Module I: Math

SAT Practice Test 3

A right triangle has one leg that is 9 cm longer than the other, and the shorter leg is 14cm. If the hypotenuse can be written as 5, where n is an integer, what is the value of n?

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In the Cartesian coordinate system, Circle A is defined by (x−4)²+(y+3)²=9. Circle B shares the same center with Circle A and has a radius three times as large as that of Circle A. What is the equation of Circle B, written in the form (x−4)²+(y+3)²=k, where k is a constant?

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(x−4)²+(y+3)²=9

(x−4)²+(y+3)²=81

(x−4)²+(y+3)²=27

(x−4)²+(y+3)²=36

In a software company with 18 developers, the average number of years of experience is 7.5. After the team lead leaves, the new average experience of the team becomes 7 years. How many years of experience did the team lead have?

Answer:

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Preview:

Identify the equivalent form of the expression .

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x²+

In a factory, Machine A can produce w widgets and Machine B can produce z widgets. If they together produced 700 widgets, and Machine B produced 5 times as many widgets as Machine A, how many widgets did Machine A produce, to the nearest whole number?

Mark for Review

117

216

310

443

A shop offers bicycle rentals at 50 dollars for the first hour and 20 dollars for each subsequent hour. What is the total cost y, in dollars, of renting a bicycle for x hours?

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y=50+20x

y=20(x−1)−50

y=50+20(x−1)

y=20+50x

If the expression 16x²+cx+25 is equivalent to (mx+n)², where c,m,n are constants, which of m or n must be an integer?

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m only

n only

Both m and n

Neither m nor n

A nutritionist modeled the daily caloric intake C for a certain individual as a linear function of their weight W. The caloric intake was 2500 calories when the weight was 70 kg, and the caloric intake was 3000 calories when the weight was 90 kg. Based on the model, what is the daily caloric intake, in calories, when the weight is 85 kg?

Answer:

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Preview:

A cell phone company has a tiered pricing structure for its talk time. For the first 30 minutes, the company charges c₁=0.4t₁+10 dollars, where t₁ is the number of minutes up to 30. Beyond 30 minutes, the price per minute decreases, and the additional cost is calculated using the equation c₂=0.3(t₂−30) dollars, where t₂ is the total number of minutes used. If a customer uses the service for 40 minutes, what is the total charge?

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$25

$28

$30

$32

If a−b=5 and a+b=11, which value could a be?

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If , the value of y+5 is between which of the following pairs of values?

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−6 and −2

−1 and 1

1 and 5

6 and 10

Suppose k(x)=2x²+20x+5. We have another function n(x) defined as n(x)=k(x+3). What is the x value at which n(x) is minimized?

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x=−10

x=−8

x=3

x=12

If y=3x−2 and y=px−2, find the value of p for which the system has infinitely many solutions.

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−1/3

−3

In a bakery, there is a jar containing 7 chocolate chip cookies and 21 oatmeal cookies. If you draw two cookies consecutively without replacement, what is the probability that you will first draw an oatmeal cookie and then a chocolate chip cookie?

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Consider the function h(x)=5(3)^x . If j(x)=h(x−1), which of the following equations defines the function j?

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j(x)=5(3)^x⁻¹

j(x)=15(3)^x

j(x)=5(3)^x⁺¹

j(x)=35(3)^x⁻¹

The chart illustrates the correlation between the amount of books from Author X, `a`, and the amount of books from Author Y, `b`, that Daniel can buy. Which formula best describes this connection?

Mark for Review

y=8a+12

8a+12b=480

y=12a+8

12a+8b=480

The circle shown has center O. Angles a and b are subtended by the same arc and are a=60° and b=120° respectively. What are the measures of angles c and d?

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c=120°,d=60°

c=240°,d=120°

c=60°,d=120°

c=120°,d=120°

The quadratic equation can be re-expressed as (x−q)(x+q), with q being a positive constant. What is q?

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John saves p dollars per month in Account A and q dollars in Account B. He saves a total of 1000 dollars a month, and Account B's balance is four times Account A's balance. How much does he save in Account A?

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100

200

300

400

For the system of equations 2x+y=7 and x−3y=1, what is a possible value of x?

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The volume of a cube is 500,000 cubic cm. What is the surface area of the cube in square cm?

Mark for Review

37798

47604

63000

95198

Let h(x)=(x−3)(x+1)(x+5). The function j(x) is obtained by shifting h(x) upwards by 7 units. What is the value of j(−2)?

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Module I: Math

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The questions in this section address a number of important math skills.

Use of a calculator is permitted for all questions. A reference sheet, calculator, and these directions can be accessed throughout the test.

Unless otherwise indicated:

All variables and expressions represent real numbers.
Figures provided are drawn to scale.
All figures lie in a plane.
The domain of a given function f is the set of all real numbers x for which f(x) is a real number.

For multiple-choice questions, solve each problem and choose the correct answer from the choices provided. Each multiple-choice question has a single correct answer.

For student-produced response questions, solve each problem and enter your answer as described below:

If you find more than one correct answer, enter only one answer.
You can enter up to 5 characters for a positive answer and up to 6 characters (including the negative sign) for a negative answer.
If your answer is a fraction that doesn't fit in the provided space, enter the decimal equivalent.
If your answer is a decimal that doesn't fit in the provided space, enter it by truncating or rounding at the fourth digit.
If your answer is a mixed number (such as 3 1 2 ), enter it as an improper fraction ( 7 2 ) or its decimal equivalent (3.5).
Don't enter symbols such as a percent sign, comma, or dollar sign.

The questions in this section address a number of important math skills.

Use of a calculator is permitted for all questions. A reference sheet, calculator, and these directions can be accessed throughout the test.

Unless otherwise indicated:

All variables and expressions represent real numbers.
Figures provided are drawn to scale.
All figures lie in a plane.
The domain of a given function f is the set of all real numbers x for which f(x) is a real number.

For multiple-choice questions, solve each problem and choose the correct answer from the choices provided. Each multiple-choice question has a single correct answer.

For student-produced response questions, solve each problem and enter your answer as described below:

If you find more than one correct answer, enter only one answer.
You can enter up to 5 characters for a positive answer and up to 6 characters (including the negative sign) for a negative answer.
If your answer is a fraction that doesn't fit in the provided space, enter the decimal equivalent.
If your answer is a decimal that doesn't fit in the provided space, enter it by truncating or rounding at the fourth digit.
If your answer is a mixed number (such as 3 1 2 ), enter it as an improper fraction ( 7 2 ) or its decimal equivalent (3.5).
Don't enter symbols such as a percent sign, comma, or dollar sign.

Module I: Math

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Module I: Math

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Module I: Math

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