TOPIC 1: GRAPHS

Question 1

10 Main Types of Graphs

Answer 1

1. Line
2. Parabola
3. Cubic
4. Power
5. Exponential
6. Logarithm
7. Trigonometric
8. Circle
9. Ellipse
10. Hyperbola

Question 2

4 Essential Features of Graphs

Answer 2

1. Axial intercepts
2. Stationary / Turning points
3. Line of symmetry
4. Asymptotes

Question 3

What is a polynomial?

Answer 3

An algebraic expression where each term is a non-negative integer power of x

*Including power zero = 1

Question 4

Degree/order of a polynomial

Answer 4

Highest power of x

Question 5

Rational function

Answer 5

Fraction where both numerator and denominator are polynomials

Question 6

Finding stationary / turning point

Answer 6

1. dy/dx table (x, dy/dx, slope)
2. d2y/d2x (> 0 - min ; < 0 - max)

Question 7

Finding vertical asymptote(s)

Answer 7

Let denominator = 0

Question 8

Finding horizontal / oblique asymptote

Answer 8

y = A + B/C

Horizontal / oblique asymptote = A

Question 9

Equation of circle

Answer 9

(x-h)² + (y-k)² = r²

Question 10

Equation of ellipse

Answer 10

(x-h)²/a² + (y-k)²/b² = 1

Question 11

Equation of hyperbola

Answer 11

(x-h)²/a² - (y-k)²/b² = 1
(y-k)²/b² - (x-h)²/a² = 1

Question 12

Finding difference between circle, ellipse & hyperbola

Answer 12

Circle:
* Coefficient of both x² and y² is 1

Ellipse
* Coefficient of x² and y² are different, BUT both positive
* RHS = 1

Hyperbola
* Coefficient of x² and y² are different, BUT opposite signs
* RHS = 1

Question 13

Sketching graphs of parametric equations

Answer 13

1. Find intercepts (when x=0 & when y=0)
2. When t = (the range) to find the end-point
3. Sketch graph

OR: Use GC

Question 14

Common MUST KNOW trigo identities

Answer 14

sin²t + cos²t = 1
1 + tan²t = sec²t
1 + cot²t = cosec²t

sin2t = 2(sint)(cost)
cos2t = cos²t - sin²t / 2cos²t - 1 / 1 - 2sin²t