Quadratic Equations - Year 11 Maths

Summary of topic:

(for www.hegartymaths.com relevant clip numbers see below)

During this half term you will learn:

• To be fluent with all aspects of quadratic equations, including simultaneous equations and inequalities
• How to complete an algebraic proof
• To use iteration to find approximate solutions to equations that are otherwise unsolvable
• Function notation

Further reading:

Other:

(www.hegartymaths.com relevant clip numbers in brackets)

• Factorise quadratic expressions in the form ax2 + bx + c (223 – 228)
• Solve quadratic equations by factorisation (230 – 232) and completing the square (235-239)
• Solve quadratic equations that need rearranging, including those which arise from equations including fractions. (244)
• Set up and solve quadratic equations (245)
• Solve quadratic equations by using the quadratic formula (241, 242)
• Solve exactly, by elimination of an unknown, two simultaneous equations in two unknowns:
  - linear / linear, including where both need multiplying (190-195)
  - linear / quadratic (246)
  - linear / x2 + y2 = r2;
• Interpret the solution in the context of the problem (245)
• Solve linear (269, 270) and quadratic inequalities (277), including using correct notation to show inclusive and exclusive inequalities.
• Solve ‘Show that’ and proof questions using consecutive integers (n, n + 1), squares a2, b2, even numbers 2n, odd numbers 2n +1 (325, 326)
• Change the subject of a formula, including cases where the subject is on both sides of the original formula, or involving fractions and small powers of the subject (280-286)
• Use iteration to find approximate solutions to equations, for simple equations in the first instance, then quadratic and cubic equations. (322)
• Understand how this relates to limits of accuracy
• Use function notation (288)
• Find f(x) + g(x) and f(x) – g(x), 2f(x), f(3x) etc algebraically (289)
• Find the inverse, f –1(x), of a linear function (295, 296)
• For two functions f(x) and g(x), find gf(x) (293, 294)