6.6.1 Logarithmic graphs and estimating parameters Quiz: Pearson Edexcel Maths, Unit 6

The 20 questions

1. When linearising y = ab^x with natural logs, what does the y-intercept represent?

   • a
   • b
   • ln a
   • ln b

2. When linearising y = ab^x using base 10 logs, what is the gradient of the line?

   • b
   • log b
   • log a
   • a

3. What is plotted on the vertical axis when linearising y = ax^n?

   • log y
   • x
   • log x
   • y

4. What is the gradient of the linearised form of y = ax^n?

   • log n
   • a
   • n
   • log a

5. What does the y-intercept represent when plotting log y against log x for y = ax^n?

   • a
   • n
   • log a
   • log n

6. Which type of graph paper can be used to plot exponential data without manual log calculations?

   • Log-log paper
   • Isometric paper
   • Frequency paper
   • Polar paper

7. Given log y = 0.5x + 2, what is the value of a if y = ab^x?

   • 0.5
   • 10
   • 100
   • 2

8. If ln y = 3x + 1.5, what is the value of parameter b?

   • 1.5
   • e^1.5
   • 3
   • e^3

9. A line of best fit for log y against x has gradient 0.4. What is b in y = ab^x?

   • 10
   • e^0.4
   • 10^0.4
   • 0.4

10. If log y = 2 log x + 1, find the value of n in y = ax^n.

    • 1
    • 2
    • 10
    • 100

11. Estimate a if log y vs log x gives an intercept of 0.6 and base 10 is used.

    • 3.98
    • 1.6
    • 4.00
    • 0.6

12. Which logarithm base is standard when using natural scale data for exponential decay?

    • Base e
    • Base 3
    • Base 10
    • Base 2

13. What type of relationship is indicated by a straight line on log-log graph paper?

    • Power function
    • Linear function
    • Quadratic function
    • Exponential function

14. What type of relationship is indicated by a straight line on semi-log graph paper?

    • Polynomial function
    • Exponential function
    • Sine function
    • Power function

15. If y = 5x^3, what is the equation of the linearised logarithmic form?

    • log y = log 5x + 3
    • log y = 3 log x + log 5
    • y = 3 log x + 5
    • log y = 5 log x + 3

16. What statistical method estimates parameters a and b from experimental linear data?

    • Binomial expansion
    • Integration
    • Line of best fit
    • Hypothesis test

17. If ln y = 2 ln x + 4, what is the value of a in y = ax^n?

    • e^4
    • 2
    • e^2
    • 4

18. What represents the constant a when plotting log y against x for y = ab^x?

    • y-intercept
    • exponent
    • base
    • gradient

19. What represents the parameter n when plotting log y against log x for y = ax^n?

    • gradient
    • coefficient
    • y-intercept
    • intercept

20. What is the general name for graph paper with logarithmic scales on both axes?

    • Log-log paper
    • Cartesian paper
    • Probability paper
    • Semi-log paper

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