Maths

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Across
  1. 5. (Polynomials) A term in an algebraic expression or polynomial that does not contain any variables and whose numerical value remains entirely fixed (represented by c in standard quadratic form).
  2. 7. (Linear) The geometric property of a pair of linear equations that have the exact same slope but different intercepts, resulting in zero solutions.
  3. 9. (Linear) The algebraic method where you express one variable in terms of the other from the first equation and plug it into the second equation.
  4. 10. (Quadratic) The 10th-11th century ancient Indian mathematician who is historically credited with deriving the step-by-step method of completing the square to solve any general quadratic equation, foundational to the "quadratic formula" used today.
  5. 11. (General Math) The standard geometric and algebraic term for a single, distinct element or value within a data set, an ordered sequence, or an algebraic expression.
  6. 12. (Quadratic/Geometry) Often forming the basis of real-world quadratic word problems in Chapter 4 (like the classic right-angled triangle problems), this is the specific term for the longest side of a triangle whose square equals the sum of the squares of the other two sides.
  7. 13. (AP) The value of the common difference (d) in an arithmetic progression where every single term in the sequence remains identical (e.g., 5, 5, 5, 5...).
  8. 15. (Quadratic) The direction a parabola faces when the coefficient a in ax^2 + bx + c is less than 0.
  9. 17. (Quadratic) Historical context in Chapter 4 notes that this ancient society tackled quadratic problems early on by finding two numbers based on their known sum and product.
  10. 18. (Quadratic) The foundational algebraic technique used in Chapter 4 to solve a quadratic equation by splitting the middle term to break the expression down into a product of two linear components.
  11. 19. (AP) An arithmetic sequence that contains a limited, countable number of terms and concludes with a definitive last term an.
Down
  1. 1. (Linear) A system of linear equations that produces an infinite number of solutions because the two equations mathematically represent the exact same line.
  2. 2. (Quadratic) The specific values of x that satisfy a quadratic equation ax^2 + bx + c = 0, structurally synonymous with the "zeroes" of a polynomial.
  3. 3. (Linear) The geometric relationship between two lines that cross at exactly one coordinate, representing a unique solution for the linear system.
  4. 4. (AP) The precise, standard mathematical expression or rule—such as an = a + (n-1)d—used explicitly throughout Chapter 5 to calculate specific values without writing out the entire sequence.
  5. 6. 10 Math Revision Puzzle
  6. 8. (Linear) The algebraic method of solving simultaneous equations by adding or subtracting them to cancel out one of the variables.
  7. 12. (Polynomials) The graphical line where the value of y is 0; the number of times a polynomial graph crosses it equals its number of real zeroes.
  8. 14. (Quadratic) The 7th-century ancient Indian mathematician (C.E. 598–665) credited in the Chapter 4 introduction with providing an explicit formula to solve quadratic equations structured in the form ax^2 + bx = c.
  9. 16. (Quadratic) The term describing the two roots of a quadratic equation when the discriminant equals zero (b^2 - 4ac = 0), meaning the roots sit on the exact same point on the x-axis.
  10. 20. (Quadratic) The classification of numbers that a quadratic equation's roots fail to be if the value under the square root radical (b^2 - 4ac) is negative.