ChalkBee

Polynomial (Cubic & Quartic) Functions (Year 11)

Free printable Year 11 Mathematical Methods worksheet on cubic and quartic functions: factorising to find roots, expanding, evaluating and graphing (ACMMM017-019).

✓ Answer key checked by math, never wrong
Year 11 · Math worksheet
Name
Date
Math

Functions: Polynomial (Cubic & Quartic) Functions

Expand, factorise, solve and evaluate cubic and quartic functions, and describe their end behaviour and graphs. (ACARA Mathematical Methods Unit 1: ACMMM017-019.)

  1. 1.
    Expand f(x) = (x + 2)(x - 2)(x - 3) into the form ax3 + bx2 + cx + d.
  2. 2.
    Expand f(x) = (x + 3)(x + 1)(x - 2) into the form ax3 + bx2 + cx + d.
  3. 3.
    Expand f(x) = (x + 2)(x - 1)(x - 2) into the form ax3 + bx2 + cx + d.
  4. 4.
    Solve f(x) = x3x^{3} - 4x^2 + x + 6 = 0 by factorising to find all real roots.
  5. 5.
    Solve f(x) = x3x^{3} - 4x^2 + x + 6 = 0 by factorising to find all real roots.
  6. 6.
    Solve f(x) = x3x^{3} - 4x^2 + x + 6 = 0 by factorising to find all real roots.
  7. 7.
    For f(x) = x3x^{3} - 2x^2 - x + 2, evaluate f(2).
  8. 8.
    For f(x) = x3x^{3} + 2x^2 - 9x - 18, evaluate f(-1).
  9. 9.
    A polynomial has leading term x4x^{4}. Describe its end behaviour: what happens to f(x) as x -> +infinity and as x -> -infinity?
  10. 10.
    A polynomial has leading term -x3x^{3}. Describe its end behaviour: what happens to f(x) as x -> +infinity and as x -> -infinity?
  11. 11.
    Solve the quartic f(x) = (x + 3)(x + 1)(x - 1)(x - 3) = 0. State all four roots and the end behaviour.
  12. 12.
    Sketch y = x3x^{3} - 2x^2 - 5x + 6. The graph below plots the curve; confirm it cuts the x-axis at each root and identify the y-intercept.
    -3-2-101234-27-19-11-351321xyx=-2x=1x=3y-int (0, 6)
    Cubic through its three real roots.
Made with ChalkBee · chalkbee.com

More like this

Other Year 11 worksheets