Algebra TOPICS TO KNOW FOR Additional Math + Syllabus
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Algebra TOPICS TO KNOW FOR Additional Math
- ✅ Algebra (expressions,
equations, indices, surds)
- ✅ Sequences and Series
- ✅ Functions and Graphs
- ✅ Coordinate Geometry
- ✅ Trigonometry
- ✅ Vectors and Matrices
- ✅ Calculus (limits,
differentiation, integration)
- ✅ Probability
- ✅ Statistics
Algebraic Expressions
Algebraic expressions are combinations of variables,
numbers, and operations. Example: 3x + 2y - 5.
Equations and Inequalities
Equations show equality (e.g., 2x + 3 = 11). Inequalities
compare values (e.g., x > 5). Solve by isolating the variable.
Factorization
Factorization involves writing expressions as products.
Example: x^2 + 5x + 6 = (x + 2)(x + 3).
Laws of Indices
Laws include: a^m * a^n = a^(m+n), (a^m)^n = a^(mn), a^0 =
1.
Surds
Surds are irrational roots. Example: √2 + √8 = √2 + 2√2 =
3√2.
Sequences and Series
Arithmetic Sequences
A sequence with a common difference. Example: 2, 4, 6, 8 (d
= 2). nth term: a + (n-1)d.
Geometric Sequences
A sequence with a common ratio. Example: 2, 4, 8, 16 (r =
2). nth term: ar^(n-1).
Series and Sigma Notation
Sum of terms. Example: Σ (from i=1 to 4) of i = 1 + 2 + 3 +
4 = 10.
Functions and Graphs
Functions and Relations
A function assigns each input to one output. Example: f(x) =
x^2.
Graphs of Functions
Plot points for values of x. Example: y = x^2 is a parabola.
Inverse and Composite Functions
Inverse: f⁻¹(x). Composite: f(g(x)).
Coordinate Geometry
Coordinate Geometry
Study of points, lines, and shapes in the coordinate plane.
Distance formula: √[(x2-x1)^2 + (y2-y1)^2].
Equation of a Line
y = mx + c, where m is the slope and c is the y-intercept.
Midpoint and Gradient
Midpoint: ((x1+x2)/2, (y1+y2)/2). Gradient: (y2 - y1)/(x2 -
x1).
Trigonometry
Trigonometric Ratios
sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan =
opposite/adjacent.
Sine and Cosine Rule
Sine Rule: a/sinA = b/sinB. Cosine Rule: c^2 = a^2 + b^2 -
2ab cosC.
Graphs and Identities
Graphs of sin, cos, tan. Identities: sin^2x + cos^2x = 1.
Vectors and Matrices
Vectors
Represented as (x, y). Operations include addition, scalar
multiplication, magnitude.
Matrices
Rectangular arrays. Operations: addition, multiplication,
inverse, determinant.
Calculus
Limits and Continuity
Limit of f(x) as x approaches a value. Continuity means no
breaks in the graph.
Differentiation
Find the derivative. Example: d/dx (x^2) = 2x. Applications:
slope, maxima/minima.
Integration
Reverse of differentiation. ∫x dx = x^2/2 + C. Used to find
area under curves.
Probability
Basic Probability
Probability = favorable outcomes / total outcomes. Example:
P(Head) = 1/2.
Venn Diagrams
Used to show sets and their relationships. Useful for
solving probability problems.
Tree Diagrams
Show all possible outcomes of an event sequence.
Statistics
Data Representation
Use bar charts, histograms, pie charts to show data.
Measures of Central Tendency
Mean = average, Median = middle, Mode = most frequent.
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