SAT Exam Review

Flashcards generated from the lecture notes to help you prepare for your upcoming exam. This set of flashcards are in question and answer format.

If line l intersects parallel lines j and k, and q = 10c+11 and r = 15c+41, what is the value of p?

p = 131

What is the estimated average change in rent associated with a $5,000 increase in income, based on the provided plot?

Approximately $200

What is the minimum value of the function f(x) = x² - 48x + 2304?

0

In the equation 42/x + (-7(px + q)) = 23/35, which has infinitely many solutions, and given p < 0, what is the value of q?

q = -9

How many distinct real solutions exist for the equation x² = -841?

Zero

In the equation 18x² - (18n - m)x - mn = 0, where m and n are positive constants, if the product of the solutions is kmn, what is the value of k?

k = -1/18

If x+3 is a factor of x²+kx+2k, where k is a constant, what is the value of k?

k = 6

In the linear function h, given h(28) = 15 and h(26) = 22, which equation defines h?

h(x) = -7/2x + 113

A softball equipment company made $26,000 from the sale of bats and gloves. If 500b + 300g = 26,000, how many dollars less is the sales price of each glove than each bat?

Each glove is $200 less than each bat.

If f(x) = ax² + bx + c passes through (7,0) and (-3,0), and a is an integer greater than 1, which of the following could be the value of a + b?

-3

If i = √-1, what is the value of (i + i² + i³) / (i⁴ + i⁵)?

-1

If 8x + 8y = 18 and x² - y² = 3/8, what is the value of 2x - 2y?

1/3

The equation 3x² - 36x + k = 0 has exactly two real solutions. If k is a constant and k < m, what is the least possible value of m?

m = 108

If 10/x = y/(y + 3x), what is the value of 3/y?

1/7

If 3x - 5y = 2, what is 8x/32y ?

8x/32y = 4

If the system of equations y = x² - 6x - c and y = 3.5 has exactly one real solution, and c is a negative constant, what is the value of c?

c = -5.5

A rectangular prism has a height of 50 cm and a square base. If dividing the prism parallel to the base results in each prism having a surface area of 31/56S, what is the side length of the square base?

6 cm

The expression (-3x⁴ + 13) + (-8x⁴ - 9) is equivalent to cx⁴ + 4. What is the value of c?

c = -11

In 2023, a streaming service decreased its movies by 9% from 2022. If movies in 2023 is m times the number in 2022, what is the value of m?

m = 0.91

Solve for x: 24 - √(x) = 49

x = No Solution

What system of linear equations is represented by the given lines?

8x+4y = 32 and -10x-4y = -64

Scott selected 20 employees at random from 400, and 16 are enrolled in exactly three professional development courses. Based on this, what is the estimated number of employees at the company enrolled in exactly three professional development courses?

320

Lisa gives Sam a 15-second head start. Sam runs 5 m/sec, Lisa runs 8 m/sec. How many seconds passed when Lisa caught up to Sam?

The number of seconds passed is 25.

In the figure shown, line b intersects parallel lines p and r. What is the value of d?

d = 32

The table shows the linear relationship between the number of cars, c, on a commuter train and the maximum number of passengers and crew, p. Which equation represents the linear relationship between c and p?

55c - p = -9

A square is inscribed in a circle. The radius of the circle is 20√2 / 2 inches. What is the side length, in inches, of the square?

20

If 4√2x = 16, what is the value of 6x?

72

A polygon has 75 sides. The measure of each of the 75 interior angles is (1-a) 180°. What value is a?

a = 64/75

Circle R is defined by the equation (x+3)² + y² = 64. If circle S is the result of shifting the graph of circle R to the right 7 units in the xy-plane, what is the equation of circle S?

(x-4)² + y² = 64

The amount, in micrograms, of a certain radioactive isotope h hours after its initial creation is modeled by the function M(h) = 302(0.87)^(h). According to the model, the amount of the isotope is predicted to decrease by d% every 75 minutes. What is the value of d?

d = 13

What is the sum of 1 + 2 + 3 + 4 + 5 + … + 50?

1275

The function g is defined by g(x) = x(x - 2)(x+6)². The value of g(7-w) is 0, where w is a constant. What is the sum of all possible values of w?

Sum of possible w values = 13

The maximum value of q is 14 more than 7 times the value of r. Which inequality represents the relationship between q and r?

q ≤ 7r + 14

A concrete block has a mass of 1,690 kg and dimensions 1.1 m x 0.8 m x 0.8 m. What is the density, in kg/m³, of the concrete block?

Approximately 2401

The number of zebras in a population in 2018 was 1.27 times the number of zebras in this population in 2014. If the number of zebras in this population in 2014 is p% of the number of zebras in this population in 2018, what is the value of p, to the nearest whole number?

p = 79%

A certain ant colony contains 96,000 ants. A disease infects the colony, causing the number of ants to decrease by one-half every 4 days. How many ants remained in the colony 20 days after the infection started?

3,000

Jennifer has 40% more stamps than Peter. However, if she gives 45 of her stamps to Peter, then Peter will have 10% more stamps than Jennifer. How many stamps did Jennifer begin with?

Jennifer began with 175 stamps.

The expression (11x² - kx + 63) can be rewritten as (px - q)(x - r), where p, q, and r are integer constants. Which of the following MUST be an integer?

63/p

Which equation has the same solution as the given equation 7(2x - 3) = 63?

2x - 3 = 9

The length of the edge of the base of a right square prism is 6 units. The volume of the prism is 2,880 cubic units. What is the height, in units, of the prism?

80

Which of the following is a solution to the given equation w² + 12w - 40 = 0?

w = -6+2√19

What is the minimum value of the given function f(x) = x² - 48x + 2304?

The minimum value is 0.

A website's unique visitors decreased by 25% to a previous average of 620. A new promotion is projected to increase visitors to 180% of the last quarter. What is the projected average number of unique visitors per day during its promotion?

Projected average is 837 unique visitors.

Simplify (27/64)^(-2/3)

16/9

In ΔRST, the measure of ∠R is 63°. Which of the following could be the measure, in degrees, of ∠S?

116

Given the function g(x) = -9/(x-d), which equation could define function h if h(x) = g(x-3)?

h(x) = -9/(x-3)

A circle with the equation x² - 4x + y² - 1 = 1 is graphed in the xy-plane. What is the length of the radius of this circle?

3

What is the y-intercept of the graph of y = 3^(x+2) in the xy-plane?

(0, 9)

Right triangle ABC is similar to triangle DEF, where A corresponds to D. AB = 42, BC=56, CA=70. What is the value of cos D?

cos D= 3/5

How many solutions does the given equation -49x = -98x have?

Infinitely many

Group X has 40 packages with a mean mass of 24 kg, and group Y has 110 packages with a mean mass of 9 kg. What is the mean mass of all 150 packages?

13 kg

If u + t = 5 and u - t = 2, what is the value of (u+t)(u² - t²)?

50

Given g(x) = (x + 14)(t - x). In the xy-plane, the graph of y = g(x) passes through the point (24, 0). What is the value of g(0)?

g(0) = 336

If s and t are positive, which of the following expressions is equivalent to √(s⁵t⁵)?

(st)^(5/2)

Which expression is equivalent to 5x⁵ - 6x⁴ + 8x³?

x³(5x² - 6x + 8)

The equation 5x + 3y = -8 represents line l. Line m is obtained by shifting line l up 2 units in the xy-plane. The x-intercept of the graph of line m is (a, b). What is the value of a?

a = -2/5

The nth term of a sequence is represented by sn, and each term after the first term is one-half of the preceding term. If the first term of the sequence is 56, which of the following equations expresses sn in terms of n?

s_n = 56(1/2)^(n-1)

The equation of a parabola is written in the form y = ax² + bx + c, where a, b, and c are constants. When graphed in the xy-plane, the parabola has vertex (-1, 4) and does not intersect the x-axis. Which of the following could be the value of a - b - c?

-5

If -6 < -4r + 10 ≤ 2, what is the least possible value of 4r + 3?

11

If a point (39, y) is a solution to the system x < 53 and x-7y < 16, which of the following could be the value of y?

4

What is a positive solution to the equation (x + 2)(x - 5)(x + 9) = 0?

5

Compare the means of data set S: 2, 3, 8, 8, 11, 24 and data set T: 3, 8, 8, 11, 24.

The mean of data set S is less than the mean of data set T.

What is the sum of the solutions of 2x² + 24x + 64 = 0?

-12

Circle A is defined by (x + 2)² + y² = 9. Circle B is the result of shifting circle A down 6 units and doubling the radius. Which equation defines circle B?

(x+2)^2 + (y+6)^2 = 36

Given the system of equations (x - 2) - 4(y+7) = 117 and (x-2) + 4(y+7) = 442, what is the value of 6(x-2)?

6(x-2) = 1677

The function f is defined by f(x) = x + (1/x). For what value of x does f(x) = 5?

x = (5 ± √21)/2

What is b?

b=3