The Official SAT® Subject Test Study Guides. ALSO AVAILABLE. Chemistry ▫. Physics ▫. World History. Mathematics Level 1 ▫. Mathematics Level 2. Ivy Global. SAT Online Subject Test. Mathematics Level 2. PDF downloads are for single print use only: •. To license this file for multiple prints, please email. This means that you should register for the Level 2 Mathematics Subject Test in June after you complete a precalculus course. You can register for SAT Subject.
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SAT MATh 1 & 2 SubjecT TeST. 2. –6. –6. 1. 1. 10 y. K. H. G x. 6. 4. SAT MATheMATIcS LeVeL 2 PRAcTIce TeST. 3. 8. 2. 1. 3. 4. 2. 1. 3. 12 x x. +. −. −. −. = (A). 56 free SAT subject math level 1 2 practice tests. SAT Subject Math Level 2 Practice Test: Odd and Even Functions SAT Math Subject Test Pdf Download. McGraw-Hill's SAT Subject Test Math Level 2 with 8 practice tests pdf The SAT Math Level 2 test is one of the Subject Tests offered by the College Board.
A product can often be factored in more than one way Decide which math principles apply and use them to solve the problem. Rename the following percents as decimals Example 3 Divisors of 28 are Math Levels 1 and 2 you will become much more comfortable with the SAT and considerably more confident about getting a good score
Or go out to an early movie Make sure you allow enough time to arrive at the test site at least 15 minutes before the start time Your classroom should have an operational clock Both tests require the use of a calculator.. Or talk for hours and hours on the.. In the morning Fill in the answer bubbles cleanly and completely Random guessing will have no effect on your score Relax the day before the SAT Let your preparation give you the confidence you need to be calm and focused during the test Pace yourself and move through the test relatively quickly So use your calculator..
On the morning of the test Remember that because you are working through this book You may use a calculator on the SAT Diagnostic Level These include: Taking the Diagnostic Test in this chapter and then working out your scores will help you determine how you should apportion your study time Mathematics Level 1 exam differs in three important ways from the directions for other standardized tests you have taken At this point.
Stick to the time.. You need to indicate on the answer key which test you are taking You will also get a sense of how long you can spend on each question. Doing this will give you an idea of how it feels to take the test in one hour. The instructions on the answer sheet of the actual test will tell you to fill out the top portion of the answer sheet exactly as shown.. The answer sheet has numbered ovals on the sheet Diagnosing Strengths and Weaknesses Volume of a right circular cone with radius r and height h: S 5 4pr2 Volume of a pyramid with base area B and height h: In the shaded box labeled Test Code fill in four ovals: Unless otherwise indicated You must use at least a scientific calculator.
The figures that accompany questions on the test are designed to give you information that is useful in solving problems. Diagnostic Level 1 You must decide whether or not to use a calculator for each question.. The domain of any function f is assumed to be the set of all real numbers x for which f x is a real number Be sure your calculator is set in degree mode You will need a calculator to answer some but not all of the questions Degree measure is the only angle measure used on this test For each of the following problems Given the figure below..
Then fill in the corresponding oval on the answer sheet.. How much greater is the area of the outside square than the area of the inside square? In the figure below If the exact numerical value is not one of the choices..
What is the sine of 30 degrees? What is the probability that a person gets a red gumball? If this pattern continues At what point s does f x 5 x2 1 3x 1 2 intersect the x-axis? Each arrangement after the first one is generated by adding a row of squares to the bottom of the previous arrangement.
If the distance between the two points P a.. A gumball machine contains 40 blue gum balls The x-intercept of n must be A negative and greater than the x-intercept of m B negative and less than the x-intercept of m C zero D positive and greater than the x-intercept of m E positive and less than the x-intercept of m.. Line m has a negative slope and a negative y-intercept Sequential arrangements of blocks are formed according to a pattern.. Line n is parallel to line m and has a positive y-intercept..
What are the x The angle of the sun above the horizon is Find the approximate length of the shadow of a person who is Trees are to be planted inside a circular tree orchard so that there are 5 trees per square meter.
If trees are available only in allotments of packages of What is the slope of the line that is perpendicular to y 2 2x 5 1? The equation x2 1 9 5 2y2 is an example of which of the following curves? A B C D E hyperbola circle ellipse parabola line Define the x-coordinate of the midpoint between The circumference of the tree orchard is 30 meters How many distinct edges does the resulting object have?
Suppose one takes a tetrahedron ABCD with base ACD as shown below and combines it with another tetrahedron by connecting their corresponding bases.. If f x 5 3x 2 1 and if f 21 is the inverse function of f.. What is the sum of the first 40 even positive integers? Place the following list of numbers with the given labels in order of greatest to least The area of the larger square is x 1 2 That is..
The correct answer is C. The distance between the two points P and Q is defined to be 5. The correct answer is E The correct answer is B. If line m has a negative slope and a negative y-intercept Given the list. Set f x 5 0 and solve by factoring and using the zero-factor property To find the answer The correct answer is C The correct answer is D.. Use a special triangle to get sin 30 The result of this is 7x 1 4 5 Use the Pythagorean theorem on one of the triangles to get c2 5 a2 1 b That is Since line n is parallel to line m with a positive y-intercept we know that line n will have a positive x-intercept.
The correct answer is D. The correct answer is A.. The probability that a person gets a red gumball is just 20 the number of red gumballs divided by the total number of gumballs The result 7x 1 4 3 of this is Now multiply both sides of the equation by 12 to clear the 12 2 denominators..
The correct answer is A The correct answer is C.. The correct answer is B The equation 2y2 2 x2 5 9 can be written as 2 That is. The G 5 F 5 We know that there are 5 trees per square meter and there are 5A 5 6 trees in a package Just rewrite the equation to 2y2 2 x2 5 9 to see that it is y2 x2 9 a hyperbola.
The area of the parallelogram is just 4 5 5 Circumference is given by the formula C 5 2pr. Write in slope-intercept form to get the slope of the given line to be 2 5 m Value of y varies inversely with the square of x Calculate the average of the x coordinates of 21 and 4 define as m and also calculate the average of the y coordinates 1 and 3 define as n..
The correct answer is A. The answer can be found by looking at the tangent of The correct answer is D H 5 By exponent rules.. One tetrahedron has 6 edges Given the information. Stick to the time You will also get a sense of how long you can spend on each question.. Taking the Diagnostic Test in this chapter and then working out your scores will help you determine how you should approtion your study time.
The answer sheet has numbered ovals on the sheet. The instructions on the answer sheet of the actual test will tell you to fill out the top portion of the answer sheet exactly as shown You must decide whether or not to use a calculator for each question You must use at least a scientific calculator Diagnostic Level 2 Unless otherwise indicated..
The figures that accompany questions on the test are designed to give you information that is useful in solving problems In a quadrilateral with angles A If we cut off the top of the pyramid parallel to the base 3 inches from the tip.. Then fill in the corresponding oval on the answer sheet For each of the following problems..
Consider a pyramid with a square base side of 6 inches and with a height of 12 inches In the figure below. Diagnosing Strengths and Weaknesses. AC is a diameter The equation of the tangent to a circle at point What is the radius of the circular path?
A bug travels all the way around a circular path in 30 minutes traveling at A purse contains a total of 15 coins. A B C D E 10 dimes and 5 nickels 7 dimes and 8 nickels 11 dimes and 4 nickels 9 dimes and 6 nickels 8 dimes and 7 nickels www In triangle ABC shown below What is the probability that the first 2 draws from a pack of cards are clubs and the third is a spade? Assume all cards are drawn without replacement.. The perimeter of the triangle is The graph of f x 5 10 2 4e22x is shown below.
If the distance between a foot ladder and a vertical wall is 5 feet along the ground In triangle OAB. If secu 5 The value of k so that the sequence k We first take the common denominator in this problem by multiplying and dividing the entire expression by bc and then multiply out the b Multiplying out the two expressions For this problem. The 15 percentage of profit in terms of the original price is given as 5 10 percent In this problem. For this problem The length of an arc subtending an angle u at the center u of a circle of radius r is L 5 2pr To find the domain of the function f x 5 x The volume of a pyramid 3 1 with a square base with a side of The radius of the circle.
To find g t Plugging in the value of C and solving for r.. We have been given a function f x 5 ax2 1 bx 1 c.. Using this formula To find a and b. The volume of a pyramid is given as V 5 Ah. This is obtained by plugging in 5 for x in the expression for f x. The volume of a pyramid with a square base 1 with a side of 6 and a height of 12 is V1 5 36 12 5 Since the bug traverses a circular path in half an hour at We observe that for choice D.
This is because we cannot have a division by zero Plugging in x 5 2y in the second equation The distance between two points x For a circle..
Using this information and the Pythagorean theorem.. The distance between points A and B is the same as the length of a side of the cube. We use the property of tangents to circles here. To obtain the area of rectangle ABGH. This gives us x 5 For the given cube with sides of 4 each To obtain the distance between points B 1. The slope of the line joining the center at point 3. For the function x2 2 6x. To obtain the value of x The probability of obtaining a club on the first draw is By definition A pack of cards contains 13 each of clubs We refer to the figure below for this problem..
Let there be x dimes and y nickels. Then we have x 1 y 5 15 the total number of coins is Solving the above two equations simultaneously.. If AX is the perpendicular bisector of side OB. Plugging in 3 for x Be careful of rounding errors. Since triangle OAB is an isosceles triangle.. To calculate the area of the triangle O Thus Since the perimeter of the triangle is given to be equal to To get the y-coordinate of point A The x-coordinate of point A is the same as that of point X.
Solving the equation for k If the sequence k 2 Using the sec u Decide which math principles apply and use them to solve the problem.
Look for your answer among the choices If the answer you found is not there.. Choice D TIP In the figure above.. The principles that apply are those governing operations with signed numbers DPQS is a right triangle.
SAT Subject Test: Math Review If you have trouble working with letters.. As for choices B and C The correct answer Since PQ 5 PS.
Two math principles apply: Remember the Reference Information! The Reference Information at the start of the math section provides valuable information about special right triangles Any number other than zero squared gives a positive result Since x and y are negative. A B C D xy xy 2 x 2 y 2 x1y E x 3y The problem asks you to pick an answer choice that is a negative number If x and y are negative numbers For example This way But remember that your calculator is not some sort of magic brain When you use your calculator.
The first third of the questions are easy Calculators can be helpful in doing basic arithmetic computations. And make sure to hit the Clear key after each finished operation.
For how many integers x is They will help you The most important thing to remember is to set up your work on paper first Take a look at these three examples Then make your number substitutions on the calculator Multiple-Choice Math Strategies Whatever the case You see the same information as you see in the word problem.
You can probably do Question 1 with your eyes closed. All it does is say that the shortest book is pages. When you hit the difficult stuff So for Question 1 the answer is indeed choice E.
In a set of five books Question 25 may cause you to wince a little. For Question 12 you probably have to open your eyes and do some calculations on scratch paper. You can bet that your first-choice. If x pages is the average arithmetic mean of the number of pages in the five-book set Simple and wrong The obvious answer is almost always the correct answer.
Then the average length of all five books would be: Then take your best guess Make certain that the answer that you select is the answer to the question that is being asked The problem does not ask for the value of x Use all the help you can get! When you have less than a clue about a difficult question..
Beware of the The answers to pages The answer is choice A When Guessing at Hard Questions.. OK then They never jump out at Then x would be greater than but less than So the average would be: Now assume that the other three books contain As a result Trust your judgment and your reasoning Get started by testing choice C If a rectangle has sides of 2x and 3x and an area of When you plug 3 into the figuring Since 96 is larger than 24 the area in the question Get it?
One of them has to be correct Always Start from the Middle When working on multiple-choice math questions. Math Review.. There is only one integer between 27 and The only choice left is A When Working Backward This way..
Testing answer choices can often be a much easier and surer way of solving a problem than attempting a lengthy calculation. Which means. If the farmer has 70 chickens. Now try this testing business with a more difficult question: TIP Leave a paper are some examples: If you need to set up an If x 2 4 is 2 greater than y How will you lose some of those feet? That way You know the farmer has animals. If his animals have a total of heads and a total of feet. Check it out: The only answer left is choice E All right This technique can make problems much easier to solve..
Give choice D —80—a try.. A farmer raises chickens and cows In Problems Involving Variables. And say that you really only need one pen. Then p 5 The unit cost of pens is the same regardless of how many pens are purchased.
If the cost of p pens is d dollars Without the knowledge of the size of the a.. Read too quickly and you might miss this fact entirely..
The correct order is Now consider the fraction To begin.. When a number between 0 and 1 is squared. This problem is fairly straightforward.. The value of is larger still.. The only difference between the two problems is that this time you are told that the value of a is between 0 and Since a. Questions in the Three-Statement Format Can be Solved by the Process of Elimination You may find a three-statement format in certain questions in the multiple-choice math section.
If x is positive and y is negative For example.. If x and y are negative numbers so that x is greater than y.. So Use It for Scratchwork The test booklet is yours.. Because statement II must appear in the correct answer Since both are negative numbers Here is an example: If x 2 y is positive The best way to answer this kind of question is to tackle one statement at a time.
Subtracting a negative number is really adding a positive number.. Math Review. The correct answer is actually choice E The procedure for solving such equations occasionally results in what are known as extraneous solutions An extraneous solution is a number that is correctly obtained from the equation-solving process Make Certain to Check Your Answer..
Solve for x: When you do Now use the information in the figure to find the areas and then subtract You know that the larger triangle has a right angle and two equal sides What you really need to do is figure out the areas of the original large triangle and the smaller triangle and find the difference..
The smaller triangle has a right angle and its side is parallel to the side of the larger triangle For multiplechoice math questions Since NM is a side of both triangles Mark it up with the Since you just found out that triangle NMP has sides of 9 and OQ 5 It is one of the most useful and common SAT geometry facts.
Consider the problem below. If T is the midpoint of PQ Line segment PQ is tangent to the circle with center O at point T. The diagram now depicts right triangle OTQ.
Using his bike How long will it take the two boys to complete the route if they work together Time actually spent Time needed to do entire job alone Daryl Francisco x 20 x 30 x x 1 51 20 30 Multiply by 60 to clear fractions: Daryl can complete a paper route in 20 minutes In fact TU appears to be longer than PS If you find questions that you know will give you nightmares.
Save Them for Last You know which little demons haunt your math skills.. The triangle PSR has sides of 6 and TU appears to be approximately Since TU 5 SR Figure not drawn to scale They will take up a lot of your time In the rectangle PQRS shown..
Is that sufficiently accurate to get the right answer? Look at the choices As an alternative You can do this by using the Pythagorean theorem If the answer you found is not there Decide which math principles apply and use them to solve the problem Look for your answer among the choices. So use your eye as an estimator if you need to This will help you avoid unnecessary algebraic calculations The positive integers..
These number systems are discussed in a later section The numbers that are used for counting 1. In order to understand the real number system. The only exception to this is on the Level 2 test The most common irrational numbers that you will see on your test are square roots For example. A real number is said to be a rational number if it can be written as the ratio of two integers Percents and decimal numbers are rational as well It is also rational since it can be written as and is..
Example The number is an integer.. The number to the right of the 5 is a 9. Numbers and Operations Review In either case.
The rules for the rounding of numbers are very simple.. Rounding of Numbers.. Examples Round the following numbers as indicated: As before.. Drop the two digits to the right of this From time to time. The number to the right of the 4 is a In the case of whole numbers When rounding decimal numbers The answer is The digit just to the right of it is Round each of the numbers below to the indicated number of decimal places Classify each of the following numbers as whole..
Solve the following problems Drop the digit to the right of this. Drop the digits to the right of this B The hundred thousands digit is A 27 is real. The digit to the right of it is Place Value Whole numbers are expressed in a system of tens Example 2 Odd and Even Numbers A whole number is even if it is divisible by Example 1 means: Ten digits— Example When we take a whole number and write it out as in the two examples above..
The set of positive integers. Each digit differs not only in face value but also in place value Prime Numbers To factor a composite number into its prime factors The first ten primes are The positive integer 1 is called a unit Then move on to dividing by the prime number 5 and other successive primes until a prime quotient is obtained In a consecutive series of whole numbers. Consecutive Whole Numbers Numbers are consecutive if each number is the successor of the number that precedes it If this is successful..
Example Find the prime factors of Express the original number as a product of all its prime divisors If three consecutive whole numbers are given.. Example 1 Composite numbers can be factored In particular All other positive integers that are neither 1 nor prime are composite numbers..
Take the point on the number line that lies one unit to the right of the origin and label it with the number In this way Example 4 Choose some convenient distance as a unit of length.. It is called the number line Ordering of Whole Numbers On the number line The Number Line A useful method of representing numbers geometrically makes it easier to understand numbers One can also say This point is called the origin.
Select some point on the line and label it with the number The point on the number line that is one unit to the right of 1 is labeled Draw a horizontal line For any two whole numbers a and b Example 3 The operations of addition and multiplication on whole numbers are said to be closed because the answer in each case is also a whole number.
If 0 is added to any whole number. Zero is called the identity element for addition Even though there may be a long column of numbers The operations of subtraction and division on whole numbers are not closed because the unique answer is not necessarily a member of the set of whole numbers.
One way is to write: This principle is called the commutative property of addition The basic operations on whole numbers are addition These are all binary operations—that is.. The fact that the same answer Most people use this property without realizing it when they add a column of numbers from the top down and then check their results by beginning over again from the bottom..
Subtraction Subtraction is the inverse of addition.. The order in which the numbers are written is important If a number is multiplied by Zero times any number is 0: Division is the inverse of multiplication Zero divided by any number other than 0 is 0: Division by 0 is not defined has no meaning The whole number a is then said to be an integer multiple of b Example 4 Multiples of 3 are Example 3 Divisors of 28 are It is not commutative: Find all of the common prime factors of 30 and Which property is illustrated by the following statement?
Write the number Give an example to show that subtraction on the set of real numbers is not commutative.. In each of the statements below. Express as a product of prime numbers. Find all of the factors of What are the first seven positive multiples of 9? List all of the prime numbers between 50 and What are the divisors of 60? A The commutative property of addition The divisors of 60 are The prime numbers between 50 and 90 are The associative property of addition The associative property of multiplication A fraction indicates division: If the denominator of a fraction is If m is a counting a m3a a m a a number and is a fraction..
The upper b part.. TIP 5 4 or? Since www.. Inequality of Fractions quickly If two fractions are not equivalent Example 1 Which is less Since 5 and If two fractions have different denominators Then use the common denominator to compare numerators For the fractions c a and: Each time a prime appears in the numerator p over the same prime in the denominator Repeat this process until there is no prime factor remaining that is common to both the numerator and the denominator: Fractions are expressed in simplest form when the numerator and denominator have no common factor except To simplify a fraction to an equivalent fraction in simplest form Simplifying to Simplest Form The principle that m3a a 5 m3b b can be particularly useful in simplifying fractions to simplest form In the following problems..
This system can be extended to fractions by using a period called a decimal point. Decimal fractions are less than 1—for example.. The digits after a decimal point form a decimal fraction. Decimal fractions can be combined with whole numbers to make decimals—for example Adding zeros to the right of a decimal after the last digit does not change the value of the decimal If the digit to the right of it is The number immediately to the right is To round off.
As the number of digits to the right of the decimal point increases If the digit to the right is Example 1 Round off Rounding Off Sometimes Rounding off whole numbers can be done by a similar method The scaled score is the only score reported to either students or colleges, and ranges from to , with being the best possible score.
The standard deviation of the test scores in was From Wikipedia, the free encyclopedia.
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