OVERVIEW
Since there is no penalty for a wrong answer, you should enter an answer for every question even if it means guessing. Guess smartly by crossing out in your test booklet those choices that you know are unlikely or impossible. Before guessing, however, think through a problem and try to solve it mathematically—guessing should be your last resort.
Make sure you practice with the calculator that you will bring to the exam room. If it takes batteries, replace the batteries with fresh ones the day before the exam.
TIP
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.
Ruling Out Answer Choices
If you get stuck on a multiple-choice problem, guess after ruling out answer choices as there is no point deduction for a wrong answer. You can increase your chances of guessing the right answer by first eliminating any answer choices that you know are impossible or unlikely. You may be able to rule out an answer choice by asking questions such as
■ Must the answer be a certain type of number: positive or negative? greater than 1 or less than 1? involve a radical?
■ Can an accompanying figure be used to estimate the answer? If so, based on the estimate, can you eliminate any of the answer choices?
■ Do any of the answer choices look very different from the other three answer choices. For example, suppose the four answer choices to a multiple-choice question are
The test makers often try to disguise the correct answer by making it look similar to other choices. If you need to guess, eliminate choice (A) as its structure looks different than the other three choices, which all include the product of π and a parenthesized expression.
Example :: No-Calculator Section :: Multiple-Choice
A new fitness class was started at a chain of fitness clubs owned by the same company. The scatterplot above shows the total number of people attending the class during the first 5 months in which the class was offered. The line of best fit is drawn. If n is the number of the month, which of the following functions could represent the equation of the graph’s line of best fit?
(A) f(n) = 300n + 125 (B) f(n) = 300 + 125n (C) f(n) = 400 + 150n (D) f(n) = 200n + 300 Solution
The equations of the line in the answer choices are in the slope-intercept form y = mx + b where m is the slope of the line and the constant b represents the y-intercept.
■ Review the graph to see if you can eliminate any answer choices. You can tell from the graph that the y-intercept is 300, which eliminates choices (A) and (C).
■ Pick two convenient data points on the line of best fit where no estimation is needed, such as (0, 300) and (4, 800). Use these points to find the slope, m, of the line:
■ Since b = 300 and m = 125, the equation of the line in y = mx + b slope-intercept form is y = 125x + 300 or, equivalently, y = 300 + 125x.
The correct choice is (B).
Example :: Calculator Section :: Multiple-Choice
In June, the price of a DVD player that sells for $150 is increased by 10%. In July, the price of the same DVD player is decreased by 10% of its current selling price. What is the new selling price of the DVD player?
(A) $140 (B) $148.50 (C) $150 (D) $152.50
Solution
Is the new selling price equal to the original price of $150, less than the original price, or greater than the original price?
Rule out choice (C) since “obvious” answers that do not require any work are rarely correct. In June the price of a DVD player is increased by 10% of $150. In July the price of the DVD player is decreased by 10% of an amount greater than $150 (the June selling price). Since the amount of the price decrease was greater than the amount of the price increase, the July price must be less than the starting price of $150. You can, therefore, eliminate choices (C) and (D).
This analysis improves your chances of guessing the correct answer. Of course, if you know how to solve the problem without guessing, do so:
STEP 1 June price = $150 + (10% × $150) = $150 + $15 = $165
STEP 2 July price = $165 − (10% × $165) = $165.00 − $16.50 = $148.50
STEP 3 The correct choice is (B).
TIP
Not e ve ry proble m in the calculator se ction re quire s or be ne fits from using a calculator. Many of the proble ms do not re quire a calculator or can be solve d faste r without using one .
Calculators
Calculators are permitted on only one of the two math sections. When you take the SAT, you should bring either a scientific or graphing calculator that you are comfortable using and that you used during your practice sessions. Using a calculator wisely and selectively can help you to solve some problems in the calculator section more efficiently and with less chance of making a computational error.
When working in the calculator section of the SAT,
■ Approach each problem by first deciding how you will use the given information to obtain the desired answer.
Then decide whether using a calculator will be helpful.
■ Remember that a solution involving many steps with complicated arithmetic is probably not the right way to tackle the problem. Look for another method that involves fewer steps and less complicated computations.
■ Use a calculator to help avoid careless arithmetic errors, while keeping in mind that you can often save time by performing very simple arithmetic mentally or by using mathematical reasoning rather than calculator arithmetic.
Example :: Calculator Section :: Grid-In
The set of equations above describes projectile motion influenced by gravity after an initial launch velocity of v0, where t is the number of seconds that have elapsed since the projectile was launched, v(t) is its speed, and h(t) is its height above the ground. If a model rocket is launched upward with an initial velocity of 88 meters per second, what is the maximum height from the ground the rocket will reach correct to the nearest meter?
Solution
■ When the rocket reaches its maximum height, its velocity is 0. Use the velocity-time function to find the value of t that makes v(t) = 0:
■ Substitute 9 for t in the position-time function:
Grid-in 395
Example :: Calculator Section :: Multiple-Choice
A certain car is known to depreciate at a rate of 20% per year. The equation V(n) = p(x)n can be used to calculate the value of the car, V, after n years where p is the purchase price. If the purchase price of the car is $25,000, to the nearest dollar, how much more is the car worth after 2 years than after 3 years?
(A) 1,600 (B) 2,400 (C) 3,200 (D) 4,000 Solution
In the equation V(n) = p(x)n, x represents the exponential decay factor since the car is losing value. Hence, x represents 1 minus the rate of depreciation.
COMPUTATION METHOD 1
Use your calculator to find the difference between V(2) and V(3), where p = 25,000 and x = 1 − 0.2 = 0.8:
COMPUTATION METHOD 2
Avoid the need for a calculator by simplifying the expression before performing the multiplication:
The correct choice is (C).
**Remember, since this is an e-Book, all Answer Sheets are for reference only. For Tune-Up Exercises, please record all of your answers separately.