UK Year 12 Maths made completely easy!

We got you covered with our complete help for Year 12 maths, whether it’s for Lower Sixth form, AS-Level Maths, Core 1 and Core 2 Maths, or Functional skills level 3.

Aligned with your class or textbook, you will get year 12 maths help on topics like Trigonometric identities, Derivatives, Integrals, Solving simultaneous equations, Factorising quadratic equations, Sequences and series, and so many more. Learn the concepts with our video tutorials that show you step-by-step solutions to even the hardest algebra problems. Then, strengthen your understanding with tons of Algebra 2 practice.

All our lessons are taught by experienced Year 12 Maths teachers. Let’s finish your homework in no time, and ACE that exam.

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Common Questions
I’m revising for A-level maths. Will I have access to both Year 12 and Year 13 maths help?

Of course. Your StudyPug membership gives you unlimited access to all math help across all courses. To save your precious study time, you can skip, review and learn any materials anytime based on your needs.

What class should I take after year 12 maths?

A prerequisite for this course is Year 11 Maths, and after you mastered year 12 maths, your follow up course should be Year 13 Maths.

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UK Year 12 Maths Topics

We have plenty of free lessons for you to watch

1.Linear Equations

1.1Introduction to linear equations (free lessons)
1.2Introduction to nonlinear equations
1.3Special case of linear equations: Horizontal lines
1.4Special case of linear equations: Vertical lines
1.5Parallel line equation (free lessons)
1.6Perpendicular line equation
1.7Combination of both parallel and perpendicular line equations
1.8Applications of linear equations

2.Linear Inequalities

2.1Express linear inequalities graphically and algebraically (free lessons)
2.2Solving one-step linear inequalities
2.3Solving multi-step linear inequalities

3.Inequalities in Two Variables

3.1Graphing linear inequalities in two variables (free lessons)
3.2Graphing simultaneous linear inequalities (free lessons)
3.3Graphing quadratic inequalities in two variables
3.4Graphing simultaneous quadratic inequalities
3.5Applications of inequalities
3.6What is linear programming?
3.7Linear programming word problems

4.Introduction to Relations and Functions

4.1Relationship between two variables (free lessons)
4.2Understand relations between x- and y-intercepts
4.3Domain and range of a function (free lessons)
4.4Identifying functions
4.5Function notation (free lessons)

5.Linear Functions

5.1Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} (free lessons)
5.2Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2) (free lessons)
5.3Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
5.4Gradient intercept form: y = mx + b (free lessons)
5.5General form: Ax + By + C = 0 (free lessons)
5.6Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1) (free lessons)
5.7Rate of change
5.8Graphing linear functions using table of values
5.9Graphing linear functions using x- and y-intercepts (free lessons)
5.10Graphing from gradient-intercept form y=mx+b
5.11Graphing linear functions using a single point and gradient
5.12Word problems of graphing linear functions
5.13Parallel and perpendicular lines in linear functions (free lessons)
5.14Applications of linear relations

6.Absolute Value Functions

6.1Absolute value functions (free lessons)
6.2Solving absolute value equations
6.3Solving absolute value inequalities

7.Solving Simultaneous Equations

7.1Determining number of solutions to linear equations (free lessons)
7.2Solving simultaneous equations by graphing
7.3Solving simultaneous equations by elimination
7.4Solving simultaneous equations by substitution
7.5Money related questions in linear equations (free lessons)
7.6Unknown number related questions in linear equations
7.7Distance and time related questions in linear equations
7.8Rectangular shape related questions in linear equations
7.9Simultaneous linear-quadratic equations (free lessons)

8.Factorising Polynomial Expressions

8.1Common factors of polynomials (free lessons)
8.2Factorising polynomials by grouping
8.3Solving polynomials with the unknown "b" from x2+bx+cx^2 + bx + c
8.4Solving polynomials with the unknown "c" from x2+bx+cx^2 + bx + c
8.5Factorising polynomials: x2+bx+cx^2 + bx + c (free lessons)
8.6Applications of polynomials: x2+bx+cx^2 + bx + c
8.7Solving polynomials with the unknown "b" from ax2+bx+cax^2 + bx + c
8.8Factorising polynomials: ax2+bx+cax^2 + bx + c
8.9Factorising perfect square trinomials: (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2 or (a−b)2=a2−2ab+b2(a - b)^2 = a^2 - 2ab + b^2 (free lessons)
8.10Find the difference of squares: (a−b)(a+b)=(a2−b2)(a - b)(a + b) = (a^2 - b^2)
8.11Evaluating polynomials
8.12Using algebra tiles to solve polynomials
8.13Solving polynomial equations (free lessons)
8.14Word problems of polynomials

9.Quadratic Functions

9.1Characteristics of quadratic functions (free lessons)
9.2Transformations of quadratic functions
9.3Quadratic function in general form: y=ax2+bx+cy = ax^2 + bx+c
9.4Quadratic function in vertex form: y = a(x−p)2+qa(x-p)^2 + q
9.5Completing the square
9.6Converting from general to vertex form by completing the square
9.7Shortcut: Vertex formula (free lessons)
9.8Finding the quadratic functions for given parabolas (free lessons)
9.9Applications of quadratic functions

10.Quadratic Equations and Inequalities

10.1Solving quadratic equations by factoring
10.2Solving quadratic equations by completing the square
10.3Using quadratic formula to solve quadratic equations
10.4Nature of roots of quadratic equations: The discriminant
10.5Applications of quadratic equations
10.6Solving quadratic inequalities

11.Polynomial Functions

11.1What is a polynomial function? (free lessons)
11.2Polynomial long division (free lessons)
11.3Polynomial synthetic division
11.4Remainder theorem
11.5Factor theorem
11.6Rational zero theorem
11.7Characteristics of polynomial graphs
11.8Multiplicities of polynomials
11.9Imaginary zeros of polynomials
11.10Determining the equation of a polynomial function
11.11Applications of polynomial functions
11.12Solving polynomial inequalities
11.13Fundamental theorem of algebra

12.Surds

12.1Operations with surds (free lessons)
12.2Conversion between entire radicals and mixed surds
12.3Adding and subtracting surds (free lessons)
12.4Multiplying surds
12.5Solving surd equations

13.Laws of indices

13.1Product rule of exponents (free lessons)
13.2Quotient rule of exponents
13.3Power of a product rule
13.4Power of a quotient rule
13.5Power of a power rule (free lessons)
13.6Negative exponent rule
13.7Combining the exponent rules
13.8Scientific notation
13.9Convert between radicals and rational exponents (free lessons)
13.10Solving for exponents

14.Algebraic Fractions

14.1Simplifying algebraic fractions and restrictions
14.2Adding and subtracting algebraic fractions (free lessons)
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

15.Functions

15.1Function notation (free lessons)
15.2Operations with functions
15.3Adding functions
15.4Subtracting functions
15.5Multiplying functions
15.6Dividing functions
15.7Composite functions (free lessons)
15.8Inverse functions
15.9One to one functions
15.10Difference quotient: applications of functions

16.Transformations of Functions

16.1Transformations of functions: Horizontal translations
16.2Transformations of functions: Vertical translations
16.3Reflection across the y-axis: y=f(−x)y = f(-x) (free lessons)
16.4Reflection across the x-axis: y=−f(x)y = -f(x)
16.5Transformations of functions: Horizontal stretches
16.6Transformations of functions: Vertical stretches
16.7Combining transformations of functions
16.8Even and odd functions

17.Exponential Functions

17.1Exponents: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)} (free lessons)
17.2Exponents: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}
17.3Exponents: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)} (free lessons)
17.4Exponents: Negative exponents
17.5Exponents: Zero exponent: a0=1 a^0 = 1
17.6Exponents: Rational exponents
17.7Graphing exponential functions
17.8Graphing transformations of exponential functions
17.9Finding an exponential function given its graph

18.Logarithmic Functions

18.1What is a logarithm?
18.2Converting from logarithmic form to exponential form (free lessons)
18.3Evaluating logarithms without a calculator
18.4Common logarithms
18.5Natural log: ln
18.6Evaluating logarithms using change-of-base formula
18.7Converting from exponential form to logarithmic form (free lessons)
18.8Solving exponential equations with logarithms
18.9Product rule of logarithms (free lessons)
18.10Quotient rule of logarithms
18.11Combining product rule and quotient rule in logarithms
18.12Evaluating logarithms using logarithm rules
18.13Solving logarithmic equations (free lessons)
18.14Graphing logarithmic functions
18.15Finding a logarithmic function given its graph

19.Applications of Exponential and Logarithmic Functions

19.1Exponential growth and decay by a factor
19.2Exponential decay: Half-life (free lessons)
19.3Exponential growth and decay by percentage
19.4Finance: Compound interest
19.5Continuous growth and decay
19.6Logarithmic scale: Richter scale (earthquake)
19.7Logarithmic scale: pH scale
19.8Logarithmic scale: dB scale
19.9Finance: Future value and present value

20.Circles and Parabolas

20.1Angles in a circle (free lessons)
20.2Chord properties
20.3Tangent properties
20.4Circles and circumference
20.5Arcs of a circle
20.6Areas and sectors of circles
20.7Inscribed quadrilaterlas in circles
20.8Central and inscribed angles in circles
20.9Circles in coordinate plane
20.10Parabola

21.Introduction to Trigonometry

21.1Use sine ratio to calculate angles and side (Sin = oh \frac{o}{h} ) (free lessons)
21.2Use cosine ratio to calculate angles and side (Cos = ah \frac{a}{h} )
21.3Use tangent ratio to calculate angles and side (Tan = oa \frac{o}{a} )
21.4Combination of SohCahToa questions (free lessons)
21.5Solving expressions using 45-45-90 special right triangles (free lessons)
21.6Solving expressions using 30-60-90 special right triangles
21.7Word problems relating ladder in trigonometry
21.8Word problems relating guy wire in trigonometry
21.9Other word problems relating angles in trigonometry

22.Trigonometry

22.1Angle in standard position
22.2Coterminal angles (free lessons)
22.3Reference angle
22.4Find the exact value of trigonometric ratios
22.5ASTC rule in trigonometry (All Students Take Calculus) (free lessons)
22.6Unit circle (free lessons)
22.7Converting between degrees and radians
22.8Trigonometric ratios of angles in radians
22.9Radian measure and arc length

23.Sine Rule and Cosine Rule

23.1Sine rule
23.2Cosine rule
23.3Applications of the sine rule and cosine rule

24.Graphing Trigonometric Functions

24.1Sine graph: y = sin x
24.2Cosine graph: y = cos x
24.3Tangent graph: y = tan x
24.4Cotangent graph: y = cot x
24.5Secant graph: y = sec x
24.6Cosecant graph: y = csc x
24.7Graphing transformations of trigonometric functions
24.8Determining trigonometric functions given their graphs

25.Trigonometric Identities

25.1Quotient identities and reciprocal identities (free lessons)
25.2Pythagorean identities
25.3Sum and difference identities
25.4Cofunction identities
25.5Double-angle identities (free lessons)

26.Sequences and Series

26.1Arithmetic sequences (free lessons)
26.2Arithmetic series (free lessons)
26.3Geometric sequences
26.4Geometric series
26.5Infinite geometric series
26.6Sigma notation
26.7Arithmetic mean vs. Geometric mean

27.Probability

27.1Determining probabilities using tree diagrams and tables (free lessons)
27.2Probability of independent events
27.3Finding probabilities using two-way frequency tables
27.4Probability with Venn diagrams

28.Set Theory

28.1Set builder notation

29.Permutations and Combinations

29.1Fundamental counting principle
29.2Factorial notation
29.3Path counting problems
29.4Permutation vs. Combination
29.5Permutations
29.6Combinations
29.7Problems involving both permutations and combinations
29.8Pascal's triangle
29.9Binomial theorem

30.Statistics

30.1Median and mode
30.2Mean
30.3Range and outliers
30.4Application of averages
30.5Influencing factors in data collection (free lessons)
30.6Data collection

31.Data and Graphs

31.1Reading and drawing histograms
31.2Reading and drawing line graphs
31.3Box-and-whisker plots and scatter plots
31.4Stem-and-leaf plots
31.5Reading and drawing Venn diagrams

32.Parametric Equations and Polar Coordinates

32.1Defining curves with parametric equations
32.2Polar coordinates

33.Limits

33.1Finding limits from graphs
33.2Continuity
33.3Finding limits algebraically - direct substitution
33.4Finding limits algebraically - when direct substitution is not possible
33.5Infinite limits - vertical asymptotes
33.6Limits at infinity - horizontal asymptotes
33.7Intermediate value theorem
33.8Squeeze theorem

34.Derivatives

34.1Definition of derivative
34.2Power rule
34.3Slope and equation of tangent line
34.4Chain rule
34.5Derivative of trigonometric functions
34.6Derivative of exponential functions
34.7Product rule
34.8Quotient rule
34.9Implicit differentiation
34.10Derivative of inverse trigonometric functions
34.11Derivative of logarithmic functions
34.12Higher order derivatives
34.13Critical number & maximum and minimum values

35.Integrals

35.1Antiderivatives
35.2Riemann sum
35.3Definite integral
35.4Fundamental theorem of calculus

36.Integration Applications

36.1Areas between curves
36.2Volumes of solids with known cross-sections
36.3Volumes of solids of revolution - Disc method
36.4Volumes of solids of revolution - Shell method
36.5Average value of a function
36.6Arc length
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