Free resources for Algebra in Mathematics: lessons, PDFs and video courses. Algebra study material for GCSE, A-Level, AS-Level, 11+ with Khan Academy, Wikipedia and video solutions.
Algebra is the language of mathematics: it uses symbols and letters to represent numbers and relationships. Core skills include simplifying expressions, solving linear and quadratic equations, working with inequalities, factoring, and manipulating exponents and radicals. These skills appear in nearly every question on the SAT Math section and GCSE/A-Level papers.
Linear equations (y = mx + b) describe straight lines, where m is the slope and b the y-intercept. Quadratic equations (ax² + bx + c = 0) are solved by factoring, completing the square, or the quadratic formula x = (−b ± √(b²−4ac)) / 2a. Systems of equations are solved by substitution or elimination, and the discriminant b²−4ac tells how many real solutions a quadratic has.
On the SAT, 'Heart of Algebra' is the single largest content area, covering linear equations, systems, and inequalities. Consistent practice with word problems — translating sentences into equations — is the most effective way to raise your score.
Pick the correct answer — instant feedback!
1. Solve: 2x + 6 = 14. What is x?
2. In y = mx + b, what does b represent?
3. What is the discriminant of ax² + bx + c = 0?
x = (−b ± √(b² − 4ac)) / 2a. It solves any quadratic equation ax² + bx + c = 0.
Algebra is the largest category on the SAT Math section — roughly a third of all questions involve linear equations, systems, or inequalities.
The slope m measures steepness: the change in y for each unit change in x (rise over run).
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