ASSIGNMENT #1 - EXAM REVIEW TEST

Size: px

Start display at page:

Download "ASSIGNMENT #1 - EXAM REVIEW TEST"

Evan Holland
6 years ago
Views:

1 UNIT 1 ASSIGNMENT #1 - EXAM REVIEW TEST 1) List 4 types of problems in this unit. a) break even b) mixture c) rate d) relative value /4 2) A sales clerk can choose between two maoney plans: straight 15% or $300 per month plus 3% commission. How much would the clerk have to sell under each plan to earn the same paycheck? plan 1 = 15%/month y represents total income plan 2 = 3%/month + $300 x represents sales y = 0.15x substitute 0.15x = 0,03x y = 0.03x x-0.03x = x = 300 x = 2500 He would have to sell 2500 things for plan 1 and 250 things for plan 2. /8 3) Draw a linear system with... a) one solution b) no solution /4 4) The greater of 2 numbers equals 3 times the smaller number. The smaller number incresed by 5 equals the greater number decreased by 45. What are the numbers? x = low # low # + 5 = high # - 45 y = high # high # = 3 x low # x + 5 = y - 45 y = 3x y = 75 y = x x + 50 = 3x y = x = 2x 25 = x Therefore the smaller number is 25 and the greater number is 75. /8

2 UNIT 2 them? 1) Write out these formulas a) midpoint b) distance c) slope mdp = (x1 + x2, y1 + y2) d = % x + y m = y / x 2 2 d) equation od a line y = mx + b /8 2) A cable is to be laid between 2 points A (6, 28) and B (14, 12). All units are to be in metres. What is its length? A = (6, 28) d = % x + y B = (14, 12) = %(14-6) 2 + (12-23) 2 = %8 2 + (-11) 2 = % = %185 = 13.6 Therefore the legth of the cable is 13.6m /5 3) What are the 3 names of the centre of a triangle and how do you find Which one is the one that will have equal lengths from each vertice? a) centroid: from midpoint of one side join two opposite verticies and find intersection of 2 lines using medians. circumcentre: from midpoint of one side draw a perpendicular bisector. Use opposite slope of known side and midpoint coordinates to get equation of a line. Find intersection of two lines. orthocentre: draw altitude by making perpendicular bisector of one sikde and joining to opposite verticies. Find intersection of two lines. Use opposite slope of known line and the verticies coordinates to find equation of line. The centroid gives equal lengths from each vertice /7 4) Identify the x intersepts and y intercepts of the equation x 2 + y 2 = 64. Find the length of the diameter. Draw a graph. The centre is the origin. - the σ of 64 x intercepts = (8,0) (-8,0) = 8 y intercepts = (0,8) (0, -8)

3 Radius = 16cm The length of the diameter is 16cm. /6

4 UNIT 3 1) What are the four types of factoring and give the equations. a) common y = x 2 + bx + c b) perfect square y = x 2-25 c) complex y = ax 2 + bx + c d) quadratic formula x = -b + σ b 2-4ac 2ac /8 2) Expand these equations and simplify them. a) (x + 4)(x - 7) b) (2x - 9)(3x - 5) x 2 + 4x - 7x x 2-27x -10x + 45 x 2-3x x 2-37x + 45 /6 3) What is the correlation between the vertex and the optimal value of the relation? Vertex is the maximum or minimum y value and the midpoint between the two zeros. The optimal value is the maximum or minimum y value. /4 above 4) Tim throws a ball vertically upward from the top of a cliff. This is the equation represented for the ball: h = t - 5t 2. H is the height in metres and r is the time in seconds. Draw a graph to represent the ball. a) How high is the clif 0 = t - 5t 2 0 = -5t t = -5(t 2 + 5t ) = -5(t 2 + 5t + 25) = -5(t + 5) It is 190m hight. b) How long does it take for the ball to get to a height of 50 m The cliff. 50 = t - 5t 2 0 = 5t 2-10t = t 2-2t = (t - 3) (t + 1) t = 3 or -1 t = 3 It takes 3 seconds to reach 50 metres. /8

5 UNIT 4 represents to represent 39.64m 1) Using this equation y = (x - 1)(x+7) a) find the axis of symmetry mid = 1 + (-7)/2 = -3 b) find the vertex y = (x 2 + 6x - 7) = (x 2 + 6x +9) = (x + 3) 2-16 Vertex = (-3, -16) c) write the relation in vertex form y = (x-3) 2-16 /5 2) Find the equation in vertex form with whose line has a vertex of (0,7) and passes through (-2, -3) y = a(x) = a(-2) = a(4) = a y = -2.5x /3 3) Describe, using transformations, how the graph of y = x 2 can be transformed into the graph of the equation y = -2(x + 3) - 8. Draw the new parabola as well as y = x 2 - compressed by the factor of -2 - shifted to the left by 2 - below y = x 2 by 8 - it goes down - a negative slope /6 4) A water balloon is thrown into the air. The equation that the balloon in flight is h = Draw a graph the balloon. a) How high is the balloon after 1s? h = -4.9(1) (1) h = h = 24.5m b) What is the maximum height of the balloon? h = -4.9t t h = -4.9(t 2-5.5t ) h = -4.9(t 2-5.5t + 7.6) h = -4.9(t ) max height equals /8

6 UNIT 5 the longest? 1) What are the three sides of a triangle called and which is Draw a triangle and give an example. a) hypotenuse the longest side b) adjacent c) opposite /5 2) State why triangle DEF is similar to triangle DGH. picture of triangle - EF2GH (PLT) - DFE ~ DHG - DEF ~ DGH DEF ~ DGH (AA), (PLT) /5 triangle. c = 18.6 /4 3) Write the ratios of trigonometry. Draw an example a) cos = adjacent/hypotenuse b) sin = opposite/hypotenuse c) tan = opposite/adjacent /8 4) Find the missing side a) ABC, given: a = 9.2. b = 11.8, angle C = 125Ε c 2 = a 2 + b 2-2abcosC c 2 = (11.8)(9.2)cos125 c 2 = cos125 c 2 = (-0.57) c 2 = c 2 =

S56 (5.3) Higher Straight Line.notebook June 22, 2015

S56 (5.3) Higher Straight Line.notebook June 22, 2015 Daily Practice 5.6.2015 Q1. Simplify Q2. Evaluate L.I: Today we will be revising over our knowledge of the straight line. Q3. Write in completed square form x 2 + 4x + 7 Q4. State the equation of the line