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Maths

Mechanics

Kinematics

Edexcel A Level Maths Paper 1 2022 Worked Solutions PDF

Name: Knowunity
Brand: Knowunity

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Edexcel A Level Maths Paper 1 2022 Worked Solutions PDF

@ehsan04

34 Followers

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

1457

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 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.

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.

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.

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.

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.

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.

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.

View

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.

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.

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.

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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.

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Knowunity is the #1 education app in five European countries

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Pupils love Knowunity

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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

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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.

Subjects

Maths

Mechanics

Kinematics

Edexcel A Level Maths Paper 1 2022 Worked Solutions PDF

@ehsan04

34 Followers

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

1457

12/13

Maths

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.

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.

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.

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.

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.

Page 1: Transformations and Algebraic Manipulation

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

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.

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

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.

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.

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.

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.

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.

Download in

Google Play

Download in

App Store

4.9+

Average app rating

13 M

Pupils love Knowunity

#1

In education app charts in 12 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