Skip to content

Course home

1.2 Algebra and Functions

1.2 Algebra and Functions

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354355356357358359360361362363364365366367368369370371372373374375376377378379380381382383384
Question 242

The voltage VVV (in mV) in a biological sensor over time ttt (in ms) is modeled by the function V=V(t)V = V(t)V=V(t). The curve C C\,C with equation V=V(t)V = V(t)V=V(t) is described by the following features:

  • It has a single turning point, a maximum, at (4,12)(4, 12)(4,12).
  • It crosses the vertical axis at (0,7)(0, 7)(0,7) and the horizontal axis at (10,0)(10, 0)(10,0).
  • It has a horizontal asymptote with equation V=3V = 3V=3 as t→−∞t \to -\inftyt→−∞.
  • It decreases without bound as t→+∞t \to +\inftyt→+∞, so that V(t)→−∞V(t) \to -\inftyV(t)→−∞.
a.

State the equation of the horizontal asymptote to the curve with equation y=V(−t)y = V(-t)y=V(−t).

[1]
b.

State the coordinates of the maximum turning point on the curve with equation y=V(2t)y = V(2t)y=V(2t).

[2]
c.

Given that the horizontal line V=kV = kV=k, where k k\,k is a constant, intersects C C\,C at exactly one point:

Determine the possible values for kkk.

[2]
d.

The curve C C\,C is transformed to a new curve that passes through the origin.

(i) Given that the new curve has equation y=V(t)−cy = V(t) - cy=V(t)−c, state the value of the constant ccc.

(ii) Write down an equation for another single transformation of C C\,C that also results in a curve passing 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.

Question bank