Modelling with Exponentials & Logarithms (OCR A Level Maths: Pure)

Exam Questions

3 hours42 questions

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4 marks

State whether the following functions could represent exponential growth or exponential decay.

(i)

$f (x) = 5 e^{2 x}$

(ii)

$f (t) = 100 e^{- t}$

(iii)

$f (a) = 20 e^{- ka}, k > 0$

(iv)

f (t) = {Ae}^{kt}, A, k > 0

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$t$ ,hours	0	1	2	3	4
$N$ , no. of bacteria	100	210	320	730	1580
$\ln N$ (3SF)	4.61	5.35	5.77	6.59	7.37

$t$ , hours	0	2	4	6
$N$ , no. of bacteria	100	180	340	620
$\log_{3} N$ (3SF)	4.19	4.73	5.31	5.85

$t$ , hours	0	2	4	6
$N$ , no. of bacteria	200	350	600	1100

$a,$ years in business	1	2	3	4
$P$ ,annual profit	£3100	£4384	£5369	£6200

$t$ , hours	0	1.5	3	4.5	6
$N$ , no. of bacteria	120	190	360	680	1230

$a$ , years in business	1	2	3	4
$\log P$ ( $£ P$ is annual profit)	3.74	3.86	3.94	4.01

Modelling with Exponentials & Logarithms (OCR A Level Maths: Pure)

Exam Questions

1. Proof

1.1 Proof

1.2 Proof by Contradiction (A Level only)

2. Algebra & Functions

2.1 Laws of Indices & Surds

2.2 Quadratics

2.3 Simultaneous Equations

2.4 Inequalities

2.5 Polynomials

2.6 Rational Expressions (A Level only)

2.7 Graphs of Functions

2.8 Functions (A Level only)

2.9 Transformations of Functions

2.10 Combinations of Transformations (A Level only)

2.11 Partial Fractions (A Level only)

2.12 Modelling with Functions

2.13 Further Modelling with Functions (A Level only)

3. Coordinate Geometry

3.1 Equation of a Straight Line

3.2 Circles

4. Sequences and Series

4.1 Binomial Expansion

4.2 General Binomial Expansion (A Level only)

4.3 Arithmetic Sequences & Series (A Level only)

4.4 Geometric Sequences & Series (A Level only)

4.5 Sequences & Series (A Level only)

4.6 Modelling with Sequences & Series (A Level only)

5. Trigonometry

5.1 Basic Trigonometry

5.2 Trigonometric Functions

5.3 Trigonometric Equations

5.4 Radian Measure (A Level only)

5.5 Reciprocal & Inverse Trigonometric Functions (A Level only)

5.6 Compound & Double Angle Formulae (A Level only)

5.7 Further Trigonometric Equations (A Level only)

5.8 Trigonometric Proof (A Level only)

5.9 Modelling with Trigonometric Functions (A Level only)

6. Exponentials & Logarithms

6.1 Exponential & Logarithms

6.2 Laws of Logarithms

6.3 Modelling with Exponentials & Logarithms

7. Differentiation

7.1 Differentiation

7.2 Applications of Differentiation

7.3 Further Differentiation (A Level only)

7.4 Further Applications of Differentiation (A Level only)

7.5 Implicit Differentiation (A Level only)

8. Integration

8.1 Integration

8.2 Further Integration (A Level only)

8.3 Differential Equations (A Level only)

9. Parametric Equations

9.1 Parametric Equations (A Level only)

9.2 Further Parametric Equations (A Level only)

10. Numerical Methods

10.1 Solving Equations (A Level only)

10.2 Modelling involving Numerical Methods (A Level only)

11. Vectors

11.1 Vectors in 2 Dimensions

11.2 Vectors in 3 Dimensions (A Level only)