# Langy74's Shop

Average Rating4.53
(based on 211 reviews)

All my resources have been created to use with classes I teach. Often I've created resources because, for a particular topic, I haven't been happy with the number/standard of the examples in a textbook. Sometimes I've created worksheets for certain topics (e.g. graph transformations) because I feel my classes will make greater progress on a printed worksheet than trying to work from a textbook. I always aim to produce high-quality resources that improve the students' learning and understanding.

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All my resources have been created to use with classes I teach. Often I've created resources because, for a particular topic, I haven't been happy with the number/standard of the examples in a textbook. Sometimes I've created worksheets for certain topics (e.g. graph transformations) because I feel my classes will make greater progress on a printed worksheet than trying to work from a textbook. I always aim to produce high-quality resources that improve the students' learning and understanding.

#### Convex, concave curves and points of inflection (new A level maths)

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This 11-page resource covers all the required knowledge and techniques for determining if curves are convex/concave and finding points of inflection, as required for the new A level. In each section it contains notes, explanations and examples to work through with your class followed by an exercise of questions for students to attempt themselves (answers included). The sections/topics are: 1.Convex and concave curves (a) determine from a sketch if curve is convex, concave or neither (b) find the values of x for which a graph is convex (or concave) © show algebraically that a function is convex (or concave) 2.Points of inflection (a) find the point(s) of inflection on a graph (b) determine whether a point of inflection is stationary or non-stationary © show that a curve has no points of inflection (d) use point(s) of inflection to determine the values of x for which a curve is convex (or concave) This projectable and printable resource will save you having to create or write out any notes/examples when teaching the topic, and will make things easier for your students as they can just work directly on the given spaces provided for solutions. Answers to all exercises are included. Here is an example of one of my A level resources that is freely available: https://www.tes.com/teaching-resource/differentiation-and-integration-with-exponential-and-trigonometric-functions-new-a-level-11981186

#### Proof by contradiction (new A level maths)

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This short worksheet can be used to deliver the topic of proof by contradiction in the new A level specification for all exam boards. A useful resource to help deliver this new topic - fully worked solutions are included for all examples and questions in the exercise. It begins with 5 examples to work through with your class (the full proofs are given in the teacher’s version). The examples are carefully chosen so that, for the final example, students have seen the results/techniques they need to prove that the square root of 5 is irrational. Students are expected to be familiar with a proof of the infinity of primes, so on the next page this proof is given in full, together with some numerical examples that should help students understand part of its argument. There is then an exercise with 9 questions for students to attempt themselves (full proofs provided). A homework/test is also included (7 questions), with fully-worked solutions provided. Here is an example of one of my A level resources that is freely available: https://www.tes.com/teaching-resource/differentiation-and-integration-with-exponential-and-trigonometric-functions-new-a-level-11981186

#### Using vectors and ratio to find coordinates of a point

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These resources are for teaching how to answer the following type of question, common on new GCSE papers: Points A and B have coordinates (2,3) and (8,-6). Point N is on line AB so that AN:NB = 2:1. Find the coordinates of N. The powerpoint presentation starts with a refresher question about using ratio and then has a number of examples of the above question, with diagrams, to work through as a class. The printable version of the presentation can be given to students for them to complete as you go through the presentation. The worksheet has 14 questions for students to complete on their own, initially with the aid of a diagram and then without for later questions. Fully worked solutions are provided.

#### Conditional probability (new A level maths) - notes, examples, exercises and a homework/test

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This 21-page resource covers all the required knowledge for conditional probability in the A2 part of the new A level. In every section it contains examples to work through with your class followed by an exercise of questions for students to attempt themselves (answers included). The sections are: Venn diagrams and set notation (revision of AS level work) Conditional probability using Venn diagrams Conditional probability using two-way tables Conditional probability using tree diagrams This projectable and printable resource will save you having to draw any tables/diagrams when teaching the topic and will make things easier for your students as they can just work directly on the provided tables and diagrams. The 2 page assessment covers all aspects of the topic and fully worked solutions are provided. Here is an example of one of my A level resources that is freely available: https://www.tes.com/teaching-resource/differentiation-and-integration-with-exponential-and-trigonometric-functions-new-a-level-11981186

#### Using logarithmic graphs for models (new A level maths)

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This resource was designed to help students learn how graphs with logarithmic scales are connected to models of the form y=ab^x and y=ax^n. The first section focuses on models of the form y=ab^x. There are examples to work through as a class, with axes provided, to establish that if y=ab^x then there is a linear relationship between log(y) and x. There is then a page of examples to practice changing from y=ab^x into the linear equation, and vice versa. The examples conclude with 2 questions where students are given experimental data and required to use a graph to estimate the values of a and b in the model y=ab^x - which is typical of an examination-style question. There is then an exercise with 11 questions for students to complete on their own (again, all axes are provided). The second section focuses on models of the form y=ax^n. There are examples to work through as a class, with axes provided, to establish that if y=ax^n then there is a linear relationship between log(y) and log(x). There is then a page of examples to practice changing from y=ax^n into the linear equation, and vice versa. The examples conclude with 2 questions where students are given experimental data and required to use a graph to estimate the values of a and n in the model y=ax^n - which is typical of an examination-style question. There is then an exercise with 11 questions for students to complete on their own (again, all axes are provided). Answers to all questions in the exercises are included. Here is an example of one of my A level resources that is freely available: https://www.tes.com/teaching-resource/differentiation-and-integration-with-exponential-and-trigonometric-functions-new-a-level-11981186

#### Calculations with negative numbers

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My year 7 class struggled to learn the rules for doing calculations that involved negative numbers so I created these resources to try to help them understand the rules and to give them lots of practice. The first resource focuses on addition and subtraction, with explanations of how the calculations can be understood with reference to a number line, and then exercises with lots of practice (over 150 questions). The second resource focuses on multiplication and division, with a page dedicated to them just practising determining whether the answer of a calculation should be positive or negative, and then an exercise with lots of practice calculations (over 80 questions). The third resource contains mixed questions with all 4 operations (over 60 questions). Answers to all the questions are included. The final resource is a spreadsheet where pupils can practise calculations and get instant feedback on their accuracy. Note that the spreadsheet contains macros so when opening the file users may need to click on “Enable editing” or “Enable macros” for it to function correctly.

#### Exponential models (new A level maths) - homework/test

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This assessment covers all aspects of the exponential models topics for all examination boards. It contains 20 questions, ranging from simple multiple-choice questions that would be worth 1 mark, to demanding multi-stage problems typical of specimen examination questions. An answer sheet is provided for students to work on (with axes provided for questions that require graph work). Fully-worked solutions are included.

#### Graph transformations and modulus function homework/test (new A level)

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This 2-page resource is a great way to assess your students after teaching them combined graph transformations and the modulus function for the new A level specification. The resource is designed for students to write on the sheet in the spaces or on the axes provided for questions that require sketches. Fully worked solutions are included.

#### Translations worksheet (transformation of shapes)

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These printable worksheets make it easier to teach this topic as the questions and solutions can just be projected onto a board or screen to work through or check as a class. I normally work through the first worksheet as an example and then set the second worksheet as a task for the class to do on their own. Solutions included. Similar resources available for reflections, rotations and enlargements - please see my shop.

#### Simplifying expressions - worksheet

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This simple, one-sided worksheet is designed to help students learn/recall how to simplify expressions. It begins by explaining when terms can be put together, then there are 12 pairs of terms for students to consider, combining them where appropriate. The final section contains 16 expressions for students to practise simplifying. Answers to the sheet are included.

#### Substitution worksheet

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A simple worksheet for your classes to practise substituting values into expressions and formulas. In total there are over 50 substitutions for them to complete. Includes questions where the answers to each part should form a sequence, so students should be able to notice and correct errors themselves for these questions. I have only used postive and negative integers throughout, but this could be amended to use fractions, surds etc if you wanted to make it more challenging.

#### Collisions (cons. of momentum) - worksheet with 50 examination-style questions (Mechanics 1)

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This worksheet contains nearly 50 questions on collisions of objects - ideal practice for students preparing to sit their Mechanics 1 module exams. It has an introductory section which explains the conservation of momentum principle, then there are 18 questions with &quot;before and after&quot; diagrams to help students solve them. The remaining 29 questions are more demanding and typical of examination questions. Answers to all questions are provided.

#### Worksheets on distance-time and velocity-time graphs

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Each worksheet has a number of examples of graphs for students to learn/practise finding information from the graph. The worksheets include estimating velocity or acceleration by drawing a tangent to the curve. All solutions are included.

#### Resolving forces - worksheet to teach and practise this skill (Mechanics 1)

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I found it time-consuming tryingto teach my classes how to resolve forces by drawing diagrams on the board and asking them to copy them down - it seemed to take ages and they didn't get to work through that many examples themselves. So I created this worksheet with ready-made diagrams with all the forces and a blank copy of diagram for students to add on the resolved forces. I no longer dread teaching this skill and my classes get a lot more done in the lesson time. The worksheet starts with an introductory explanation and a worked example. There are then over 20 questions for students to attempt. Fully worked solutions are included.

#### Worksheets to learn the shapes of trigonometric graphs and solve trigonometric equations

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Teaching a class about the shape of trigonometric graphs and using them to learn rules that can be used to solve trigonometric equations can be difficult using a textbook or drawing on a whiteboard - I find it much easier with these printable worksheets with ready-drawn grids and graphs. The first worksheet gets students to work out and plot values of the sine function between 0 and 360 degrees so see the shape of the curve. There are then a number of examples using the sine graph to find angles with equivalent values using sine (e.g. sin 30 = sin 150). The worksheet finishes with some equations to solve, of the form sinx = a, where the students should use the rule(s) they have learned to find all the solutions. The next two worksheets follow the same format as the first, but now for the cosine and tangent functions. The last document practises working with all 3 graphs/functions so it can be used as a summary activity or assessment.

#### Activity to help students learn which method(s) to choose to solve a quadratic equation

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This powerpoint and accompanying worksheet is designed to help students learn which method(s) they should consider using when asked to solve a quadratic equation. There are 11 examples for students to consider, the answers are given on the presentation. This activity works best if you can give each student (or group) a set of A,B,C cards to hold up for each example so you see if they are learning how to correctly choose the most appropriate method. Note that this is designed to be appropriate for GCSE so completing the square is not considered as a suitable method for solving when the coefficient of x^2 is greater than 1.

#### Two worksheets to practise expanding (a+b)^2 and (a+b)(a-b)

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Each worksheet contains 30 questions. The first worksheet has examples of the form (a+b)^2 and (a-b)^2. The second worksheet has examples of the form (a+b)(a-b). All answers are included.

#### A range of resources for identifying equations, expressions, identities and formulae

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The powerpoint presentation can be used to introduce this topic, containing examples and explanations. The notes and examples sheet can just be handed out as a reminder during the tasks, or later as a revision resource. The first activity just requires the students to indicate on a grid whether each item is an equation, expression, identity or formula. The second activity involves cutting out each item and putting/sticking it into the correct column on the answer table. All answers are included.

#### Worksheets on the equation of a circle and tangents to a circle (GCSE)

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These worksheets can be used to introduce and practise the new GCSE topic of equation of a circle (centred at origin) and the equation of a tangent to a circle. The first worksheet starts with an activity that helps the students to realise that x^2 + y^2 = k is the equation of a circle and is followed by some questions to practise using it. The second document is an 8-page worksheet which can be used to revise all the necessary skills/knowledge required before studying the equation of a tangent to a circle. Working through this first seemed to really help my GCSE group with this topic. Answers are included. The third document is a 9-page worksheet which focusses on finding the equation of a tangent to a given circle at a particular point or with a particular gradient. All answers are included.

#### Differential equations (new A level maths)

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This 33-page resource covers all the required knowledge and techniques for the topic of differential equations, as required for the new A level. In each section it contains notes, explanations and examples to work through with your class followed by an exercise of questions for students to attempt themselves (answers included). Also included is 17-question assessment that can be used as a test or homework. The sections/topics are: 1.Finding the equation of a curve from its gradient function (a) from dy/dx = … find an expression for y (b) finding general and particular solutions 2.Variable separable equations (a) practice of separating the variables into the form f(y) dy = g(x) dx (b) solving variable separable equations 3.Forming differential equations from a description of how a quantity is changing 4.Modelling with differential equations (a) Constructing the appropriate differential equation to model a given situation (b) Solve differential equations and interpret/use the solutions © Consider the assumption(s) or limitation(s) of a model and suggest possible improvements This projectable and printable resource will save you having to create or write out any notes/examples when teaching the topic, and will make things easier for your students as they can just work directly on the given spaces provided for solutions. The comprehensive set of exercises contains around 100 questions for your students to complete. Answers to all exercises are included. Here is an example of one of my A level resources that is freely available: https://www.tes.com/teaching-resource/differentiation-and-integration-with-exponential-and-trigonometric-functions-new-a-level-11981186