Level 2 Additional Mathematics WJEC
Full course content, a smart revision plan and instant past paper feedback for Level 2 Additional Mathematics WJEC.
Content Overview
33 topics in 5 modules
βοΈ Algebra 12 topics
- Simplify numerical expressions involving surds
- Understand and use indices with negative and fractional values
- Factorisation of quadratic expressions
- Solution of quadratic equations by factorisation
- Formation and manipulation of quadratic equations
- Simplify algebraic expressions involving fractions
- Solution of algebraic equations involving fractions
- Completing the square
- Remainder theorem
- Factor theorem
- Algebraic proof
- Solution of one linear and one quadratic equation
βοΈ Coordinate Geometry 7 topics
- Distance between two points
- Gradient of the straight line joining two points
- y = mx + c
- ax + by + c = 0
- y β y1 = m(x β x1)
- Equations of lines parallel and perpendicular to a given line
- Intersection of a straight line with a curve
βοΈ Mensuration 1 topic
- Measurement including distances and angles, to more complex plane shapes and solids
βοΈ Calculus 9 topics
- Given y = f(x) find dy/dx from first principles in simple cases
- Differentiation of x^n and related sums and differences
- Second derivatives in simple cases
- Equations of tangents
- Maximum and minimum values
- Integration as the reverse of differentiation
- Indefinite integrals as the reverse of differentiation
- Evaluation of definite integrals
- Applications to simple areas, where the curve is entirely above or below the x-axis in the given interval
βοΈ Trigonometry 4 topics
- Trigonometric ratios of angles up to four right-angles
- Special values for 0, 30, 45 and their multiples
- Simple problems in three-dimensions
- The graphs and behaviour of trigonometric functions, and the application of these to the solution of simple equations
Level 2 Additional Mathematics WJEC Revision Content
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Level 2 Additional Mathematics WJEC - Algebra - Simplify numerical expressions involving surds Content Preview
Algebra
Simplify numerical expressions involving surds
Surds Basics
- Surds are numbers left in 'square root form' (or 'cube root form' etc). They are often used when the square root of a number doesn't have an exact value.
- A surd can be manipulated with the same mathematical rules as other numerical expressions.
Simplifying Surds
- To simplify a surd, find the largest square number that divides into the number under the square root sign.
- For example, to simplify β18, which can be expressed as β(9*2), it becomes 3β2.
- The process of simplifying surds is called 'rationalising the denominator'.
Multiplying and Dividing Surds
- When multiplying surds, multiply the numbers under the root. For βexample, β2 * β3 = β6.
- When dividing surds, divide the numbers under the root. For example, β8 / β2 = β4 = 2.
Adding and Subtracting Surds
- Surds can be added or subtracted when they are the same type. For example, β3 + β3 = 2β3.
- If the surds are not the same type, they cannot be added or subtracted directly. For example, β2 + β3 cannot be simplified further.
Rationalising the denominator
- When a surd is in the denominator of a fraction, the fraction needs to be manipulated until the surd is removed from the denominator. This process is called 'rationalising the denominator'.
- To rationalise the denominator, multiply the top and bottom of the fraction by the conjugate of the bottom. For example (1/β3) * (β3/β3) = β3/3.
Question: Simplify the expression 2β50 - 3β98 + 5β32.
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