1. Grade 9 Math Review

2. Algebra Simplifying (collecting like terms) Expanding (distributive property) Properties of polynomials (terms) Solving equations (simple, fractions) Writing word and algebraic equations Exponent Laws

3. Examples… Question 1: Evaluate (-3) 4 Question 2: Write as a single power. 2 3 x 2 2 x 2 4 Answer: 81 Answer:

4. Examples… Question 3: Classify each polynomial by the number of terms and degree. a)x 2 + 3x b)6a 2 b – 4b 5 + a 3 b 3 Answer a): Binomial of degree 2 (or 2 nd degree) Answer b): Trinomial of degree 6 (or 6 th degree)

5. Examples… Question 4: Simplify 7k + 5m – k – 6m Question 5: Simplify -3(2x – 6) – (8 – 6x) Answer: 6k - m Answer: = -6x + 18 - 8 + 6x = 10

6. Examples… Question 6: Solve 2y – 7 = 13 Question 7: Solve Answer: 2y – 7 = 13 2y = 20 2y – 7 + 7 = 13 + 7 2 2 2y = 20 y = 10 Answer: 6 y – 8 = y + 4 6 3 2 2(y-8) = 3(y+4) 2y – 16 = 3y + 12 -y = 28 y = -28

7. Examples… Question 8: A triangle has angle measures that are related as follows: the largest angle is eight times the smallest angle the middle angle is triple the smallest angle Determine the measure of each angle.

8. Answer #8 Let s = the measure of the smallest angle s + 3s + 8s = 12s = 12 s = Therefore, the smallest angle is, the middle angle is, and the largest angle is.

9. Equations of Lines 2 key forms (standard and slope-y- intercept form) Special cases of lines (horizontal, vertical, parallel, perpendicular) Linear Systems (# of solutions)

10. Examples… Question 9: Identify the slope and the y-intercept of the line y = -3x + 2. Question 10: Determine the slope and y- intercept of the line 3x + 5y + 15 = 0. Answer: m = -3 b = 2 Answer: Rearrange into y = mx + b first! 5y = -3x – 15 5 = 5 5 y = -3/5x – 3 Therefore, m=-3/5 and b = -3

11. Examples… Question 11: Determine the equation of the line with slope 0.5 and passing through the point (1,-4). Answer: Step 1) Substitute m, x, and y into y = mx + b and solve for b y = mx + b -4 = 0.5(1) + b -4 = 0.5 + b -4 – 0.5 = 0.5 – 0.5 + b -4.5 = b OR b = -4.5 Step 2) Create your equation using m and b: y = 0.5x – 4.5

12. Examples… Question 12: Determine the equation for the line passing through (-2,5) and (3,-5). Answer: Step 1) Calculate slope using the two points Step 2) Use x and y from one point and substitute into y = mx + b to solve for b Step 3) Create your equation with m and b

13. Examples… Question 13: Cindy is at a baseball game with her younger brother, Mike. She has $18 to spend on hamburgers and pop. Hamburgers cost $3 each and pop cost $2 each. a)If Cindy buys only hamburgers, how many can she buy? b)Determine an equation to model the cost scenario. Answer a): She can buy 6 hamburgers. Answer b): C = 3h + 2p

14. Examples… Question 14: Determine the number of solutions to the linear system y = 3x – 7 y = -3x + 5 Answer a): There is exactly one solution to this linear system

15. Examples… Question 15: Determine the equation of the line parallel to 3x – 4y = 12 and with an x-intercept of 6. Answer: y = ¾x – 4.5