Published on March 14, 2014
Review on algebra: 3 Identities Linear Equation General Form / Slope Quadratic Equations and Formula for roots Modulus Exponents Inequalities Functions
Today’s Agenda: Geometry Co-ordinate Geometry / Functions 18 Advanced Functions - Graphing (Plus) 20 Circles (16 items) 2 Lines andAngles (23 items) 5 Triangle Area/Perim/Pythag (11 items) 11 Third Side Rule/Angle Side Rule (6 items)13 SimilarTriangles (5 items) 15 Rectangle Area/Perimeter 16 Polygons (5 items) 24 Solids (13 items) 25
Co-ordinate Geometry (pg 18) Slope:
Coordinate Geometry (Pg 20) Modulus
Quadratics, Roots, Intercept
Shape of root function
How Functions shift In general, for any function h(x) and any positive number c,the following are true. The graph of h(x+c) is the graph of h(x) shifted to the left by c units. The graph of h(x−c) is the graph of h(x) shifted to the right by c units. The graph of h(x)+c is the graph of h(x) shifted upward by c units. The graph of h(x)−c is the graph of h(x) shifted downward by c units. The graph of ch(x) is the graph of h(x) stretched vertically by a factor of c if c>1. The graph of ch(x) is the graph of h(x) shrunk vertically by a factor of c if 0<c<1.
Circles advanced The graph of an equation of the form (x−a)2+(y−b)2 = r2 is a circle with its center at the point (a,b) and with radius r.
Circles Basic (Pg 2.)
Circles Exercises 1. What is the area of a circle with radius 8? 2. What is the area of a circle with diameter 12? 3. What is the area of a circle with radius 4. What is the area of a circle with circumference 8π? 5. What is the diameter of a circle with area 49π? 6. What is the circumference of a circle with area 18π?
Sectors in a Circle
A few interesting cases .
Triangle (pgs 11-15) Sides and angles:The length of any side of a triangle is less than the sum of the lengths of the other two sides, and greater than the positive difference of the lengths of the other two sides. If the lengths of two sides of a triangle are unequal, the greater angle lies opposite the longer side and vice versa. In the figure above, if ∠A > ∠B > ∠ C, then a > b > c.
Pythagoras theorem and special triangles
Quadrilaterals (pgs 16-24)
Solids (pg. 25) Find the volume and surface area of each of the solids in #1–5. 1.A rectangular solid with dimensions 4, 6, and 8. 2.A rectangular solid with dimensions 3,4, and 12. 3.A cube with edge 6. 4.A cube with edge . 5.A cylinder with height 12 and radius 6. (Find the total surface area.) 6.What is the area of a face of a cube with volume 64?
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