Hacia dónde vamos en el Ciberperiodismo 2020-2050

Another key formula you should know is the formula for the area, A, of an equilateral triangle with side s:

Since a regular hexagon can be divided into six equilateral triangles, the area, A, of a regular hexagon with side s is

STRATEGY 20: KNOW HOW TO CHANGE THE FORM OF AN EXPRESSION

Some problems can be simplified by recognizing that an algebraic expression has a familiar structure, whereas in other problems you may also need to change an expression into an equivalent form.

The difference of two perfect squares can be factored as the sum and difference of the two terms that are being squared, as in x² − y² = (x + y)(x − y). This means that any algebraic expression that you recognize as having the same general form or structure as x² − y² can be factored in this way. The expression 2a⁶ − 2b⁶ has the same structure as x² − y² with x = a³ and y = b³ so it can be factored in the same way:

To illustrate further, the equation (2y − 1)² − 9(2y − 1) = 0 can be easily solved by recognizing that it has the same form as x² − 9x = 0 where x = 2y − 1. To solve (2y − 1)² − 9(2y − 1) = 0,

■ Substitute x for 2y − 1, and solve the simpler equation for x:

■ Substitute 2y − 1 for x:

Example :: No-Calculator Section :: Grid-In

for all b ≥ 0, what is the value of x?

Solution

Change the form of each of the radical expressions using the rule that

Grid-in 19/4

Example :: No-Calculator Section :: Grid-In

If what is the value of 4r + 3s?

Solution

Since the left side of the given equation has fractional coefficients, change its form to eliminate the fractions so that the resulting expression looks like 4r + 3s. Multiply each term of the given equation by 12, the smallest whole number divisible by 3, 4, and 6:

Grid-in 10

Example :: No-Calculator Section :: Grid-In

In the inequality above, what is one possible value of 3y − 2?

Solution

You should notice that 3y − 2 has a similar structure to 6 − 9y and can be obtained from it by dividing 6 − 9y by −3. Divide each member of the inequality by −3 while keeping in mind that whenever dividing (or multiplying) the terms of an inequality by a negative number, the inequality signs must be reversed:

Grid-in any number between 0.75 and 0.80 such as .76.

Example :: Calculator Section :: Multiple-Choice

3x + 4y = 7 kx − 2y = 1

For what value of k will the above system of equations have no solution?

(A) −3 (B) − (C) 0 (D) Solution

A system of linear equations has no solution if the lines the equations represent are parallel and, as a result, have no point in common. Lines are parallel when they have the same slope. Rewrite each equation so they both have the same “y = mx + b” slope-intercept form. Then compare their slopes.

■ Solve each equation for y:

■ The slopes of the two lines are the coefficients of the x-terms. Since the lines must be parallel,

The correct choice is (B).

Example :: No-Calculator Section :: Multiple-Choice

f(x) = (x − 8)(x + 2)

Which of the following is an equivalent form of the function above in which the minimum value of

function f appears in the equation as a constant?

The minimum (or maximum) value of a quadratic function is the y-coordinate of the vertex of its graph, which appears as the constant k in the vertex form of the equation, f(x) = a(x − h)² + k.

■ Using FOIL, multiply out the binomial factors of f(x), which gives f(x) = x² − 6x − 16.

■ Change to the vertex form of the parabola equation by completing the square, which requires adding and then subtracting

■ By comparing f(x) = (x − 3)² − 25 to f(x) = a(x − h)² + k, you know that a = 1, h = 3, and k = − 25.

Since a > 0, the vertex of the parabola is a minimum point so that the minimum value of f is −25.

The correct choice is (D).

Example :: No-Calculator Section :: Grid-In

x² + y² + 8x − 10y = 80

The equation above represents a circle in the xy-plane. What is the length of the longest chord of the circle?

The equation is now in center-radius form (x − h)² + (y − k)² = r² where (h, k) = (−4, 5) and r² = 121 so r

= = 11. Since the longest chord of a circle is its diameter, the longest chord of the circle is 2 × 11 =

22.

Grid-in 22

TIPS FOR BOOSTING YOUR SCORE

■ Before starting your solution, make sure you understand what the question is asking you to find. If the problem involves numbers, the types of numbers or the form of the answer may help you decide on a solution strategy. For example, if there are whole numbers in the question, and decimal or fractions appear as answer choices, the solution may involve division.

■ If you think you have solved a multiple-choice problem correctly but do not find your answer among the four answer choices, you may need to change the form of your answer. This may involve writing a fraction in lowest terms; changing from decimal to fractional form or vice versa; rearranging or further simplifying the terms of an expression; or factoring. For

example, if you don’t find look for if you don’t find look for 3.5; if you don’t see y = 4x + 15, also look for y = 15 + 4x; if you don’t find 8x + 20, look for 4(2x + 5); if you don’t find look for a − b since

■ Unless otherwise indicated, figures provided with a question are drawn to scale. If it is stated that the figure is not drawn to scale and you are not sure how to solve the problem, try redrawing the figure so that it looks to scale. You may then be able to arrive at the correct answer choice by visually estimating a measurement or by eliminating those answer choices that appear to contradict the revised figure.

LESSON 2-2 GUESSING AND CALCULATORS ON THE SAT

Ne ve r omit the answe r to a que stion! For que stions you are not sure about, gue ss afte r afte r e liminating as many choice s as you can.