SAT Math Practice Test — Section 1:  25 Minutes / 20 Questions

Notes:
1. The use of a calculator is permitted
2. All numbers used are real numbers
3. Figures that accompany problems in this test are intended to provide information useful in solving the problems. They are drawn as accurately as possible EXCEPT when it is stated in a specific problem that the figure is not drawn to scale. All figures 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.

1.  If 5y + 3 = 7y - 3, what is the value of y ?

2.  There are 14 apartments in a given apartment building. Each apartment contains at least 3 smoke detectors but not more than 5 smoke detectors. Which of the following could be the total number of smoke detectors in the entire apartment building?

3.  How much less than x + 4 is x - 5 ?

4.  For which of the following functions is
f(-2) > f(2) ?

	(A) f(x) = 5 - x2
	(B) f(x) = (5-x)2
	(C) f(x) = 5
	(D) f(x) =
	(E) f(x) = x4 - 5

5.  The average (arithmetic mean) of a, b, and c is 9 and a + b = 6. What is the value of c ?

6.  If of y is 72, what is of y ?

7.  If 6x = 7y and 7y = 4z, what does 2z equal in terms of x ?

	(A)
	(B)
	(C) 2x
	(D) 3x
	(E) 28x

8.  During a four hour sale, a clothing store sold one-half of its sale dresses in the first hour, one-fourth in the second hour, one-fifth in the third hour, and the remainining dresses in the fourth hour. If there were a total of 40 sale dresses, how many dresses did the store sell in the fourth hour?

101.101, 1001.1001, 10001.10001, 100001.100001, …

9.  The sequence above consists of decimal numbers containing only 1's and 0's. Each term after the first is formed by adding one more 0 between the 1's to the left of the decimal, and one more 0 between the 1's to the right of the decimal. How many digits are there in the 101st term?

10.  (x - 3)²  x² - 3 ; For what value of x is the statement above FALSE?

11.  The circle above has center O and diameter XY. The next smaller circle has diameter OY and center P, while the smallest circle has diameter PY and center Q. If the circumference of largest circle is
24, what is the length of radius QY ?

12.  In the xy-plane, the equation of line l is
y = 3x + 12. If line l crosses the x-axis at the
point with coordinates (a,b), what is the value
of a ?

13.  The total profit per day, in dollars, for a factory to produce x units of a certain toy is given by the function p(x) = 20x² - 10x - c, where c is a constant and x3. If 10 units were produced yesterday generating a profit of $1820, what is the value of c ?

14.  In the xy-plane, the equation of line m is
y = 3x + 2. If line n is the reflection of line m in the y-axis, what is the equation of line n ?

	(A) y = 3x - 2
	(B) y = -3x - 2
	(C) y = -3x + 2
	(D)
	(E)

15.  If p is the greatest prime factor of 34 and q is the greatest prime factor of 90, what is the greatest prime factor of the product pq ?

16.  If x, y, and z are positive consecutive even integers, where z>y>x, which of the following is equal to x + y + z ?

17.  If , what is y, in terms of z and x ?

	(A)
	(B)
	(C) 5(z-x)
	(D) 5(z-x) + 1
	(E) 5z - x + 1

18.  At a certain video arcade, a customer can buy d tokens for 1 dollar. After purchasing the first d tokens, each additional 1 dollar purchase of d tokens earns the customer y free tokens. For example, after buying 2d tokens, the customer earns y free tokens, after buying 3d tokens, the customer earns 2y free tokens, etc. Which of the following represents the total number of tokens received for x dollars?

	(A)
	(B)
	(C) d(x-1) + y
	(D) x(d+y)
	(E) xd + y(x-1)

19.  In the figure above, square ABCD is inscribed in the circle with center O. If ABCD has an area of 8, then the area of the circle is

	(A)
	(B)
	(C)
	(D)
	(E)

20.  The smallest integer in a set of consecutive even integers is -12. If the sum of these integers is 14, how many positive integers are in this set?