Monday/Tuesday: SAT/ACT

Warm-Up:

      Solve 5x + 3(7x – 4)= 40.

      Hint: Distribute first.

Solving equations- systems of equations

Systems of equations have two (or more) variables and two (or more) equations.

In general you have to have as many equations as you have variables to have a chance at finding a solution.

Methods to solve systems of equations:

Method One: Substitution

If you have one variable already by itself, say x, and equal to some expression in terms of a different variable, say y, then you can substitute y in the other equation with the expression in x. 

Consider the system

y = 2x + 3   

3x + 2y = 20.

You can solve the system by replacing y in the second equation with 2x + 3 from the first.  You will have to distribute, as in the warm-up.  Can you solve for x first?  Here is the first step:

3x + 2(2x + 3) = 20

To solve for y, simply plug your solution for x into the expression with y by itself.

Substitution Examples: Solve in groups of three.  Each group will be selected randomly to solve one problem.

1)            x = 5y – 2       (2)    y = 3x – 2   

2x + 5y = 11                 2x – 3y = -16     

(3)  3x – 2y = 1    (4)    x – y = 12        

  2x =  24 – 2y                 x = 5y

Method Two: Addition to Cancel One of the Variables

Sometimes you have the equations both in standard form, with x’s and y’s on the same side, and they add up to some number.  If one of the variables will cancel right away by addition, then you just add the two equations together as you first step as you solve both x and then y.

For each problem, find x, y, x + y, and xy.

(1) 3x + 2y = 0       (2) 7x – 10y = 4  (3) 5x + 3y =     51

    5x – 2y = -16     -7x + 12y = -2     4x – 3y =     57

       (4) x – y = 110

             x + y = -90

Method 3: Subtraction

Similarly, you can sometimes cancel by subtracting (or adding the opposite).

Consider:

(1)        3x + 2y = 0   (2)    7x + 10y = 24

5x + 2y = -4      7x + 12y = 26

(3) 5x + 3y = 51          (4)        x – y = 110

       4x + 3y = 45                 x + y= -90  

Method 4: Multiplication

Sometimes none of the above methods will immediately work.  Then we multiply each equation by a different number so that something cancels out.

This is the powerful method Giancarlo showed us.

Examples:

(1)        7x – 4y = 29    (2)    4a + 5b = 60

4x – 7y = 26       6a + 7b = 80

(3)   12x + 15y = 264   (4)   11x – 9y = 0

  3x + 13y = 167    9x – 11y = -40

 Classwork: Systems of Equations Handout #1 with partners; present solutions randomly.

Homework: Systems of

Equations Handout #2.

Wednesday/Thursday ACT/SAT

Warm-Up: Copy

Reading Comprehension Workshop

·     Read the questions first

·     Keywords/Key phrases

·     Identifying style of writing

o   Expository – explaining a concept

o   Compare/Contrast

o   Point of view

o   Argument

o   Fiction

o   Historical

o   Perspective of writer

·     Look for clues – title, author, time period

·     Main Idea – Read intro/conclusion sentence of each paragraph

·     How to speed-read by reading words in groups.

·     Choose the best answer, don’t out-think the question by over-thinking it.

·     Read for practice and vocabulary.

We will read a number of selections from actual SAT tests.  These will form the content on which we will practice the above techniques and any others the class discovers or creates.

_________________________________________________________________

SAT/ACT Prep

Mr. Kalafus

Allison Academy

Week of 08/17/2009

Monday:

Warm-Up: Would you rather make $200 a week or $800 a month?  Explain why you chose your answer.

Introductions

Review syllabus

Practice SAT Verbal for baseline scores

Correct SAT Verbal and estimate scores

HW: Get syllabus signed

HW: Write an essay on your choice of topics:

1)      Why I want to go to college

2)      A funny thing that happened this summer

3)      My dream college/university

4)      Where do you see yourself in ten years?

5)      Three goals and how I plan to achieve them

Include a “hook” to gain the readers interest, a topic sentence/thesis, an introductory paragraph, supporting paragraph(s), and a conclusion which reaches back to your thesis and hook.

Tuesday:

Warm-Up: While cynics may ____________ the goal of international disarmament as utopian, others believe that laughing contemptuously at idealism leads nowhere.

(A) exalt            (B) confirm            (C) renew  (D) deride  (E) defend

Collect HW – essay, syllabus

Practice SAT Math for Baseline score

Correct the test and estimate the scores

HW: Write 2 paragraphs about your SAT strengths and weaknesses

            Verbal – main idea, reading comprehension, analogies, vocab

            Math – algebra, geometry, word problems, formulas, solving equations, setting

up equations, factoring, graphing, etc.

Essay

Wednesday:

Warm-Up: If 2x + y = 14 and 4x + y = 20, what is the value of 3x + y?

Collect HW – strengths and weaknesses

Solving equations - One-step, two-step, multi-step equations; Systems of equations

HW: Algebra review handout

Thursday:

Warm-Up: If 100 monkeys type 150 pages in 1.5 days, how many pages can 50 monkeys type in 20 days?

Collect and check HW: algebra practice

Activity: circles

            Draw a circle

            Measure and label radius, circumference, diameter.

            Divide the circumference by the diameter.

            Take a class average of the diameters

Activity 2: Analogies p. 536

Helpful analogies hint: create a sentence using the relationship between two words and see if it fits for the answer choices.

HW: Write three SAT analogies questions.