Cool Worksheets for Edexcel Year 1 Maths: Exponential Functions & Logarithms

Kat ◡̈

16/10/2025

Maths

Edexcel maths year 1 - exponential functions and logarithms notes

642

•

16 Oct 2025

•

4 pages

Cool Worksheets for Edexcel Year 1 Maths: Exponential Functions & Logarithms

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Kat ◡̈

@katmccrindell_xoxo

Understanding exponential functions and logarithms is crucial for success in ... Show more

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Exponential functions
f(x) = a* (where a is a constant)
Example....
All Cross the
प
at I as Any number
to the power of 0 is I
asymtote
Diffe

Logarithms

This page delves into logarithms, a crucial topic for A level Maths logarithms questions and answers pdf.

Logarithms are introduced as the inverse of exponential functions:

Definition: If aˣ = n, then log_a $n$ = x

The laws of logarithms are presented:

Multiplication law: log_a $x$ + log_a $y$ = log_a(xy)
Division law: log_a $x$ - log_a $y$ = log_a(x/y)
Power law: log_a $x^n$ = n log_a(x)

Special cases and properties of logarithms are discussed:

Highlight: log_a $a$ = 1 and log_a $1$ = 0

The page also covers the natural logarithm (ln) and provides examples of solving logarithmic equations:

Example: 3ˣ = 2ˣ⁺¹ Solution: x = ln $2$ / $ln(3$ - ln(2)) ≈ 1.71 (3 sig figs)

These concepts are essential for Exponentials and logarithms AS Level Maths Edexcel coursework.

Exponential Modelling

This final page demonstrates the practical application of exponential functions in modelling real-world phenomena, essential for Exponential Modelling A Level Maths Edexcel.

A detailed example is provided, modeling the density of a pesticide over time:

Example: P = 160e^ $-0.006t$ , where P is the density of pesticide and t is time in days

The page walks through various calculations and interpretations:

Calculating the density after 15 days
Interpreting the initial conditions $t = 0$
Finding the rate of change of density

Highlight: The rate of change of the pesticide density is given by dP/dt = -0.006P, indicating a decreasing density over time.

This example illustrates the power of exponential models in describing decay processes and demonstrates key skills required for A level Maths exponentials and logarithms Exam questions.

The page concludes with a discussion on interpreting the model and its limitations, providing valuable insights for students preparing for Exponentials and logarithms A Level Maths pdf assessments.

Exponential Functions

This page introduces exponential functions and their properties, essential for Edexcel year 1 maths exponential functions worksheets.

Exponential functions are defined as f $x$ = aˣ, where a is a constant. These functions have unique properties:

Highlight: All exponential functions cross the y-axis at y = 1, as any number to the power of 0 is 1.

The page also covers differentiation of exponential functions:

Example: If f $x$ = eˣ, then f' $x$ = eˣ If f $x$ = e^ $kx$ , then f' $x$ = ke^(kx)

Transformations of exponential functions are explored, including vertical and horizontal shifts, reflections, and stretches. Several examples are provided to illustrate these concepts:

Example: y = 10eˣ (vertical stretch) y = 3 + 4e^(2x) (combination of transformations)

The page concludes with a comparison of exponential functions and their reciprocals, such as y = 2ˣ and y = $1/2$ ˣ, which are reflections of each other in the y-axis.

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Maths

16 Oct 2025

642

4 pages

Cool Worksheets for Edexcel Year 1 Maths: Exponential Functions & Logarithms

Kat ◡̈ @katmccrindell_xoxo

Understanding exponential functions and logarithms is crucial for success in A Level Maths exponentials and logarithms Exam questions.

The study of exponential functions begins with understanding basic properties and... Show more

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Logarithms

This page delves into logarithms, a crucial topic for A level Maths logarithms questions and answers pdf.

Logarithms are introduced as the inverse of exponential functions

Definition If aˣ = n, then log_a $n$ = x

The laws of logarithms are presented

Multiplication law log_a $x$ + log_a $y$ = log_a(xy)
Division law log_a $x$ - log_a $y$ = log_a(x/y)
Power law log_a $x^n$ = n log_a(x)

Special cases and properties of logarithms are discussed

Highlight log_a $a$ = 1 and log_a $1$ = 0

The page also covers the natural logarithm (ln) and provides examples of solving logarithmic equations

Example 3ˣ = 2ˣ⁺¹ Solution x = ln $2$ / $ln(3$ - ln(2)) ≈ 1.71 (3 sig figs)

These concepts are essential for Exponentials and logarithms AS Level Maths Edexcel coursework.

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Exponential Modelling

This final page demonstrates the practical application of exponential functions in modelling real-world phenomena, essential for Exponential Modelling A Level Maths Edexcel.

A detailed example is provided, modeling the density of a pesticide over time

Example P = 160e^ $-0.006t$ , where P is the density of pesticide and t is time in days

The page walks through various calculations and interpretations

Calculating the density after 15 days
Interpreting the initial conditions $t = 0$
Finding the rate of change of density

Highlight The rate of change of the pesticide density is given by dP/dt = -0.006P, indicating a decreasing density over time.

This example illustrates the power of exponential models in describing decay processes and demonstrates key skills required for A level Maths exponentials and logarithms Exam questions.

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Access to all documents

Improve your grades

Join milions of students

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Exponential Functions

This page introduces exponential functions and their properties, essential for Edexcel year 1 maths exponential functions worksheets.

Exponential functions are defined as f $x$ = aˣ, where a is a constant. These functions have unique properties

Highlight All exponential functions cross the y-axis at y = 1, as any number to the power of 0 is 1.

The page also covers differentiation of exponential functions

Example If f $x$ = eˣ, then f' $x$ = eˣ If f $x$ = e^ $kx$ , then f' $x$ = ke^(kx)

Transformations of exponential functions are explored, including vertical and horizontal shifts, reflections, and stretches. Several examples are provided to illustrate these concepts

Example y = 10eˣ (vertical stretch) y = 3 + 4e^(2x) (combination of transformations)

The page concludes with a comparison of exponential functions and their reciprocals, such as y = 2ˣ and y = $1/2$ ˣ, which are reflections of each other in the y-axis.

Sign up to see the contentIt's free!

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