,0)(15, 0)(15,0).
  • It has a single horizontal asymptote with equation y=2.5y = 2.5y=2.5 as x→−∞x \rightarrow -\inftyx→−∞.
a.

State the equation of the asymptote to the curve with equation y=f(−x)y = \mathrm{f}(-x)y=f(−x).

[1]
b.

State the coordinates of the turning point on the curve with equation y=f(2.5x)y = \mathrm{f}(2.5x)y=f(2.5x).

[1]
c.

Given that the line with equation y=ky = ky=k, where kkk is a constant, intersects CCC at exactly one point,

state the possible values for kkk.

[2]
d.

The curve CCC is transformed to a new curve that passes through the origin.

(i) Given that the new curve has equation y=f(x)−ay = \mathrm{f}(x) - ay=f(x)−a, state the value of the constant aaa.

(ii) Write down an equation for another single transformation of CCC that also passes through the origin.

[2]
Markscheme

1.2 Algebra and Functions Questions

  1. A Level
  2. /Maths
  3. /1.2 Algebra and Functions

566 exam-style questions on OCR A Level Maths 1.2 Algebra and Functions, covering 1.2.1 Indices, 1.2.2 Surds, 1.2.3 Simultaneous equations, 1.2.4 Quadratic functions, 1.2.5 Completing the square, 1.2.6 Solving quadratic equations, 1.2.7 Inequalities, 1.2.8 Expressing solutions of inequalities, 1.2.9 Representing inequalities graphically, 1.2.10 Manipulating polynomials, 1.2.11 Simplifying rational expressions, 1.2.12 The modulus function (A-level only), 1.2.13 Graphs of functions, 1.2.14 Sketching curves from equations, 1.2.15 Sketching reciprocal curves, 1.2.16 Interpreting solutions graphically, 1.2.17 Intersection points of graphs, 1.2.18 Proportional relationships, 1.2.19 Graph of the modulus of a linear function (A-level only), 1.2.20 Solving modulus equations graphically (A-level only), 1.2.21 Definition of a function (A-level only), 1.2.22 Inverse and composite functions (A-level only), 1.2.23 Simple graph transformations, 1.2.24 Combinations of graph transformations (A-level only), 1.2.25 Partial fractions (A-level only), and 1.2.26 Models in context. Each one has a worked solution and a mark scheme showing where the marks go.

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