New SAT Math (No Calculator) Practice Test 11
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In the xy-plane, the parabola with equation y = (x − 11)2 intersects the line with equation y = 25 at two points, A and B. What is the length of ?
10
12
14
16
kx – 3y = 4
4x – 5y = 7
In the system of equations above, k is a constant and x and y are variables. For what value of k will the system of equations have no solution?
−
−
The line y = kx + 4, where k is a constant, is graphed in the xy-plane. If the line contains the point (c, d), where c ≠ 0 and d ≠ 0, what is the slope of the line in terms of c and d ?
The function f is defined by a polynomial. Some values of x and f(x) are shown in the table above. Which of the following must be a factor of f(x) ?
x − 2
x − 3
x − 4
x − 5
2x − 3y = −14
3x − 2y = −6
If (x, y) is a solution to the system of equations above, what is the value of x − y ?
−20
−8
−4
8
If 5⁄x = , what is the value of x⁄5?
10
5
2
1⁄2
The number of states that joined the United States between 1776 and 1849 is twice the number of states that joined between 1850 and 1900. If 30 states joined the United States between 1776 and 1849 and x states joined between 1850 and 1900, which of the following equations is true?
30x = 2
2x = 30
x⁄2 = 30
x + 30 = 2
Which of the following is equal to a2⁄3, for all values of a ?
If 3r = 18, what is the value of 6r +3 ?
6
27
36
39
A painter will paint n walls with the same size and shape in a building using a specific brand of paint. The painter’s fee can be calculated by the expression nKℓh, where n is the number of walls, K is a constant with units of dollars per square foot, ℓ is the length of each wall in feet, and h is the height of each wall in feet. If the customer asks the painter to use a more expensive brand of paint, which of the factors in the expression would change?
h
l
K
n
In triangle ABC, the measure of ∠B is 90°, BC = 16, and AC = 20. Triangle DEF is similar to triangle ABC, where vertices D, E, and F correspond to vertices A, B, and C, respectively, and each side of triangle DEF is 1⁄3 the length of the corresponding side of triangle ABC. What is the value of sin F ?
At a lunch stand, each hamburger has 50 more calories than each order of fries. If 2 hamburgers and 3 orders of fries have a total of 1700 calories, how many calories does a hamburger have?
Two isosceles triangles are shown above. If 180 − z= 2y and y = 75, what is the value of x ?
If 7⁄9x − 4⁄9x = 1⁄4 + , what is the value of x ?
x3 (x2 − 5) = − 4x
If x > 0, what is one possible solution to the equation above?
C = 5⁄9(F − 32)
The equation above shows how a temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?
I. A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5⁄9 degree Celsius.
II. A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
III. A temperature increase of 5⁄9 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
I only
II only
III only
I and II only
What are the solutions to 3x2 + 12x + 6 = 0?
x = −2 ± √2
x = −2 ±
x = −6 ± √2
x = −6 ± 6√2
The equation is true for all values of x ≠ 2⁄a, where a is a constant. What is the value of a ?
−16
−3
3
16
y = a(x − 2)(x + 4)
In the quadratic equation above, a is a nonzero constant. The graph of the equation in the xy-plane is a parabola with vertex (c, d). Which of the following is equal to d ?
−9a
−8a
−5a
−2a
In the figure above, lines k, ℓ , and m intersect at a point. If x + y = u + w, which of the following must be true?
I. x = z
II. y = w
III. z = t
I and II only
I and III only
II and III only
I, II, and III
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