Grade 10 Make Up Package

Quadratics I and II (Chapter 3 and 4)

This package is a set of exercises that should improve your knowledge and understanding of the concepts in chapter 3 and chapter 4. The exercises are set up in sections (units). After you complete each section, show the teacher. If your work is done correctly, I will initial on this sheet, and you can proceed to the next section. If you have problems, I will help you to correct your work.

Once all sections have been completed, you will be able to write another test on this material.

Evaluation:

By completing this package, your knowledge and application mark(s) on this unit can be improved to a level of 75%. The reason for this is that the difficulty of questions on the retest is not as high as on the original test. The goal of the retest is to try to achieve the basic expectations of the unit – a level 3 (75%). There will not be questions that exceed the expectations of the unit.

Date Completed / Teacher Signature
Unit #1: Questions # 1 - 8
Unit #2: Questions # 9 - 12
Unit #3: Questions # 13 – 16
Unit #4: Question # 17, 18
Unit #5: Question # 19, 20
Unit #6: Question # 21 – 24
Unit #7: Questions # 25 - 27

Chapter 3

Factoring & Expanding

  1. Expand and simplify each expression.

a) (q – 2)(3q + 1)

b) (5m – 1)(2m + 3)

  1. Factor each expression.

a)4ab – b2

b)16x2y – 14xy + 12xy2

  1. Factor

a)n2 – 9n 20

b)3x2 – 18x + 27

c)2x2 + 5x + 2

  1. Factor each expression. Draw a tile diagram of chart for each equation.

a)12x2 + 8x

b)-8x2 + 14x + 4

Finding Zeros, Solving Equations in Factored Form

  1. Fill in the Blanks.

Quadratic relations have first differences that are ______and second differences that are ______.

To find the zeros of a relation, substitute ______into the equation, and solve for x.

  1. Find the zeros of each relation

a) y = (x + 2)(x + 4)

b) y = -(x + 1)(x – 5)

c)y = x2 + 4x

d)A = L(12 – L)

  1. How can you tell, just by looking at the equation, that the parabola is concave up or concave down?

Writing Equations Given Zeros and a Point.

  1. Find the equation of a quadratic in standard form …

a)That has zeros 4 and -2 and a y-intercept of -8.

b)Zeros 2 and 6, vertex (4, 8)

c)The parabola has x-intercepts of 5 and -3 and a maximum value of 6

Maximum Area

  1. An area is being designated as a natural habitat. One side of the rectangular area is a large lake. Not including this side, there is 48km of fencing. What dimensions will ensure a maximum area? Create a chart with at least 4 values and create an algebraic model.

Revenue Problems

  1. A company selling calculators for $80 each sells 60 per day. A survey indicates that for each $5 increase in price, 2 fewer calculators will be sold per day. How much should the company charge to maintain the revenue?

Arches Problems

  1. Angus is playing golf. Angus and the hole are 100m apart. The golf ball is at its highest point at 10m (50m away from the hole). Determine the height of the ball when it is 15m from the hole. Determine a quadratic relation for height vs. distance traveled.

Real Life Quadratic Relations – Given Equations

  1. A ball is thrown straight down from a cliff. The relation h = -5t2 – 5t + 180 gives the height of the ball, h, in meters at t seconds after it is thrown. How long does it take to reach a height of 80m?

Chapter 4

Completing the Square, Partial Factoring

  1. Rewrite in vertex form by completing the square and state the vertex.
  2. y = x2 – 4x + 3
  3. y = x2 + 8x + 9
  4. y = 2x2 + 12x – 7
  1. For each quadratic relation …
  1. use partial factoring to find two points that are equidistance from the axis of symmetry
  2. find the coordinates of the vertex
  3. express the relation in vertex form
  4. sketch the graph

a)y = x2 – 6x + 5

b)y = -2x2 + 12x – 11

c)y = -1/2x2 + 2x + 3

Vertex Form

  1. For each quadratic relation, find:
  1. the coordinates of the vertex
  2. the equation of the axis of symmetry
  3. the direction of opening

a)y = -4(x + 3)2 – 2

b)y = 2(x – 4)2

c)y = -(x + 7)2 + 4

Writing Equations in Vertex Form Given Vertex and Point

  1. Find in vertex form, the equation of the quadratic relation:

a)with vertex at (0, 3) passing through (2, -5)

b)with vertex at (5, -3) passing through (1, -8)

Transformations

  1. Draw an input / output diagram for each of the following and state the transformations applied to y = x2 to create it.

a)y = -2(x + 3)2 – 1

b)y = 1/2(x – 2)2 + 4

c)y = (x + 2)2 – 1

  1. Write the relation for a parabola that satisfies each condition.

a)The graph of y = x2 is stretched vertically by a factor of 3/2, then translated left 4 units.

b)The graph of y = x2 is reflected about the x-axis, stretched vertically by a factor of 2, then translated to the right 5 units and down 8 units.

Problem Solving Using Vertex

  1. From 1995 to 1999, the average ticket price for a regular movie theatre (all ages) can be modeled by C = 0.06t2 – 0.27t + 5.36, where C is the price in dollars and t is the number of years since 1995 (t = 0 for 1995).

a)When were tickets at their lowest during this period?

b)What was the average ticket price in 1998?

c)What does the model predict the average ticket price will be in 2010?

  1. The underside of a bridge has the slope of a parabolic arch. It has a maximum height of 30m and a width of 50m. Can a sailboat with a mast 27m above the water pass under a bridge at a distance of 8m away from the axis of symmetry of the arch? Justify your solution.

Finding Roots Including Quadratic Formula

  1. Solve.

a)x2 – 4 = 0

b)(x – 4)2 = 1

  1. Solve by completing the square.

a)x2 + 6x – 8 = 0

b)-3x2 + 12x = 7

  1. Solve for x using the quadratic formula. Give the exact answer.

a)2x2 – 4x – 5 = 0

b)x2 + 7x = -2

  1. Calculate the discriminant and state the number of roots.

a)2x2 – 3x + 4 = 0

b)2x2 + 4x + 2 = 0

Real Life Quadratic Relation – Complete Problems

  1. A ball is thrown up into the air. Its height h, in meters, after t seconds is h = -4.9t2 + 38t + 1.75.

a)What is the height of the ball after 3 seconds?

b)For what length of time is the ball above 50m?

c)What is the maximum height of the ball?

d)When does the ball strike the ground?

Problem Solving with Quadratic Formula

  1. A rectangle is 3cm longer than it is wide. The diagonal is 15cm. Find the dimensions of the rectangle.
  1. A framer at a photo gallery wants to frame a print with a matte of uniform width all around the print. To make it pleasing to the eye, the area of the matte should equal the area of the print. If the print measures 40cm by 60cm, how wide should the matte be?