SAT math questions

A business owner plans to purchase the same model of chair for each of the 81 employees. The total budget to spend on these chairs is $14,000, which includes a 7% sales tax. Which of the following is closest to the maximum possible price per chair, before sales tax, the business owner could pay based on this budget?

$161.53

When the quadratic function f is graphed in the xy-plane, where y=f(x), its vertex is (-3,6). One of the x-intercepts of this graph is (-174,0). What is the other x-intercept of the graph?

(-7/4,0)

In the xy-plane, a parabola has vertex (9,-14) and intersects the x-axis at two points. If the equation of the parabola is written in the form y=ax^2+bx+c, where a, b, and c are constants, which of the following could be the value of a+b+c?

-12

2(kx-n)=-28/15x-36/19 In the given equation, k and n are constants and n>1. The equation has no solution. What is the value of k?

-14/15

y>14 4x+y<18 The point (X,53) is a solution to the system of inequalities in the xy-plane. Which of the following could be the value of X?

-9

64x^2+bx+25=0 In the given equation, b is a constant. For which of the following values of b will the equation have more than one real solution?

-91

The population of City A increased by 7% from 2015 to 2016. If the 2016 population is K times the 2015 population, what is the value of K?

1.07

57x^2+(57b+a)x+ab=0 In the given equation, a and b are positive constants. The product of the solutions to the given equation is kab, where k is a constant. What is the value of k?

1/57

Line p is defined by 2y+18x=9. Line r is perpendicular to line p in the xy-plane. What is the slope of line r?

1/9

In triangle JKL, cosK=24/51 and angle J is a right angle. What is the value of cosL?

15/17

Circle A in the xy-plane has the equation (x+5)^2+(y-5)^2=4. Circle B has the same center as circle A. The radius of circle B is two times the radius of circle A. The equation defining circle B in the xy-plane is (x+5)^2+(y-5)^2=k, where k is a constant. What is the value of k?

16

A gift shop buys souvenirs at a wholesale price of 7.00 dollars each and resells them each at a retail price that is 290% of the wholesale price. At the end of the season, any remaining souvenirs are marked at a discounted price that is 80% off the retail price. What is the discounted price of each remaining souvenir, in dollars?

203/50

In the xy-plane, line ℓ passes through the point (0,0) and is parallel to the line represented by the equation y=8x+2. If line ℓ also passes through the point (3,d), what is the value of d?

24

Square X has a side length of 12 centimeters. The perimeter of square Y is 2 times the perimeter of square X. What is the length, in centimeters, of one side of square Y?

24

x^2-34x+c=0 In the given equation, c is a constant. The equation has no real solutions if c>n. What is the least possible value of n?

289

y=-1.5 y=x^2+8x+a In the given system of equations, a is a positive constant. The system has exactly one distinct real solution. What is the value of a?

29/2

The function f is defined by f(x)=x+15/5, and f(a)=10, where a is a constant. What is the value of a?

35

Data set A consists of the heights of 75 buildings and has a mean of 32 meters. Data set B consists of the heights of 50 buildings and has a mean of 62 meters. Data set C consists of the heights of the 125 buildings from data sets A and B. What is the mean, in meters, of data set C?

44

The expression 4x^2+bx-45, where b is a constant, can be rewritten as (ℎx+k)(x+j), where ℎ, k, and j are integer constants. Which of the following must be an integer?

45/h

A certain apprentice has enrolled in 85 hours of training courses. The equation 10x+15y=85 represents this situation, where X is the number of on-site training courses and Y is the number of online training courses this apprentice has enrolled in. How many more hours does each online training course take than each on-site training course?

5

Data set A consists of 10 positive integers less than 60. The list shown gives 9 of the integers from data set A. 43, 45, 44, 43, 38, 39, 40, 46, 40 The mean of these 9 integers is 42. If the mean of data set A is an integer that is greater than 42, what is the value of the largest integer from data set A?

52

An isosceles right triangle has a hypotenuse of length 58 inches. What is the perimeter, in inches, of this triangle?

58 +58√2

A sample of oak has a density of 807 kilograms per cubic meter. The sample is in the shape of a cube, where each edge has a length of 0.90 meters. To the nearest whole number, what is the mass, in kilograms, of this sample?

588

The graph of 9x-10y=19 is translated down 4 units in the xy-plane. What is the x-coordinate of the x-intercept of the resulting graph?

59/9

4x-6y+10y+2 ty=1/2+2x In the given system of equations, t is a constant. If the system has no solution, what is the value of t?

8

Two identical rectangular prisms each have a height of 90 centimeters cm. The base of each prism is a square, and the surface area of each prism is K cm2. If the prisms are glued together along a square base, the resulting prism has a surface area of 92/47 Kcm2. What is the side length, in cm, of each square base?

8

The first term of a sequence is 9. Each term after the first is 4 times the preceding term. If W represents the nth term of the sequence, which equation gives W in terms of N?

9(4^n-1)

Bacteria are growing in a liquid growth medium. There were 300,000 cells per milliliter during an initial observation. The number of cells per milliliter doubles every 3 hours. How many cells per milliliter will there be 15 hours after the initial observation?

9,600,000

In triangles LMN and RST, angles L and R each have measure 60°, LN=10, and RT=30. Which additional piece of information is sufficient to prove that triangle LMN is similar to triangle RST?

The measures of angles M and T are 70° and 50°, respectively.

The minimum value of X is 12 less than 6 times another number N. Which inequality shows the possible values of X?

X ≥6n-12

For groups of 25 or more people, a museum charges $21 per person for the first 25 people and $14 for each additional person. Which function f gives the total charge, in dollars, for a tour group with n people, where n≥25?

f(n)=14n+175