SAT Math Practice Quiz 1

If 2a+3=6 , then \dfrac{3}{4a+6} =

\dfrac{1}{4}
\dfrac{1}{2}
1
2
3

If 4^{2x+2}=64 , then x=

In terms of x , what is the average (arithmetic mean ) of 4x-2 , x+2 , 2x+3 , and x+1 ?

In the figure, the area of rectangle CDEF is twice the area of rectangle ABCF . If CD=2x+2 , what is the length of AE , in terms of x ?

2x=2
2x+4
3x+1
3x+2
3x+3

What is the least positive integer that is divisible by both 2 and 5 and leaves a remainder of 2 when it is divided by 7?

If 2y^2+x-4 = 0 , and \dfrac{x}{2}=y^2 , then x =

1
2
3
4
5

In the table, f(x) is a linear function. What is the value of k ?

\begin{array}{|l|l|} \hline x&f(x) \\ \hline 0&-4 \\ \hline 1&-1 \\ \hline 2&2 \\ \hline 3&k \\ \hline 4&8 \\ \hline \end{array}

2
3
4
5
6

If a laser printer can print x pages per minute, how many minutes, in terms of x , would it take the laser printer to print a 100-page document?

100x
100-x
100+x
\dfrac{x}{100}
\dfrac{100}{x}

Jackie use 30 percentage of her monthly earnings for rent and 50 percentage of the remaining amount for food and transportation. If she spends $525 for food and transportation, how much does she pay for rent?

$400
$450
$500
$550
$600

In the figure, if congruent right triangles ABD and DCA share leg AD , then \alpha =

90
100
110
120
130

If \dfrac{x+1}{2}+\dfrac{4x-1}{4}=5.5 , then x =

2.5
3.0
3.5
4.0
4.5

If a\downarrow b=\sqrt[b]{a} , 10 \downarrow 3 =

1.12
1.69
2.15
2.71
3.33

Which of the ordered pairs is the solution to the equations

\begin{cases} x+2y=5 & \\ x-2y=9 & \end{cases}

(-7,-1)
(-1,7)
(7,-1)
(-7,1)
(1,7)

What is the solution set for the equation |2x-3| = 13 ?

{-8}
{-5}
{-5,-8}
{-5,8}
{5,-8}

\dfrac{6!}{2!3!}=

1
6
15
30
60

The length of AC is 3 times the length of CD n the figure. If B is the midpoint of AC, and the length of CD is 5, what is the length of BD ?

10
12.5
13.5
15
17.5

Which of the following lines is parallel to y = -2x+3 and has a y-intercept of 4

y = -2x+4
y=-2x-4
y = 2x-4
y=2x+4
y = \dfrac{1}{2} x+4

What is the area of the quadrilateral ABCD in the figure?

32
33
34
35
36

If f(x)=x^2+x and g(x) = \sqrt{x} , then f(g(3)) =

1.73
3.46
4.73
7.34
12.00

At a certain software company, the cost, C , of developing and producing a computer software program is related to the number of copies produced, x , by the equation C= 30000+2x . The company's total revenues, R , are related to the number of copies produced, x , by the equation R=6x-10000 . How many copies must the company produce so that the total revenue is equal to the cost?

5000
6000
75000
9000
10000

If the two square shown in the figure are identical, what is the degree measure of angle ADE ?

120
135
150
165
175

Points A(\sqrt{2},4 ) , B(6,-\sqrt{3} ) , and C are collinear. If B is the midpoint of line segment AC , approximately what are the (x,y) coordinates of point C ?

(3.71,1.13)
(3.71,5.73)
(7.41,-7.46)
(10.59, -7.46)
(10.59, 5.73)

What is the solution set to the equation 4+x^2=2x^2-5 ?

\{x:x=3\}
\{x:x=-3\}
\{x:x=\pm3\}
\{x:x=-1\}
\{x:x=1\}

Which of the following triplets can be the length of the sides of a triangle?

2,3,5
1,4,2
7,4,4
5,6,12
9,20,8

In the figure, if \sin x = 0.500 , what is the approximate value of \tan x ?

0.577
0.707
1.000
1.155
2.000

In the figure, if line l has a slope of 1 and passes through th origin, which of the following points has (x,y) coordinates that \dfrac{x}{y}>1 ?

A
B
C
D
E

On a recent chemistry test, the average (arithmetic mean) score among 5 students was 83, where the loest and highest possible scores were 0 and 100, respectively. If the teacher decides to increase each student's score bt 2 points, and if none of the students originally scored more than 98, which of the following must be true?

I. After the scores are increased, the average score is 85.

II. When the scores are increased, the difference between the highest and lowest scores increases.

III. After the increase, all 5 scores are greater than or equal to 25.

1-2\sin^2 \theta -2\cos^2 \theta=

-2
-1
0
1
2

If a>b and c>d , which of the following must be true?

ac>bd
a+b>c+d
a+c>b+d
a-b>c-d
ad>bc

Stella leaves her house and starts driving due south 30 miles, then drives due west for 60 miles, and finally due north for 10 milesto reach her office.which of the following approximate straight-line distance, in miles, from her house to office?

63
67
71
75
80

If f(x)=x^2-1 , g(x)=(x-1)^{-1}, and x {=}\mathllap{/\,}1 , then f(x)g(x) =

2x+1
x+1
x-1
x^3-1
2x-1

Sarah is scheduling the first periods of her school day. She needs to fill those periods with calculus, art, literature, and physics, and eachof these courses is offered during each of the first four periods. How may different schedules can Sarah choose from?

1
4
12
24
120

If an empty rectangular water tank that has dimensions 100 centimeters, 20 centimeters is to be filled using a right cylindrical bucks with a base radius of 9 centimeters and a height of 20 centimeters, approximately how many buckets of water will it take to fill the tank?

14
16
18
20
22

In the triangle ACE , AE is parallel to BD , what is the approximate length of DE ?

2.33
2.67
3.33
3.67
6.67

If f(x)=\sqrt{x^2-4} , what is the domain?

All the real numbers
All x shch that x \geq 2
All x shch that x \leq -2
All x shch that -2 \leq x \leq 2
All x shch that x \leq -2 or x \geq 2

What is the area of a triangle with vertices (1,1), (3,1), and (5,7)?

6
7
9
10
12

Which of the following inequalities is equivalent to -2(x+5) < -4 ?

x>-3
x<-3
x>3
x<3
x >7

If i=\sqrt{-1} , for which of the following values of n does i^n+(-i)^n have a positive values?

23
24
25
26
27

The maximum value of the function f(x)=1-\cos x between 0 and 2\pi

0
1
1.5
2
2.5

In the figure, if y >60 and AB = BC, which of the following must be true?

I. \alpha +y>180\degree

II. y>z

III. \alpha=y+z

I only
II only
III only
I and II
II and III

If f(x)=\dfrac{1}{x} , and 0< x<1 , what is the range of f(x)?

All real numbers
All real numbers between 0 and 1
All real numbers greater than 0
All real numbers greater than 1
All real numbers greater than or equal to 1

To identical spheres of radius 6 intersect so that the distance between their centers is 10. The points of intersection of the two spheres form a circle. What is the area of this circle?

5\pi
6\pi
8\pi
10\pi
11\pi

If a remainder of 4 is obtained when x^3+2x^2-x-k is devided by x-2 , what is the value of k ?

4
6
10
12
14

Ms. Hobbes has a portfolio that includes $50,000 in stock, $75,000 in cash, and no other holdings. If she wishes to redistribute her holdings so that 80 percent of the portfolio is in cash, how many dollars of stock must she convert to cash?

10,000
15,000
20,000
25,000
30,000

A sphere of radius 5 has the same volume as a cube with an edge of approximately what length?

5.00
5.50
6.24
8.06
9.27

The equation of x^2=y^2 is represented by which of the following graphs?

A
B
C
D
E

If point A(3,5) is located on a circle in the coordinate plane, and the center of the circle is the origin, which of the following points lie outside this circle?

(1.0,6.0)
(1.5,5.5)
(2.5,4.5)
(4.0,4.0)
(5.0,3.0)

If f(x) = 3x-1, n represents the slope of the line with the equation y = f^{-1}(x), and p represents the slope of a line that is perpendicular to the line with the equation y=f(x), then np=

The parabola with the equation y=4x-\dfrac{1}{2}x^2 has how many points with (x,y) coordinates that are both positive integers?

3
4
7
8
Infinitely many

In the figure, each of the three circles is tangent to the other two, and each side of the equilateral triangle is tangent to two of the circles. If the length of one side of the triangle is x, what is the radius, in terms of x, of one of the circles?

\dfrac{x}{1+2\sqrt{3} }
\dfrac{x}{2+2\sqrt{3} }
\dfrac{x}{1+\sqrt{3} }
\dfrac{2x}{1+\sqrt{3} }
\dfrac{2x}{1+2\sqrt{3} }

Multiple Choice Question