Pre-Algebra: Chapter 8 Review
Review all the concepts that we tackled in this Chapter:
- Relations and Functions – use the vertical line test (lesson 1)
- Scatter plots – trends are positive, negative or none (lesson 2)
Graphing linear equations – make a T chart and pick easy points to graph, like x = 0, 1, 2 (lesson 3) - Equations as functions – f(x) = x^2 – 1. For f(2), just plug in a 2 for x. You can think of the f(x) as the same as “y”. (lesson 4)
- Problem solving with graphs – make graphs and interpret the data! (lesson 5)
- Slope – rise ÷ run or (y2 – y1) ÷ (x2 – x1) (lesson 6)
- X and Y intercepts – just set x=0 and solve for y to get the y-intercept and set y =0, solving for x to find the x-intercept. The intercepts are the points that cross the x and y axes. (lesson 7)
- Systems of Equations – plot both equations on 1 graph and see where the 2 lines intersect. That is the solution to both equations. However, the lines may be parallel – which means no solution or they may lie one right on top of the other – which means many solutions (lesson 8)
- Graphing Inequalities – graph the 2 equations as if they had equal signs. Then, pick another point, like my favorite (0, 0) to see if it works as well. If not, shade the opposite side, if it does, shade the side where (0, 0) lives. For < or > symbols the boundary line is DASHED OR DOTTED. For ≤ or ≥, the boundary line is SOLID. (lesson 9)
Algebra: Chapter 6-7
Factoring Strategies
Use all the strategies we’ve learned so far to factor a variety of problems. Don’t forget to use:
- Monomial factorization (lesson 6-1)
- The differences of 2 squares (lesson 6-2), (a^2 – b^2) = (a – b)(a + b)
- Trinomial squares (lesson 6-3), a^2 + 2ab + b^2 = (a + b)^2 or with a negative (-2ab)
- The BOX METHOD (lesson 6-4 and 6-5) for x^2 + bx + c or ax^2 + bx + c type of equations
- Factoring by grouping (lesson 6-6) for polynomials with 4 or more terms.
The toughest part is figuring out what technique to use! Go slow and you’ll be OK!