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### much, much more.

### QUESTIONS BY TOPIC

StudyWell is a website for students studying A-Level Maths (or equivalent. course). We have lots of resources including A-Level content delivered in manageable bite-size pieces, practice papers, past papers, questions by topic, worksheets, hints, tips, advice and### much, much more.

PURE MATHS - STUDYWELL StudyWell is a website for students studying A-Level Maths (or equivalent. course). We have lots of resources including A-Level content delivered in manageable bite-size pieces, practice papers, past papers, questions by topic, worksheets, hints, tips, advice and### much, much more.

### VECTORS - STUDYWELL

Vectors 2D vectors are explored in the first year of A-Level Maths and you would be expected to use arithmetic and solve problems with 2D vectors. 3D vectors are explored briefly in the second year of A-Level Maths. Vectors in AS-Maths two-dimensional vectors vector arithmetic vectors in context Vectors in A2 Maths TBC Other Areas in AS-Maths MECHANICS - STUDYWELL AS Mechanics Topics Quantities & Units understand the quantities and units of length, time, mass, velocity, acceleration, force, weight Kinematics understand position, displacement, distance, velocity, speed and acceleration understand and interpret graphs for motion on a straight line understand, use and derive the SUVAT equations use calculus in kinematics for motion on a straight NON RIGHT ANGLED TRIANGLES In order to use these rules, we require a technique for labelling the sides and angles of the non-right angled triangle. This may mean that a relabelling of the features given in the actual question is needed. See the non-right angled triangle given here. Angle A is opposite side a, angle B is opposite side B and angle C is opposite side c. CIRCLES - PAST EDEXCEL EXAM QUESTIONS - STUDYWELL Coordinate Geometry Circles - Past Edexcel Exam Questions 1. (Question 5 - C2 May 2018) The circle C has equation x 2+ y 2x+ 14y = 0: Find (a) the coordinates of the centre of C,### PROOF BY DEDUCTION

Proof by deduction is a process in maths where we show that a statement is true using well-known mathematical principles. With this in mind, try not to confuse it with Proof by Induction or Proof by Exhaustion. The word deduce means to establish facts through reasoning or make conclusions about a particular instance by referring to a general rule or principle.### BINOMIAL EXPANSION

Binomial Expansion 11. (Question 5 - C2 Jan 2011) Given that 40 4 = 40! 4!b!, (a) write down the value of b. In the binomial expansion of (1 + x)40, the coe cients of x4 and x5 are p and q respectively.### DI ERENTIATION

Di erentiation 7. (Question 11 - C1 May 2016) The curve C has equation y = 2x3 + kx2 + 5x+ 6, where k is a constant. (a) Find dy dx. The point P, where x = 2, lies on C. The tangent to C at the point P is parallel to the line with equation 2y 17x 1 = 0. HOME FOR A-LEVEL MATHS StudyWell is a website for students studying A-Level Maths (or equivalent. course). We have lots of resources including A-Level content delivered in manageable bite-size pieces, practice papers, past papers, questions by topic, worksheets, hints, tips, advice and### much, much more.

### QUESTIONS BY TOPIC

StudyWell is a website for students studying A-Level Maths (or equivalent. course). We have lots of resources including A-Level content delivered in manageable bite-size pieces, practice papers, past papers, questions by topic, worksheets, hints, tips, advice and### much, much more.

PURE MATHS - STUDYWELL StudyWell is a website for students studying A-Level Maths (or equivalent. course). We have lots of resources including A-Level content delivered in manageable bite-size pieces, practice papers, past papers, questions by topic, worksheets, hints, tips, advice and### much, much more.

### VECTORS - STUDYWELL

Vectors 2D vectors are explored in the first year of A-Level Maths and you would be expected to use arithmetic and solve problems with 2D vectors. 3D vectors are explored briefly in the second year of A-Level Maths. Vectors in AS-Maths two-dimensional vectors vector arithmetic vectors in context Vectors in A2 Maths TBC Other Areas in AS-Maths MECHANICS - STUDYWELL AS Mechanics Topics Quantities & Units understand the quantities and units of length, time, mass, velocity, acceleration, force, weight Kinematics understand position, displacement, distance, velocity, speed and acceleration understand and interpret graphs for motion on a straight line understand, use and derive the SUVAT equations use calculus in kinematics for motion on a straight NON RIGHT ANGLED TRIANGLES In order to use these rules, we require a technique for labelling the sides and angles of the non-right angled triangle. This may mean that a relabelling of the features given in the actual question is needed. See the non-right angled triangle given here. Angle A is opposite side a, angle B is opposite side B and angle C is opposite side c. CIRCLES - PAST EDEXCEL EXAM QUESTIONS - STUDYWELL Coordinate Geometry Circles - Past Edexcel Exam Questions 1. (Question 5 - C2 May 2018) The circle C has equation x 2+ y 2x+ 14y = 0: Find (a) the coordinates of the centre of C,### PROOF BY DEDUCTION

Proof by deduction is a process in maths where we show that a statement is true using well-known mathematical principles. With this in mind, try not to confuse it with Proof by Induction or Proof by Exhaustion. The word deduce means to establish facts through reasoning or make conclusions about a particular instance by referring to a general rule or principle.### BINOMIAL EXPANSION

Binomial Expansion 11. (Question 5 - C2 Jan 2011) Given that 40 4 = 40! 4!b!, (a) write down the value of b. In the binomial expansion of (1 + x)40, the coe cients of x4 and x5 are p and q respectively.### DI ERENTIATION

Di erentiation 7. (Question 11 - C1 May 2016) The curve C has equation y = 2x3 + kx2 + 5x+ 6, where k is a constant. (a) Find dy dx. The point P, where x = 2, lies on C. The tangent to C at the point P is parallel to the line with equation 2y 17x 1 = 0.### VECTORS - STUDYWELL

Vectors 2D vectors are explored in the first year of A-Level Maths and you would be expected to use arithmetic and solve problems with 2D vectors. 3D vectors are explored briefly in the second year of A-Level Maths. Vectors in AS-Maths two-dimensional vectors vector arithmetic vectors in context Vectors in A2 Maths TBC Other Areas in AS-Maths### PRACTICE PAPERS

StudyWell is a website for students studying A-Level Maths (or equivalent. course). We have lots of resources including A-Level content delivered in manageable bite-size pieces, practice papers, past papers, questions by topic, worksheets, hints, tips, advice and### much, much more.

MECHANICS - STUDYWELL StudyWell is a website for students studying A-Level Maths (or equivalent. course). We have lots of resources including A-Level content delivered in manageable bite-size pieces, practice papers, past papers, questions by topic, worksheets, hints, tips, advice and### much, much more.

### ALGEBRA & FUNCTIONS

Algebra and Functions The following list of topics are usually covered in the first year of A-Level Maths or equivalent. In the second year, algebraic fractions, the modulus function, composite & inverse functions, combinations of transformations and partial fractions are covered. Algebra & Functions in AS-Maths completing the square cubics curve sketching discriminant indices inequalities### TRANSFORMATIONS

A y -transformation affects the y coordinates of a curve. You can identify a y -transformation as changes are made outside the brackets of y = f ( x). We examine y -transformations first since they behave as expected. Upward shift: f ( x) → f ( x) + 4, this is a y -shift. This does not affect x coordinates but all the y coordinates go up by### 4.

### TREE DIAGRAMS

Tree Diagrams, like Venn Diagrams, provide a simple visual way of representing events and their associated probabilities. They can be used to calculate more complicated probabilities. Tree Diagrams display the probabilities different event outcomes on the ‘branches’ of the diagram. Typically, the events are considered sequentially (one after the other) moving along the branches from LINEAR INTERPOLATION & CODING Split the interval evenly between 37 values and let the first value be 0.3. Q1 is then given by 4th value: 0.3 + 3 × 0.1 37 ≈ 0.3081. Hence, the lower quartile is £308,100. Q2 = 100 2 th value = 50th value – the 50th value is the 29th value in the second interval. Q2 is given by: 0.3 + 28 × 0.1 37 ≈ 0.3757. Hence, the median is### 375,700.

35 BASIC PURE MATH QUESTIONS 35 Basic Pure Math Questions. The following is a list of basic pure maths questions that students should be able to tackle if they are prepared for a subset of the AS-Level Pure Maths exam. They have been designed to cover the techniques that will be needed in order MOTION IN A STRAIGHT LINE Recall that acceleration at a given time measures the instantaneous change in velocity – see Quantities & Units in Mechanics. For motion in a straight line with constant acceleration, the speed along the line changes by the same amount every second. Hence, if speed is measured in metres per second (m/s) then acceleration is measured### PROOF BY EXHAUSTION

Proof by Exhaustion is the proof that something is true by showing that it is true for each and every case that could possibly be considered.This is also known as Proof by Cases– see Example 1.This is different from Proof by Deduction whereby we use algebraic symbols and construct logical arguments from known facts to show that something is true for all numbers. HOME FOR A-LEVEL MATHS StudyWell is a website for students studying A-Level Maths (or equivalent. course). We have lots of resources including A-Level content delivered in manageable bite-size pieces, practice papers, past papers, questions by topic, worksheets, hints, tips, advice and### much, much more.

### QUESTIONS BY TOPIC

StudyWell is a website for students studying A-Level Maths (or equivalent. course). We have lots of resources including A-Level content delivered in manageable bite-size pieces, practice papers, past papers, questions by topic, worksheets, hints, tips, advice and### much, much more.

### PRACTICE PAPERS

StudyWell is a website for students studying A-Level Maths (or equivalent. course). We have lots of resources including A-Level content delivered in manageable bite-size pieces, practice papers, past papers, questions by topic, worksheets, hints, tips, advice and### much, much more.

PURE MATHS - STUDYWELL StudyWell is a website for students studying A-Level Maths (or equivalent. course). We have lots of resources including A-Level content delivered in manageable bite-size pieces, practice papers, past papers, questions by topic, worksheets, hints, tips, advice and### much, much more.

MECHANICS - STUDYWELL AS Mechanics Topics Quantities & Units understand the quantities and units of length, time, mass, velocity, acceleration, force, weight Kinematics understand position, displacement, distance, velocity, speed and acceleration understand and interpret graphs for motion on a straight line understand, use and derive the SUVAT equations use calculus in kinematics for motion on a straight### TRANSFORMATIONS

A y -transformation affects the y coordinates of a curve. You can identify a y -transformation as changes are made outside the brackets of y = f ( x). We examine y -transformations first since they behave as expected. Upward shift: f ( x) → f ( x) + 4, this is a y -shift. This does not affect x coordinates but all the y coordinates go up by### 4.

NON RIGHT ANGLED TRIANGLES In order to use these rules, we require a technique for labelling the sides and angles of the non-right angled triangle. This may mean that a relabelling of the features given in the actual question is needed. See the non-right angled triangle given here. Angle A is opposite side a, angle B is opposite side B and angle C is opposite side c. 35 BASIC PURE MATH QUESTIONS 35 Basic Pure Math Questions. The following is a list of basic pure maths questions that students should be able to tackle if they are prepared for a subset of the AS-Level Pure Maths exam. They have been designed to cover the techniques that will be needed in order### PROOF BY EXHAUSTION

Proof by Exhaustion is the proof that something is true by showing that it is true for each and every case that could possibly be considered.This is also known as Proof by Cases– see Example 1.This is different from Proof by Deduction whereby we use algebraic symbols and construct logical arguments from known facts to show that something is true for all numbers.### PROOF BY DEDUCTION

Proof by deduction is a process in maths where we show that a statement is true using well-known mathematical principles. With this in mind, try not to confuse it with Proof by Induction or Proof by Exhaustion. The word deduce means to establish facts through reasoning or make conclusions about a particular instance by referring to a general rule or principle. HOME FOR A-LEVEL MATHS StudyWell is a website for students studying A-Level Maths (or equivalent. course). We have lots of resources including A-Level content delivered in manageable bite-size pieces, practice papers, past papers, questions by topic, worksheets, hints, tips, advice and### much, much more.

### QUESTIONS BY TOPIC

StudyWell is a website for students studying A-Level Maths (or equivalent. course). We have lots of resources including A-Level content delivered in manageable bite-size pieces, practice papers, past papers, questions by topic, worksheets, hints, tips, advice and### much, much more.

### PRACTICE PAPERS

StudyWell is a website for students studying A-Level Maths (or equivalent. course). We have lots of resources including A-Level content delivered in manageable bite-size pieces, practice papers, past papers, questions by topic, worksheets, hints, tips, advice and### much, much more.

PURE MATHS - STUDYWELL StudyWell is a website for students studying A-Level Maths (or equivalent. course). We have lots of resources including A-Level content delivered in manageable bite-size pieces, practice papers, past papers, questions by topic, worksheets, hints, tips, advice and### much, much more.

MECHANICS - STUDYWELL AS Mechanics Topics Quantities & Units understand the quantities and units of length, time, mass, velocity, acceleration, force, weight Kinematics understand position, displacement, distance, velocity, speed and acceleration understand and interpret graphs for motion on a straight line understand, use and derive the SUVAT equations use calculus in kinematics for motion on a straight### TRANSFORMATIONS

A y -transformation affects the y coordinates of a curve. You can identify a y -transformation as changes are made outside the brackets of y = f ( x). We examine y -transformations first since they behave as expected. Upward shift: f ( x) → f ( x) + 4, this is a y -shift. This does not affect x coordinates but all the y coordinates go up by### 4.

NON RIGHT ANGLED TRIANGLES In order to use these rules, we require a technique for labelling the sides and angles of the non-right angled triangle. This may mean that a relabelling of the features given in the actual question is needed. See the non-right angled triangle given here. Angle A is opposite side a, angle B is opposite side B and angle C is opposite side c. 35 BASIC PURE MATH QUESTIONS 35 Basic Pure Math Questions. The following is a list of basic pure maths questions that students should be able to tackle if they are prepared for a subset of the AS-Level Pure Maths exam. They have been designed to cover the techniques that will be needed in order### PROOF BY EXHAUSTION

Proof by Exhaustion is the proof that something is true by showing that it is true for each and every case that could possibly be considered.This is also known as Proof by Cases– see Example 1.This is different from Proof by Deduction whereby we use algebraic symbols and construct logical arguments from known facts to show that something is true for all numbers.### PROOF BY DEDUCTION

Proof by deduction is a process in maths where we show that a statement is true using well-known mathematical principles. With this in mind, try not to confuse it with Proof by Induction or Proof by Exhaustion. The word deduce means to establish facts through reasoning or make conclusions about a particular instance by referring to a general rule or principle.### VECTORS - STUDYWELL

Vectors 2D vectors are explored in the first year of A-Level Maths and you would be expected to use arithmetic and solve problems with 2D vectors. 3D vectors are explored briefly in the second year of A-Level Maths. Vectors in AS-Maths two-dimensional vectors vector arithmetic vectors in context Vectors in A2 Maths TBC Other Areas in AS-Maths### TREE DIAGRAMS

Tree Diagrams, like Venn Diagrams, provide a simple visual way of representing events and their associated probabilities. They can be used to calculate more complicated probabilities. Tree Diagrams display the probabilities different event outcomes on the ‘branches’ of the diagram. Typically, the events are considered sequentially (one after the other) moving along the branches from SAMPLING - STUDYWELL Methods of Sampling. Simple Random Sampling – a selection process where each member of the population has an EQUAL chance of being selected. Stratified Sampling – Stratum is another word for class, level or grade.Strata is then the plural of stratum. Stratified sampling is a sampling technique that preserves the given strata### proportions.

### INDICES - STUDYWELL

Indices. Indices are also known as powers, exponents or sometimes even orders. Note that indices is plural and index is singular. a is the power/exponent and x is the base. In English, when a letter is smaller and on the upper right side of the bigger letter, we call it a superscript. In Maths, it is often a power. STUDYWELL MATHEMATICAL PROOF SOLUTIONS Get ahead of the game - instantly download the Proof TEST and its SOLUTIONS and master proof by deduction, proof by exhaustion and disproof by counterexample. Don't cram at exam time, study now while you're on-the-go. See below for an example question and details on how to access your files in the next few minutes.### PROOF BY DEDUCTION

Proof by deduction is a process in maths where we show that a statement is true using well-known mathematical principles. With this in mind, try not to confuse it with Proof by Induction or Proof by Exhaustion. The word deduce means to establish facts through reasoning or make conclusions about a particular instance by referring to a general rule or principle. MOTION IN A STRAIGHT LINE Recall that acceleration at a given time measures the instantaneous change in velocity – see Quantities & Units in Mechanics. For motion in a straight line with constant acceleration, the speed along the line changes by the same amount every second. Hence, if speed is measured in metres per second (m/s) then acceleration is measured### VENN DIAGRAMS

A Venn diagram, named after John Venn in the 19th century, provide a convenient way to represent a sample space. Click here to remind yourself of what a sample space is. A Venn diagram is a rectangle representing the whole space and circles inside representing various subspaces. For example, A could represent the event that a person had### blue eyes.

MUTUALLY EXCLUSIVE & INDEPENDENT EVENTS Mutually Exclusive Events. Two events A and B are said to be mutually exclusive if it is not possible that both of them occur at the same time. For example, consider the toss of a coin. Let A be the event that the coin lands on heads and B be the event that the coin lands on tails. It follows that, in a single fair coin toss, events A and B are CUMULATIVE FREQUENCY DIAGRAMS Cumulative Frequency Diagrams. ‘Cumulative’ is the adjective for accumulate. It means to add up successively. It follows that cumulative frequency is where the grouped frequencies are added up at each step. Cumulative Frequency Diagrams look very similar to Frequency Polygons but since frequency is added up each time, the### graph should trend

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