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Grade 9 Math Review Algebra • • • • • • Simplifying (collecting like terms) Expanding (distributive property) Properties of polynomials (terms) Solving equations (simple, fractions) Writing word and algebraic equations Exponent Laws Examples… Question 1: Evaluate (-3)4 Answer: 81 Question 2: Write as a single power. 23 x 22 x 24 Answer: 2 9 Examples… Question 3: Classify each polynomial by the number of terms and degree. a) x2 + 3x b) 6a2b – 4b5 + a3b3 Answer a): Binomial of degree 2 (or 2nd degree) Answer b): Trinomial of degree 6 (or 6th degree) Examples… Question 4: Simplify 7k + 5m – k – 6m Answer: 6k - m Question 5: Simplify -3(2x – 6) – (8 – 6x) Answer: = -6x + 18 - 8 + 6x = 10 Examples… Question 6: Solve 2y – 7 = 13 Answer: 2y – 7 = 13 2y = 20 2y – 7 + 7 = 13 + 7 2y = 20 2 y = 10 y 8 y 4 Question 7: Solve 3 2 Answer: 6 y – 8 = y + 4 6 3 2 2 2(y-8) = 3(y+4) 2y – 16 = 3y + 12 -y = 28 -1 -1 y = -28 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. Answer #8 Let s = the measure of the smallest angle s + 3s + 8s = 180 12s = 180 12 s= 12 15 Therefore, the smallest angle is 15, the middle angle is 45 , and the largest angle is 120 . Equations of Lines • 2 key forms (standard and slope-yintercept form) • Special cases of lines (horizontal, vertical, parallel, perpendicular) • Linear Systems (# of solutions) Examples… Question 9: Identify the slope and the y-intercept of the line y = -3x + 2. Answer: m = -3 b = 2 Question 10: Determine the slope and yintercept of the line 3x + 5y + 15 = 0. Answer: Rearrange into y = mx + b first! 5y = -3x – 15 5 = 5 5 y = -3/5x – 3 Therefore, m=-3/5 and b = -3 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 Step 2) Create your equation using m and b: -4 = 0.5 + b -4 – 0.5 = 0.5 – 0.5 + b -4.5 = b OR b = -4.5 y = 0.5x – 4.5 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 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 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 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