The sat math section potx

In the math sections, the problems will be easy at the begin-ning and will become increasingly difficult as you progress.. Here are some helpful strategies to help you improve your math

 P a r t 1 : F i v e - C h o i c e Q u e s t i o n s

The five-choice questions in the Math section of the SAT will comprise about 80% of your total math score

Five-choice questions test your mathematical reason-ing skills This means that you will be required to apply several basic math techniques for each problem In the math sections, the problems will be easy at the begin-ning and will become increasingly difficult as you progress Here are some helpful strategies to help you improve your math score on the five-choice questions:

■ Read the questions carefully and know the answer being sought In many problems, you will

be asked to solve an equation and then perform

an operation with that variable to get an answer

In this situation, it is easy to solve the equation and feel like you have the answer Paying special attention to what each question is asking, and then double-checking that your solution answers the question, is an important technique for per-forming well on the SAT

■ If you do not find a solution after 30 seconds, move on You will be given 25 minutes to answer

questions for two of the Math sections, and 20 minutes to answer questions in the other section

In all, you will be answering 54 questions in 70 minutes! That means you have slightly more than one minute per problem Your time allotted per question decreases once you realize that you will want some time for checking your answers and extra time for working on the more difficult prob-lems The SAT is designed to be too complex to fin-ish Therefore, do not waste time on a difficult problem until you have completed the problems you know how to do The SAT Math problems can

be rated from 1–5 in levels of difficulty, with 1 being the easiest and 5 being the most difficult The following is an example of how questions of vary-ing difficulty have been distributed throughout a

math section on a past SAT The distribution of questions on your test will vary

From this list, you can see how important it is

to complete the first fifteen questions before get-ting bogged down in the complex problems that follow After you are satisfied with the first fifteen questions, skip around the last ten, spending the most time on the problems you find to be easier

■ Don’t be afraid to write in your test booklet That is what it is for Mark each question that

you don’t answer so that you can easily go back to

it later This is a simple strategy that can make a lot of difference It is also helpful to cross out the answer choices that you have eliminated

■ Sometimes, it may be best to substitute in an answer Many times it is quicker to pick an

answer and check to see if it is a solution When

you do this, use the c response It will be the

mid-dle number and you can adjust the outcome to

the problem as needed by choosing b or d next,

depending on whether you need a larger or smaller answer This is also a good strategy when you are unfamiliar with the information the problem is asking

■ When solving word problems, look at each phrase individually and write it in math lan-guage This is very similar to creating and

assign-ing variables, as addressed earlier in the word problem section In addition to identifying what

is known and unknown, also take time to trans-late operation words into the actual symbols It is best when working with a word problem to repre-sent every part of it, phrase by phrase, in mathe-matical language

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1 4 7

■ Make sure all the units are equal before you

begin This will save a great deal of time doing

conversions This is a very effective way to save

time Almost all conversions are easier to make at

the beginning of a problem rather than at the

end Sometimes, a person can get so excited about

getting an answer that he or she forgets to make

the conversion at all, resulting in an incorrect

answer Making the conversion at the start of the

problem is definitely more advantageous for this

reason

■ Draw pictures when solving word problems if

needed Pictures are always helpful when a word

problem doesn’t have one, especially when the

problem is dealing with a geometric figure or

location Many students are also better at solving

problems when they see a visual representation

Do not make the drawings too elaborate;

unfor-tunately, the SAT does not give points for artistic

flair A simple drawing, labeled correctly, is

usu-ally all it takes

■ Avoid lengthy calculations It is seldom, if ever,

necessary to spend a great deal of time doing

cal-culations The SAT is a test of mathematical

con-cepts, not calculations If you find yourself doing

a very complex, lengthy calculation—stop! Either you are not doing the problem correctly or you are missing a much easier way Use your calcula-tor sparingly It will not help you much on this test

■ Be careful when solving Roman numeral prob-lems Roman numeral problems will give you

several answer possibilities that list a few different combinations of solutions You will have five

options: a, b, c, d, and e To solve a Roman

numeral problem, treat each Roman numeral as

a true or false statement Mark each Roman numeral with a “T” or “F,” then select the answer that matches your “Ts” and “Fs.”

These strategies will help you to do well on the five-choice questions, but simply reading them will not You must practice, practice, and practice That is why there are 40 problems for you to solve in the next section Keep in mind that on the SAT, you will have fewer questions at a time By doing 40 problems now,

it will seem easy to do smaller sets on the SAT Good luck!

 4 0 P r a c t i c e F i v e - C h o i c e Q u e s t i o n s

■ All numbers in the problems are real numbers

■ You may use a calculator

■ Figures that accompany questions are intended to provide information useful in answering the questions Unless otherwise indicated, all figures lie in a plane Unless a note states that a figure is drawn to scale, you should NOT solve these problems by estimating or by measurement, but by using your knowledge of mathematics

Solve each problem Then, decide which of the answer choices is best, and fill in the corresponding oval on the answer sheet below

– T H E S AT M AT H S E C T I O N –

1 4 9

1 a b c d e

2 a b c d e

3 a b c d e

4 a b c d e

5 a b c d e

6 a b c d e

7 a b c d e

8 a b c d e

9 a b c d e

10 a b c d e

11 a b c d e

12 a b c d e

13 a b c d e

14 a b c d e

15 a b c d e

16 a b c d e

17 a b c d e

18 a b c d e

19 a b c d e

20 a b c d e

21 a b c d e

22 a b c d e

23 a b c d e

24 a b c d e

25 a b c d e

26 a b c d e

27 a b c d e

28 a b c d e

29 a b c d e

30 a b c d e

31 a b c d e

32 a b c d e

33 a b c d e

34 a b c d e

35 a b c d e

36 a b c d e

37 a b c d e

38 a b c d e

39 a b c d e

40 a b c d e

ANSWER SHEET

1 Three times as many robins as cardinals visited a

bird feeder If a total of 20 robins and cardinals visited the feeder, how many were robins?

a 5

b 10

c 15

d 20

e 25

2 One of the factors of 4x2– 9 is

a (x + 3).

b (2x + 3).

c (4x – 3).

d (x – 3).

e (3x + 5).

3 In right triangle ABC, m∠C = 3y – 10, m∠B = y

+ 40, and m∠A = 90 What type of right triangle

is triangle ABC?

a scalene

b isosceles

c equilateral

d obtuse

e obscure

4 If x > 0, what is the expression (x)(2x) equivalent to?

a.2x

b 2x

c x22

d x2

e x – 2

– T H E S AT M AT H S E C T I O N –

1 5 1

REFERENCE SHEET

45˚

45˚

s

s

2s

¯¯¯¯¯3x

60˚

30˚

h

b

A =12bh

l

w h

l

A = πr2

C = 2πr

r

V = πr2h

h

Special Right Triangles

• The sum of the interior angles of a triangle is 180˚

• The measure of a straight angle is 180˚

• There are 360 degrees of arc in a circle



5 At a school fair, the spinner represented in the

accompanying diagram is spun twice

What is the probability that it will land in section

G the first time and then in section B the second

time?

a.12

b.14

c. 18

d.116

e. 38

6 If a and b are integers, which equation is always

true?

a.a b= a b

b a + 2b = b + 2a

c a – b = b – a

d a + b = b + a

e a – b

7 If x≠ 0, the expression x2+x2xis equivalent to

a x + 2.

b 2.

c 3x.

d 4.

e 5.

8 Given the statement: “If two sides of a triangle

are congruent, then the angles opposite these sides are congruent.”

Given the converse of the statement: “If two angles of a triangle are congruent, then the sides opposite these angles are congruent.”

What is true about this statement and its converse?

a Both the statement and its converse are true.

b Neither the statement nor its converse is true.

c The statement is true, but its converse is false.

d The statement is false, but its converse is true.

e There is not enough information given to

determine an answer

9 Which equation could represent the relationship

between the x and y values shown below?

x y

3 11

4 18

a y = x + 2

b y = x2+ 2

c y = x2

d y = 2 x

e y2

10 If bx – 2 = K, then x equals

a.K b+ 2

b.K b– 2

c. 2 –bK

d.K b+ 2

e k – 2.

B