# Year 11 Maths Help & Practice

Boost your maths marks with our complete Year 11 Maths help. Whether it's GCSE maths revision, National 5 Maths revision, Key Stage 4 Maths (National Curriculum), or National curriculum in Wales (Key stage 4), we've got you all covered!

Just like your class or textbook, our comprehensive help includes topics such as Trigonometry, Vectors, Solving simultaneous equations, Congruent triangles, Solving linear equations, Circle theorem, and more. StudyPug gives you not just lessons, but tutorials that teach you how to tackle even the hardest GCSE maths questions with step-by-step solutions – in videos. Then, strengthen your understanding with tons of KS4 maths practice.

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##### 1Number System

##### 2Surds

##### 3Laws of Indices

##### 4Solving Linear Equations

##### 5Linear Inequalities

##### 6Linear Relations

##### 7Linear Functions

- 7.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
- 7.2Midpoint formula: $M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)$
- 7.3Gradient equation: $m = \frac{y_2-y_1}{x_2- x_1}$
- 7.4Gradient intercept form: y = mx + b
- 7.5General form: Ax + By + C = 0
- 7.6Gradient-point form: $y - y_1 = m (x - x_1)$
- 7.7Rate of change
- 7.8Graphing linear functions using table of values
- 7.9Graphing linear functions using x- and y-intercepts
- 7.10Graphing from gradient-intercept form y=mx+b
- 7.11Graphing linear functions using a single point and gradient
- 7.12Word problems of graphing linear functions
- 7.13Parallel and perpendicular lines in linear functions
- 7.14Applications of linear relations

- 7.1Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
##### 8Linear Equations

- 8.1Introduction to linear equations
- 8.2Introduction to nonlinear equations
- 8.3Special case of linear equations: Horizontal lines
- 8.4Special case of linear equations: Vertical lines
- 8.5Parallel line equation
- 8.6Perpendicular line equation
- 8.7Combination of both parallel and perpendicular line equations
- 8.8Applications of linear equations

- 8.1Introduction to linear equations
##### 9Solving Simultaneous Equations

- 9.1Determining number of solutions to linear equations
- 9.2Solving simultaneous equations by graphing
- 9.3Solving simultaneous equations by elimination
- 9.4Solving simultaneous equations by substitution
- 9.5Money related questions in linear equations
- 9.6Unknown number related questions in linear equations
- 9.7Distance and time related questions in linear equations
- 9.8Rectangular shape related questions in linear equations

- 9.1Determining number of solutions to linear equations
##### 10Exponential Functions

- 10.1Exponents: Product rule
*(a^x)(a^y) = a^(x+y)* - 10.2Exponents: Division rule (a^x / a^y) = a^(x-y)
- 10.3Exponents: Power rule
*(a^x)^y = a^(x * y)* - 10.4Exponents: Negative exponents
- 10.5Exponents: Zero exponent:
*a^0 = 1* - 10.6Exponents: Rational exponents
- 10.7Solving exponential equations using exponent rules
- 10.8Graphing exponential functions
- 10.9Graphing transformations of exponential functions
- 10.10Finding an exponential function given its graph

- 10.1Exponents: Product rule
##### 11Operations of Polynomials

##### 12Factorising Polynomial Expressions

- 12.1Common factors of polynomials
- 12.2Factorising polynomials by grouping
- 12.3Solving polynomials with the unknown "b" from
*x^2 + bx + c* - 12.4Solving polynomials with the unknown "c" from
*x^2 + bx + c* - 12.5Factorising polynomials:
*x^2 + bx + c* - 12.6Applications of polynomials:
*x^2 + bx + c* - 12.7Solving polynomials with the unknown "b" from $ax^2 + bx + c$
- 12.8Factorising polynomials: $ax^2 + bx + c$
- 12.9Factorising perfect square trinomials:
*(a + b)^2 = a^2 + 2ab + b^2*or*(a - b)^2 = a^2 - 2ab + b^2* - 12.10Find the difference of squares:
*(a - b)(a + b) = (a^2 - b^2)* - 12.11Evaluating polynomials
- 12.12Using algebra tiles to factorise polynomials
- 12.13Solving polynomial equations
- 12.14Word problems of polynomials

- 12.1Common factors of polynomials
##### 13Transformations of Functions

- 13.1Transformations of functions: Horizontal translations
- 13.2Transformations of functions: Vertical translations
- 13.3Reflection across the y-axis:
*y = f(-x)* - 13.4Reflection across the x-axis:
*y = -f(x)* - 13.5Transformations of functions: Horizontal stretches
- 13.6Transformations of functions: Vertical stretches
- 13.7Combining transformations of functions
- 13.8Even and odd functions

- 13.1Transformations of functions: Horizontal translations
##### 14Algebraic Fractions

- 14.1Simplifying algebraic fractions and restrictions
- 14.2Adding and subtracting algebraic fractions
- 14.3Multiplying algebraic fractions
- 14.4Dividing algebraic fractions
- 14.5Solving equations with algebraic fractions
- 14.6Applications of equations with algebraic fractions
- 14.7Simplifying complex fractions
- 14.8Partial fraction decomposition

- 14.1Simplifying algebraic fractions and restrictions
##### 15Reciprocal Functions

##### 16Introduction to 3-Dimensional Figures

##### 17Properties of Triangles

##### 18Congruent Triangles

##### 19Circle Geometry

##### 20Scale Factors and Similarity

##### 21Pythagorean Theorem

##### 22Trigonometry

- 22.1Use sine ratio to calculate angles and sides (Sin = $\frac{o}{h}$ )
- 22.2Use cosine ratio to calculate angles and sides (Cos = $\frac{a}{h}$ )
- 22.3Use tangent ratio to calculate angles and sides (Tan = $\frac{o}{a}$ )
- 22.4Combination of SohCahToa questions
- 22.5Solving expressions using 45-45-90 special right triangles
- 22.6Solving expressions using 30-60-90 special right triangles
- 22.7Word problems relating ladder in trigonometry
- 22.8Word problems relating guy wire in trigonometry
- 22.9Other word problems relating angles in trigonometry
- 22.10Sine rule
- 22.11Cosine rule
- 22.12Application of the sine rule and cosine rule

- 22.1Use sine ratio to calculate angles and sides (Sin = $\frac{o}{h}$ )
##### 23Bearings

##### 24Volume

##### 25Measuring Systems

##### 26Introduction to Probability

##### 27Probability

##### 28Statistics

##### 29Data and Graphs

##### 30Vectors