 # Maths carousel resources

Here you can download all the maths resources that are available in the MASH workspace carousels.

The stats resources can be found here

Fractions
Number Title Description
1 Fractions How to simplify, add, subtract, multiply and divide fractions.
2 Simplifying fractions A more in-depth explanation of simplification of fractions, including algebraic and equivalent fractions.
3 Fractions: adding and subtracting A more in-depth explanation of addition and subtraction of fractions, with the introduction of mixed fractions.
4 Fractions: multiplying and dividing A more in-depth explanation on multiplication and division of fractions.
Inequalities
Number Title Description
5 Solving inequalities Using algebra to solve simple inequalities, drawing graphs, introduction of the modulus symbol and quadratic inequalities.
6 Solving inequalities How to manipulate inequalities, and using algebraic and graphical methods to solve inequalities.
7 Linear inequalities How to sketch regions defined by linear inequalities.
8 Manipulating inequalities Another explanation on the inequality symbols < and >, and how we can manipulate inequalities.
Indices
Number Title Description
9.1 The laws of indices How to simplify expressions involving numbers raised to a specific power, including algebraic examples.
9.2 Negative and fractional powers How to approach negative and fractional powers, and what this notation means.
9.3 Powers and roots An explanation of how to use index notation to express roots of numbers, including square roots and cube roots.
9.4 Indicial equations Equations where the power is unknown, often used in calculating compound interest.
Trigonometrical functions
Number Title Description
10 Degrees and radians An explanation of degrees and radians, and how to convert between them.
11 The Trigonometrical Ratios The ratios of sine, cosine and tangent.
12 Graphs of the trig functions How to draw the graphs of sine, cosine and tangent functions, along with some important values of the three functions.
13 Trigonometrical Identities Commonly used expressions involving sine, cosine and tangent.
14 Trigonometric Identities Derivations involving the most important identities, and using identities to solve equations involving trigonometric functions.
15 Trigonometric Identities Another explanation of the most common identities of trigonometric functions.
16 Pythagoras' theorem An explanation of Pythagoras' theorem, along with some examples.
17 The sine rule and cosine rule The use of the sine rule and cosine rule for finding unknown sides and angles in triangles.
Trigonometry
Number Title Description
18 Trigonometric ratios of an angle of any size Definitions of the ratios sine, cosine and tangent with reference to sides and angles, and how to use these in problems involving triangles.
19 Trigonometric equations How to approach equations involving trigonometric equations, using known values of trig functions and graphical techniques.
Linear equations
Number Title Description
20 Linear relationships How to define a straight line and the graphical representation.
21 Simple linear equations The definition of a linear equation and how to solve them.
22 Solving linear equations Another explanation of how to solve linear equations.
23 Simultaneous linear equations How to solve pairs of simultaneous linear equations and what their solution graphically represents.
Rearranging formulae
Number Title Description
24.1 Rearranging formulas 1 How to rearrange simple formulas
24.2 Rearranging formulas 2 How to rearrange more complicated formulas.
25 Transposition of formulae How to rearrange a formula to change which variable is the subject.
Functions and graphs
Number Title Description
26 What is a function? The definition of a function and the notation used.
27 The graph of a function How to plot the graph of a function and which conventions should be used.
28 Equations of straight lines How to find equations of straight lines given certain known information.
Factorising
Number Title Description
29 Factorising simple expressions What factorisation is and methods on factorising expressions.
30.1 Quadratic equations 1 How to solve simple quadratic equations using factorisation.
31 Factorising quadratics Another explanation of how to solve quadratic equations using factorisation.
32 Completing the square How to complete the square and its use in solving quadratic equations.
Partial fractions
Number Title Description
33.1 Partial Fractions 1 The definition of partial fractions and how to rewrite algebraic fractions.
33.2 Partial Fractions 2 Some worked examples of partial fractions.
33.3 Partial Fractions 3 How to find partial fractions of an improper fraction.
34 Partial Fractions Another explanation of partial fractions.
Polynomials
Number Title Description
35 Solving Polynomial Equations How to factorise some polynomials and the solution of polynomial equations.
Logarithms
Number Title Description
36 The laws of logarithms How to rewrite expressions involving logarithms.
37 Solving equations using logs How to use logarithms to solve equations where the power is unknown.
Differentiation
Number Title Description
38 Introduction to differentiation A brief introduction to the concept of differentiation and how it can be used to calculate the gradient (or slope) of a graph.
39 Table of derivatives A table of common functions and their derivatives.
40 Tangents and normals How to calculate the tangent or normal of a curve at a specific point.
41 Extending the table of derivatives More commonly used derivatives and some methods for differentiating more complex functions.
42.1 Linearity rules How to differentiate sums of functions and functions multiplied by a constant.
42.2 Product and quotient rules How to differentiate two functions multiplied together or one function divided by another.
42.3 Chain rule How to differentiate a function of a function.
43 Implicit Differentiation How to differentiate a function y=f(x) when we cannot write y explicitly in terms of x.
44 Differentiation of the sine and cosine functions from first principles Differentiating sine and cosine from first principles.
Integration
Number Title Description
45 Integration using a table of anti-derivatives Motivating integration as the reverse of differentiation.
46.1 Integration as the reverse of differentiation A more in-depth explanation of integration as the reverse of differentiation.
46.2 Table of Integrals A table of well-known integrals.
46.3 Linearity rules of integration How to integrate sums of functions, and functions multiplied by a constant.
46.4 Evaluating definite integrals How to integrate a functions between two limits.
46.5 Integration by parts How to integrate a product of two functions.
46.6 Integration by substitution Using a function to simplify an integral before integration.
Vectors
Number Title Description
47 Introduction to vectors The definition of a vector, how to add and subtract them, recognising multiples of vectors and how we can use them in geometrical problems.
48 The scalar product Defining the scalar product and its properties.
49 The vector product Defining the vector product and its properties.
50 Cartesian components of vectors Expressing vectors in Cartesian components, by defining unit vectors in the directions of the coordinate axes.
Matrices
Number Title Description
51 Determinants The definition of a determinant and how it can be applied mathematically.
52 Cramer's Rule A method for solving linear simultaneous equations using determinants.
53 Multiplying matrices How to multiply matrices.
Power series
Number Title Description
54 Sequences and Series The definitions and properties of sequences and series.
55 Infinite Series The definition of an infinite series and what is meant by convergence.
56 The Binomial Series How to calculate the Binomial series of functions of the form (b+a)n.
57 Power Series The definition of a power series and how to obtain their radius of convergence.
58 Maclaurin and Taylor Series How to write a generic (smooth) function as a power series.
Complex numbers
Number Title Description
59 What is a complex number? The definition of an imaginary number and a complex number.
60.1 Complex arithmetic How to add, subtract, multiply and divide complex numbers.
60.2 The Argand diagram How to represent complex numbers graphically.
60.3 The polar form Defining the modulus and argument of a complex number, and how to write a complex number in polar form.
60.4 The form z=r(cos(θ)+ jsin(θ)) An alternative way of expressing complex numbers.
60.5 Multiplication and division in polar form How to multiply and divide complex numbers using polar form.
60.6 The exponential form Another alternative form of writing complex numbers.
61 Argand Diagrams and the Polar Form Another explanation of Argand Diagrams and the Polar Form of complex numbers.
Differential equations
Number Title Description
62 Modelling with Differential Equations Using derivatives to describe real world situations mathematically.
63 First Order Ordinary Differential Equations Equations involving a function y(x) and its first derivative.
64 Solving Differential Equations with Integrating Factors How to solve first order ordinary differential equations of a particular form by multiplying both sides by an integrating factor.
65 Solving Differential Equations by Separating Variables How to solve first order ordinary differential equations of a particular form by separation of variables.
66 Second Order Ordinary Differential Equations How to solve both homogeneous and inhomogeneous second order ordinary differential equations with constant coefficients.

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