Math 4: Advanced Algebra Ms. Sheppard-Brick A Quiz Review LT ,
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1 4A Quiz Review LT , Key Facts Know how to use the formulas for projectile motion. The formulas will be given to you on the quiz, but you ll need to know what the variables stand for Horizontal: x f = x i + v xi t Vertical: y f = y i + v yi t gt 2 v yf = v yi + gt Variable Meaning Variable Meaning x i Initial horizontal position = 0 m v xi Initial horizontal velocity x f Final horizontal position v yi Initial vertical velocity y i Initial vertical position g Gravitational Constant = 10 m s! y f Final vertical position t Time When a projectile is shot at an angle, use vector components to find the initial horizontal and vertical velocity. To factor a polynomial, first factor out any common factors, then use the box method to factor the quadratic. o When you have a nonmonic quadratic ax 2 + bx + c velocity ( ), the numbers to fill in your box must multiply to a c and add to b To solve a quadratic equation, make sure one side of the equation is equal to 0. Then factor the quadratic and set all factors equal to 0. Solve all of the new equations for x. θ v xi v yi Make sure your homework is up-to-date: #1-30 in your yellow workbook should be done. Learning Targets 3.4 I can add and subtract vectors and multiply them by a constant by drawing on a grid. 3.5 I can find components of vectors. 3.6 I can add and subtract vectors and multiply them by a constant using their components 3.7 I can find the area of any triangle using trigonometry. 3.8 I can use the Law of Sines to solve triangles 3.9 I can use the Law of Cosines to solve triangles I can choose the appropriate tool(s) to solve triangles. 4.1 I can solve projectile motion problems and interpret the results. 4.2 I can factor monic quadratic expressions, and solve their equations using the Zero Product Property. 4.3 I can factor non-monic quadratic expressions, solve their equations using the Zero Product Property, and use the results to solve projectile motion problems. 1
2 Practice 1. A ball is kicked with a velocity of 8.0 m/s at an angle of 20 from a cliff 80 meters high. Variable Known? Variable Known? x i v xi x f v yi y i g y f t a. How high is the ball after 1.5 seconds? b. Assume the ball is in the air for 4 seconds. How far from the base of the cliff (horizontally) will the ball hit the ground? c. How long does it take for the ball to hit the ground? Solve an equation by graphing on your calculator to answer this question. 2
3 2. A baseball is thrown from a height of 8 meters at an angle of with an initial velocity of 5 m/s. Variable Known? Variable Known? x i v xi x f y i y f v yi g t a. How high is the ball after 1 second? b. What is the vertical velocity of the ball after 1 second? c. How long does it take for the ball to hit the ground? Factor and solve an equation to answer this question. 3
4 3. Factor the following expressions as completely as possible. Be sure to look for common factors first. a. x! + 9x + 8 b. 2x! 16x + 30 c. x! + 20x d. 2x! 5x + 2 e. 6x! 13x + 6 f. 3x! 14x! 5x 4
5 4. Solve the following equations by factoring and using the ZPP. Again, look for common factors first. a. x! 7x + 6 = 0 b. 4x! + 12x 7 = 0 c. x! 7x 18 = 0 d. 2x! + 18x! + 28x = 0 e. x! + 16 = 8x f. 6a! 4a = 10 5
6 Practice 5. Find the area of the triangle below. Show your work Use the Law of Sines to find side AB. Show your work. B 13.5 A C 7. Use the Law of Cosines to find m B. Show your work. B A 8.2 C 6
7 8. Solve the triangle (find all the missing sides and angles). Show your work. C 5.8 A B 7
8 Practice 9. Use the vectors shown below to find the following sums and products. Show your work and use a separate color for your answer vector. Don t forget arrows! a. u r w ur b. 3* a r 8
9 10. Find the vertical and horizontal components of each vector shown. Show your work. a. b. 6 m a m 22 b Show work for part a here: Show work for part b here: Horizontal a r b r Vertical 11. Show all your work for the following sums and products. a) Find the horizontal and vertical components of a + b Horizontal: Vertical: b) Find the horizontal and vertical components of b a Horizontal: Vertical: c) Find the horizontal and vertical components of 3 a Horizontal: Vertical: 9
10 Answers 1 a m b m c seconds 2. a. 6 m b. -7 m/s c. 1.6 seconds 3. a. (x + 1)(x + 8) b. 2(x 5)(x 3) c. (x + 10)(x + 10) d. (2x 1)(x 2) e. (3x 2)(2x 3) f. x(3x + 1)(x 5) 4. a. x = 6, 1 b. x = 3.5, 0.5 c. x = 9, 2 d. x = 0, 7, 2 e. x = 4 5. Area = f. a = 1,!! 6. AB = m B = m C = , m B = , AC = a. b. 10. Horizontal Vertical 11. a. H: , V: b. H: 3.468, V: c. H: , V: a r b r
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