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Edexcel A Level Maths Paper 1 2022 Worked Solutions PDF

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Edexcel A Level Maths Paper 1 2022 Worked Solutions PDF
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This A level maths paper 1 2022 worked solutions pdf math covers a range of topics including transformations, algebraic manipulation, calculus, and vector geometry. The paper tests students' ability to apply mathematical concepts to solve complex problems across pure mathematics.

Key points:

  • Includes questions on curve transformations, circle equations, limits and integrals
  • Tests algebraic manipulation skills with factoring and solving equations
  • Covers calculus topics like differentiation and integration
  • Includes vector geometry problems involving parallelograms
  • Requires application of mathematical reasoning and proof techniques

This comprehensive paper provides excellent practice for students preparing for Edexcel A Level Maths Past Papers exams.

23/02/2023

1445

Page 3: Circle Diagram

This page contains a diagram illustrating the circle from the previous question.

The diagram shows:

  • The circle with center at (5, -8)
  • The radius of the circle, which is √169 = 13
  • The point P on the circle that is furthest from the origin

Highlight: The diagram helps visualize the geometric relationships described in the algebraic equation of the circle.

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

Page 6: Cubic Functions and Inequalities

This page focuses on analyzing a cubic function and its properties.

The question provides information about a curve C with equation y = f(x), where f(x) is a cubic expression:

  • It passes through the origin
  • Has a maximum turning point at (2,8)
  • Has a minimum turning point at (6,0)

Students are asked to: a) Determine the range of x-values where f'(x) < 0 b) Find the set of k-values for which the line y = k intersects C at only one point c) Derive the equation of curve C

Vocabulary: A turning point is a point on a curve where the gradient (slope) changes from positive to negative (maximum) or from negative to positive (minimum).

Highlight: This question tests students' understanding of cubic functions, their derivatives, and how they relate to the graph's features.

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

View

Page 7: Proof by Contradiction and Inequalities

This page covers two questions on mathematical reasoning and inequalities.

Question 7(i) asks students to prove by contradiction that if the product of two integers p and q is even, then at least one of p or q must be even.

Question 7(ii) requires students to prove an inequality involving two integers x and y, given that x < 0 and (x + y)² < 9x² + y².

Definition: Proof by contradiction is a method of mathematical proof where you assume the opposite of what you want to prove, and then show that this assumption leads to a logical contradiction.

Highlight: These questions test students' ability to construct logical arguments and manipulate algebraic inequalities.

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

View

Page 9: Differential Calculus

This page continues the car speed modeling problem, focusing on differential calculus to find the maximum speed.

The main tasks are:

  • Differentiating the speed function using the product rule
  • Setting up an equation to find when the derivative equals zero
  • Manipulating the resulting equation to match the given iteration formula

Definition: The product rule is a formula used to find the derivative of two functions multiplied together.

Highlight: This question tests students' ability to apply advanced calculus techniques and algebraic manipulation skills.

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

View

Page 10: Numerical Methods

This page concludes the car speed modeling problem, focusing on using numerical methods to solve equations.

Key points:

  • Students use the iteration formula to find the time at which maximum speed occurs
  • The process involves repeated application of the formula until the values converge

Example: Starting with t₁ = 7, students apply the iteration formula repeatedly to find increasingly accurate approximations of the solution.

Highlight: This question tests students' understanding of numerical methods and their ability to interpret the results in the context of the problem.

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

View

Page 1: Transformations and Algebraic Manipulation

This page covers two main questions focusing on curve transformations and algebraic manipulation.

Question 1 deals with transforming the curve y = f(x) in different ways: a) Vertical translation by 2 units upward b) Reflection in the x-axis
c) Stretch parallel to y-axis with scale factor 3, followed by translation

Example: For part (a), the point P(-2,-5) is mapped to (-2,-3) after a vertical translation of 2 units upward.

Question 2 involves factoring a cubic expression and using the given condition to determine the value of a constant k.

Highlight: The question requires students to use algebraic manipulation skills to factor the expression and solve for the unknown constant.

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

View

Page 8: Modeling Car Speed

This page presents a problem on modeling the speed of a car between two sets of traffic lights.

Key points:

  • The speed v (in m/s) is modeled by the equation v = (10 - 0.4t)ln(t + 1)
  • Students must find the value of T (total time between traffic lights)
  • The question introduces an iteration formula to find when maximum speed occurs

Vocabulary: Iteration is a problem-solving method that uses a repetitive process to approach a desired result.

Highlight: This question combines calculus concepts with practical application, requiring students to interpret and manipulate a complex model.

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

View

Page 5: Modeling Tree Growth

This page presents a problem on modeling the growth of a tree using a quadratic equation.

Key points:

  • The height (h) of the tree is modeled by the equation h² = at + b
  • Students must find the values of a and b using given data points
  • The model is then evaluated for accuracy using an additional data point

Example: Using the given data points (2 years, 2.60m) and (10 years, 5.10m), students can set up a system of equations to solve for a and b.

Highlight: This question tests students' ability to apply mathematical modeling to a real-world scenario and critically evaluate the model's accuracy.

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

View

Page 11: Vector Geometry

This page presents a problem on vector geometry involving a parallelogram.

Key points:

  • A parallelogram PQRS is defined by two vectors: PQ and QR
  • Students must prove that the parallelogram is actually a rhombus
  • The question also requires calculating the exact area of the rhombus

Vocabulary: A rhombus is a quadrilateral with four equal sides.

Highlight: This question tests students' understanding of vector properties and their ability to apply vector operations to solve geometric problems.

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

View

Page 4: Limits and Integrals

This page covers a question on limits and integrals, testing students' understanding of calculus concepts.

The question asks students to: a) Express a given limit as an integral b) Evaluate the integral to show that it equals ln k, where k is a constant to be determined

Definition: A limit is the value that a function approaches as the input (usually x) gets closer to a specific value.

Highlight: This question combines the concepts of limits and definite integrals, requiring students to apply the fundamental theorem of calculus.

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

View

Page 2: Circle Equations

This page focuses on analyzing the equation of a circle and finding its properties.

The question provides the equation of a circle: x² + y² - 10x + 16y = 80

Students are asked to: a) Find the coordinates of the circle's center b) Calculate the radius of the circle c) Determine the exact length of the line segment from the origin to the point on the circle furthest from the origin

Vocabulary: The center of a circle is the point from which all points on the circumference are equidistant.

Example: The center coordinates are found by completing the square for both x and y terms in the equation.

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

View

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

View

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

View

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

View

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

View

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

View

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

View

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

View

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

View

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

View

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

View

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

View

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

View

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

View

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

View

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

View

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

View

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

View

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

View

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Lena, iOS user

I love this app ❤️ I actually use it every time I study.

Can't find what you're looking for? Explore other subjects.

Knowunity is the #1 education app in five European countries

Knowunity has been named a featured story on Apple and has regularly topped the app store charts in the education category in Germany, Italy, Poland, Switzerland, and the United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the #1 education app in five European countries

4.9+

Average app rating

13 M

Pupils love Knowunity

#1

In education app charts in 11 countries

950 K+

Students have uploaded notes

Still not convinced? See what other students are saying...

iOS User

I love this app so much, I also use it daily. I recommend Knowunity to everyone!!! I went from a D to an A with it :D

Philip, iOS User

The app is very simple and well designed. So far I have always found everything I was looking for :D

Lena, iOS user

I love this app ❤️ I actually use it every time I study.

View

Edexcel A Level Maths Paper 1 2022 Worked Solutions PDF
user profile picture

Σ

@ehsan04

·

33 Followers

Follow

Edexcel A Level Maths Paper 1 2022 Worked Solutions PDF

This A level maths paper 1 2022 worked solutions pdf math covers a range of topics including transformations, algebraic manipulation, calculus, and vector geometry. The paper tests students' ability to apply mathematical concepts to solve complex problems across pure mathematics.

Key points:

  • Includes questions on curve transformations, circle equations, limits and integrals
  • Tests algebraic manipulation skills with factoring and solving equations
  • Covers calculus topics like differentiation and integration
  • Includes vector geometry problems involving parallelograms
  • Requires application of mathematical reasoning and proof techniques

This comprehensive paper provides excellent practice for students preparing for Edexcel A Level Maths Past Papers exams.

23/02/2023

1445

Page 3: Circle Diagram

This page contains a diagram illustrating the circle from the previous question.

The diagram shows:

  • The circle with center at (5, -8)
  • The radius of the circle, which is √169 = 13
  • The point P on the circle that is furthest from the origin

Highlight: The diagram helps visualize the geometric relationships described in the algebraic equation of the circle.

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

Register

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

Page 6: Cubic Functions and Inequalities

This page focuses on analyzing a cubic function and its properties.

The question provides information about a curve C with equation y = f(x), where f(x) is a cubic expression:

  • It passes through the origin
  • Has a maximum turning point at (2,8)
  • Has a minimum turning point at (6,0)

Students are asked to: a) Determine the range of x-values where f'(x) < 0 b) Find the set of k-values for which the line y = k intersects C at only one point c) Derive the equation of curve C

Vocabulary: A turning point is a point on a curve where the gradient (slope) changes from positive to negative (maximum) or from negative to positive (minimum).

Highlight: This question tests students' understanding of cubic functions, their derivatives, and how they relate to the graph's features.

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

Register

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

Page 7: Proof by Contradiction and Inequalities

This page covers two questions on mathematical reasoning and inequalities.

Question 7(i) asks students to prove by contradiction that if the product of two integers p and q is even, then at least one of p or q must be even.

Question 7(ii) requires students to prove an inequality involving two integers x and y, given that x < 0 and (x + y)² < 9x² + y².

Definition: Proof by contradiction is a method of mathematical proof where you assume the opposite of what you want to prove, and then show that this assumption leads to a logical contradiction.

Highlight: These questions test students' ability to construct logical arguments and manipulate algebraic inequalities.

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

Register

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

Page 9: Differential Calculus

This page continues the car speed modeling problem, focusing on differential calculus to find the maximum speed.

The main tasks are:

  • Differentiating the speed function using the product rule
  • Setting up an equation to find when the derivative equals zero
  • Manipulating the resulting equation to match the given iteration formula

Definition: The product rule is a formula used to find the derivative of two functions multiplied together.

Highlight: This question tests students' ability to apply advanced calculus techniques and algebraic manipulation skills.

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

Register

Sign up to get unlimited access to thousands of study materials. It's free!

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Join milions of students

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By signing up you accept Terms of Service and Privacy Policy

Page 10: Numerical Methods

This page concludes the car speed modeling problem, focusing on using numerical methods to solve equations.

Key points:

  • Students use the iteration formula to find the time at which maximum speed occurs
  • The process involves repeated application of the formula until the values converge

Example: Starting with t₁ = 7, students apply the iteration formula repeatedly to find increasingly accurate approximations of the solution.

Highlight: This question tests students' understanding of numerical methods and their ability to interpret the results in the context of the problem.

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

Register

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By signing up you accept Terms of Service and Privacy Policy

Page 1: Transformations and Algebraic Manipulation

This page covers two main questions focusing on curve transformations and algebraic manipulation.

Question 1 deals with transforming the curve y = f(x) in different ways: a) Vertical translation by 2 units upward b) Reflection in the x-axis
c) Stretch parallel to y-axis with scale factor 3, followed by translation

Example: For part (a), the point P(-2,-5) is mapped to (-2,-3) after a vertical translation of 2 units upward.

Question 2 involves factoring a cubic expression and using the given condition to determine the value of a constant k.

Highlight: The question requires students to use algebraic manipulation skills to factor the expression and solve for the unknown constant.

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

Register

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Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

Page 8: Modeling Car Speed

This page presents a problem on modeling the speed of a car between two sets of traffic lights.

Key points:

  • The speed v (in m/s) is modeled by the equation v = (10 - 0.4t)ln(t + 1)
  • Students must find the value of T (total time between traffic lights)
  • The question introduces an iteration formula to find when maximum speed occurs

Vocabulary: Iteration is a problem-solving method that uses a repetitive process to approach a desired result.

Highlight: This question combines calculus concepts with practical application, requiring students to interpret and manipulate a complex model.

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

Register

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

Page 5: Modeling Tree Growth

This page presents a problem on modeling the growth of a tree using a quadratic equation.

Key points:

  • The height (h) of the tree is modeled by the equation h² = at + b
  • Students must find the values of a and b using given data points
  • The model is then evaluated for accuracy using an additional data point

Example: Using the given data points (2 years, 2.60m) and (10 years, 5.10m), students can set up a system of equations to solve for a and b.

Highlight: This question tests students' ability to apply mathematical modeling to a real-world scenario and critically evaluate the model's accuracy.

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

Register

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

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By signing up you accept Terms of Service and Privacy Policy

Page 11: Vector Geometry

This page presents a problem on vector geometry involving a parallelogram.

Key points:

  • A parallelogram PQRS is defined by two vectors: PQ and QR
  • Students must prove that the parallelogram is actually a rhombus
  • The question also requires calculating the exact area of the rhombus

Vocabulary: A rhombus is a quadrilateral with four equal sides.

Highlight: This question tests students' understanding of vector properties and their ability to apply vector operations to solve geometric problems.

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

Register

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Join milions of students

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Page 4: Limits and Integrals

This page covers a question on limits and integrals, testing students' understanding of calculus concepts.

The question asks students to: a) Express a given limit as an integral b) Evaluate the integral to show that it equals ln k, where k is a constant to be determined

Definition: A limit is the value that a function approaches as the input (usually x) gets closer to a specific value.

Highlight: This question combines the concepts of limits and definite integrals, requiring students to apply the fundamental theorem of calculus.

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

Register

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Page 2: Circle Equations

This page focuses on analyzing the equation of a circle and finding its properties.

The question provides the equation of a circle: x² + y² - 10x + 16y = 80

Students are asked to: a) Find the coordinates of the circle's center b) Calculate the radius of the circle c) Determine the exact length of the line segment from the origin to the point on the circle furthest from the origin

Vocabulary: The center of a circle is the point from which all points on the circumference are equidistant.

Example: The center coordinates are found by completing the square for both x and y terms in the equation.

1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

Register

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1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

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1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

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1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

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1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

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1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

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1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

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1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

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1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

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1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

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1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

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1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

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1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

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1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

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1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

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1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

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1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

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1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

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Access to all documents

Join milions of students

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1. The point P(-2,-5) lies on the curve with equation y = f(x), xeR
Find the point to which P is mapped, when the curve with equation y = f(

Register

Sign up to get unlimited access to thousands of study materials. It's free!

Access to all documents

Join milions of students

Improve your grades

By signing up you accept Terms of Service and Privacy Policy

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