Maths
Across
- 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).
- 7. (Linear) The geometric property of a pair of linear equations that have the exact same slope but different intercepts, resulting in zero solutions.
- 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.
- 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.
- 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.
- 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.
- 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...).
- 15. (Quadratic) The direction a parabola faces when the coefficient a in ax^2 + bx + c is less than 0.
- 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.
- 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.
- 19. (AP) An arithmetic sequence that contains a limited, countable number of terms and concludes with a definitive last term an.
Down
- 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. (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. (Linear) The geometric relationship between two lines that cross at exactly one coordinate, representing a unique solution for the linear system.
- 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.
- 6. 10 Math Revision Puzzle
- 8. (Linear) The algebraic method of solving simultaneous equations by adding or subtracting them to cancel out one of the variables.
- 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.
- 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.
- 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.
- 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.