# Mathematics in A level Physics

Collection of resources to support Physics students coping with the increased mathematical demand post-2015

### Mathematics after 16: the State of Play, Challenges and Ways Ahead

This report, from the Nuffield Foundation, focuses on the crucial period between GCSEs and entrance to higher education, and how mathematical, statistical and quantitative skills develop during this period.

### Welcome

Introductory videos for the Standards Unit: Improving Learning in Mathematics resources featuring Background, Addressing the issues, Developing the approach,The way forward and How to use the resource.

### Interpreting Distance – Time Graphs A6 *suitable for home teaching*

In this DfE Standards Unit resource students learn to interpret and construct distance–time graphs; relating speeds to gradients of the graphs and accelerations to changes in these speeds. Students have often constructed distance–time graphs before. However, experience shows that many still interpret them as if they are pictures of situations rather than abstract representations

### Interpreting Distance-Time Graphs with a Computer A5

In this DfE Standards Unit resource, students interpret linear and non-linear distance-time graphs using the computer programme Traffic. This program provides a simple yet powerful way of helping learners to visualise distance–time graphs from first principles. The program generates situations involving traffic moving up and down a straight section of road. It then allows the user to take ‘photographs’ of this situation at one-second intervals, places these side-by-side, and then gradually transforms this sequence of pictures into a distance–time graph.

### Creating and Solving Equations A2

In this resource from the DfE Standards Unit, students learn to create and solve their own equations, where the unknown appears once. Most students will have been taught rules for solving equations such as ‘change the side, change the sign’ or ‘you always do the same to

both sides’. When used without understanding, such rules result in many errors. ‘Doing the same to both sides’ is the more meaningful method, but there are two difficulties: knowing how to change both sides of an equation so that equality is preserved and knowing which operations lead towards the desired goal.

### Creating and Solving Harder Equations A3

In this resource from the DfE Standards Unit, students create and solve their own equations where the unknown appears more than once and learn that there may be more than one way of solving such equations.

### Evaluating Algebraic Expressions A4

In this resource from the DfE Standards Unit, students learn to distinguish between and interpret equations, inequations and identities and substitute into algebraic statements in order to test their validity in special cases.

### Interpreting Functions, Graphs and Tables A7

In this DfE Standards Unit resource, students learn to understand the relationship between graphical, algebraic and tabular representations of functions, the nature of proportional, linear, quadratic and inverse functions and doubling and squaring.

### Simplifying Logarithmic Expressions A13

This DfE Standards Unit resource enables students to develop their understanding of the laws of logarithms, practise using the laws of logarithms to simplify numerical expressions involving logarithms and apply their knowledge of the laws of logarithms to expressions involving variables

### Exploring Trigonometrical Graphs A12

In this resource from the DfE Standards Unit, students explore trigonometrical graphs by recognising translations, stretches and reflections from their equations, sketching the graphs and learning about the period and amplitude

### Exploring Functions Involving Fractional and Negative Powers of x C2

In this DfE Standards Unit resource, students find the stationary points of a function and determine their nature and solve appropriate equations in order to find the intercepts of a function.

### Differentiating and Integrating Fractional and Negative Powers C4

In this resource from the DfE Standards Unit, students convert functions into an appropriate form for differentiating or integrating and then differentiate and integrate negative and fractional powers of x.

### Exploring Equations of Motion 02

In this resource, from the Department for Education Standards Unit, students learn to use past paper examination questions creatively. The questions give them practice in using the equations of motion for constant acceleration and allow them to develop their ability to generalise from specific situations of motion.

### Solving Problems Using Newton's Second Law O3

In this resource, from the Department for Education Standards Unit, students will learn to understand how Newton’s second law can be applied to a range of different problems. It will encourage learners to link the stages of solutions together and appreciate the purpose and relevance of each stage of a solution.

### Active A-Level Mathematics

A collection of ideas from Susan Wall for use in the A-level mathematics classroom. The activities are written in a manner designed to engage student participation, promote discussion and enhance understanding. Each activity is accompanied by teacher notes suggesting how the task should be approached. The tasks are designed to be an integral part of the learning process allowing students to experience the joy of mathematical discovery for themselves.

### STEM Knowledge Networks

This booklet provides twelve case studies from STEM Knowledge Networks.

Case studies applicable to this sessions are:

Joined-up thinking (page 31)

Exploring common content and coordinated teaching of mathematics and physics across KS3, KS4 and KS5

New approaches to mathematics (page 34)

Improving mathematics teaching and learning

in preparation for STEM subjects at KS4 and KS5

### Mathematics and Science Departments Working Collaboratively

Cross-curricular work can be incredibly powerful, both in terms of student outcomes and staff Continuing Professional Development. However, it is easy to contemplate, but far more difficult to deliver. Effective planning is the key. At King James’s School, near Huddersfield, members of the mathematics and science departments worked collaboratively to prepare a ‘rockets’ project which was delivered jointly on one of the school’s cross-curricular days, and followed up in subsequent mathematics lessons to provide a high quality and enjoyable learning experience for staff and students alike.

### Promoting the Active and Effective Use of Statistical Techniques within the Sciences

The STEM Knowledge Network based at King Edward’s Stourbridge has developed a range of materials to further the active use of statistics within the sciences.

### Mechanics: A Level

Resources to support the teaching and learning of mechanics topics at advanced level.