04_psat_2011_st_math

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Section 4 4 4 4 4

GO ON TO THE NEXT PAGE

--18-

If- x ! 0,-then- 1}

}24

x}

-=-

(A)-}21 x}

(B)- -}1

2}

(C)- }4

1

x}

(D)--}2

x}

(E)- -}4

x}

1

If- x-=- –52-+---4---3#-7,-then- x-=-

(A)--74

(B)--49

(C)- - -32

(D)-- -49

(E)- - -74

2

Time—25 Minutes

18 Questions

Directions: This section contains two types of questions. You have 25 minutes to complete

both types. For questions 1–8, solve each question and determine which of the choices given

is best. Fill in the corresponding oval on the answer sheet. You may use any available space

for scratchwork.

1. Calculator use is permitted.

2. All numbers used are real numbers.

3. Figures are provided for some problems. All figures are drawn to scale and lie in a plane UNLESS otherwise

indicated.

4. Unless otherwise specified, 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.

The sum of the measures, in degrees, of the angles of a triangle is 180.

The number of degrees of arc in a circle is 360.

A straight angle has a degree measure of 180.

A = π r2

C = 2π r

A = lw

A = bh1

2

V = lwhV = π r2h

h

w

h

hc 2 x

x

3 x

s

s

2 sa

b

rr

b

c2 = a2 + b2 Special Right Triangles

w60˚

45˚

45˚

30˚

N o t e s

R e f e r e n c e I n f o r m

a t i o n

l l

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Section 4 4 4 4 4


--19-

If-4n---15-=-17,-then-3n-+-9-=

(A)-- 0

(B)- - 8

(C)- 15(D)- 32

(E)- 33

3

The-ratio-of-27-to-15-is-equal-to-the-ratio-of-9-to-what-

number?

(A)-- 1

(B)- - 3

(C)- - 5(D)- 10

(E)- 12

4

What-number-decreased-by-4-equals-9-times-the-original-

number?

(A)--2

(B)--1

(C)-– }1

2}

(D)- }

1

2}

(E)- 1

5

Set- J -is-the-set-of-all-negative-odd-integers,-and-set- K -is-

the-set-of-all-negative-even-integers.-Which-of-the-

following-represents-the-union-of-these-sets?

(A)-All-integers

(B)- All-negative-integers(C)- All-negative-odd-integers

(D)-All-negative-even-integers

(E)- None-of-the-above

6

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Section 4 4 4 4 4


--20-

If-m-=-8,-what-is-the-value-of-m-2?-

(A)- -64

(B)--}6

1

4}

(C)- -}

1

8}

(D)- }

1

8}

(E)- }

6

1

4}

7 Exactly-}1

2}-yard-of-rope-is-needed-to-tie-up-a-certain

bag.-Which-of-the-following-lengths-of-rope-could-be-

used-to-tie-up-the-bag-with-the-least-amount-of-rope-

remaining?

(A)- }1

6}-yard

(B)- }4

5}-yard

(C)- }2

3}-yard

(D)- }1

4}-yard

(E)- }5

6}-yard

8

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If- x +-4 y-=-6-and- x =-2 y,-then-what-is-the-value-of- x ?9

Section 4 4 4 4 4


--21-

If-it-takes-Alice-8-hours-working-at-a-constant-rate-to-

complete-her-homework,-what-part-of-the-homework-is-

completed-in-6-hours?

10

Each of the remaining 10 questions requires you to solve the problem and enter your answer by marking the ovals in the specialgrid, as shown in the examples below. You may use any available space for scratchwork.

Directions:For Student-Produced Response questions 9–18, use the grids at the bottom of the answer sheet page on which you

have answered questions 1–8.

• It is recommended, though not required, that you write

your answer in the boxes at the top of the columns.

However, you will receive credit only for darkening

the ovals correctly.

• Grid only one answer to a question, even though some

problems have more than one correct answer.

• Darken no more than one oval in a column.

• No answers are negative.

• Mixed numbers cannot be gridded. For example: the

number 1 must be gridded as 1.25 or 5/4.

(If is gridded, it will be interpreted as

not )

1

4

11

4

11

4

You may start your answers in any column,space permitting. Columns not neededshould be left blank.

• Decimal Accuracy: Decimal answers must be entered

as accurately as possible. For example, if you obtain an

answer such as 0.1666. . ., you should record the result

as .166 or .167. Less accurate values such as .16 or

.17 are not acceptable.

Acceptable ways to grid = .1666. . .

Grid inresult.

Write answerin boxes.

Fractionline

Decimalpoint

Answer: 1.25 or or 5/4

,

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Section 4 4 4 4 4


--22-

Half-the-product-of-8-and-9-is-the-square-root-of-what-

number?

11

What-is-the-average-(arithmetic-mean)-of-1}

4-and-

1}

6?12

- - A- A

- +- B- A

- 1- B-8

If- A-and- B-represent-distinct-digits-in-the-correctly-worked-addition-problem-above,-what-is-the-value-of- A?

13

D

E A

C B

In-the-figure-above,- AB is-perpendicular-to- AE .-If-the-

measure-of-E BAD-is-53-degrees,-and-the-measure-of-

ECAE -is-73-degrees,-what-is-the-degree-measure-of-

ECAD?

14

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Section 4 4 4 4 4

--23-

X

Y

In-the-figure-above,- X -and-Y -are-the-centers-of-the-two-

circles.--If-each-circle-has-a-circumference-of-9r,-what-

is-the-perimeter-of-the-rectangle?

15

Nuala-baked-64-cookies-for-a-party.-After-each-party-

guest-ate-n-cookies,-9-cookies-were-left-uneaten.-If-

there-were-more-than-9-guests-at-the-party,-and-if-n-is-an-

integer-greater-than-1,-what-is-the-value-of-n ?

16

IF YOU FINISH BEFORE TIME IS CALLED, YOU MAY CHECK YOUR WORK ONTHIS SECTION ONLY. DO NOT TURN TO ANY OTHER SECTION IN THE TEST. STOP

Boxes-of-candy-were-sold-for-a-school-fundraiser.-

Small-boxes-cost-$2-each-and-large-boxes-cost-$5-each.-

If-150-of-these-boxes-were-sold-for-a-total-of-$444,-how-

many-large-boxes-were-sold?

17

What-is-the-maximum-possible-area-of-a-rectangle-with-

a-perimeter-of-14-?

18

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04_psat_2011_st_math

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