Quiz about SAT - Category 1 Heart of Algebra

Question 1

If a = b = - 1, what is the value of (a - b)(a + b)?

Accepted Answer

0

Answer

-1

Answer

1

Answer

2

Question 2

If x = 10², what is the value of (4 + x)(4 - x)(1/x)?

Accepted Answer

-99.84

Answer

168.1

Answer

-159

Answer

152

Question 3

If a = 3, b = - 5, and c = 3, what is the value of (a + b)^c?

Accepted Answer

-8

Answer

5

Answer

8

Answer

-6

Question 4

A quality control inspector took a sample of x items from a production line and found that d of the items were defective. Which of the following could be the expression for the fraction of the sample that was not defective?

Accepted Answer

(x - d)/x

Answer

d/x

Answer

(x - d)/d

Answer

(d - x)x

Question 5

When twice the sum of - 4x + 6 and 6x - 4 is subtractd from 8x + 6, the result is

Accepted Answer

4x + 2

Answer

12x + 10

Answer

-4x - 2

Answer

4x + 8

Question 6

During its second year of operation, the Coastal Construction Company produced 3000 more units of affordable housing that it produced in its first year, when it produced c units. The company earns a profit of p dollars for each unit produced. Which of the following represents the total profit made by the Coastal Construction Company in its first two years?

Accepted Answer

(3000 +2c)p dollars

Answer

3000p dollars

Answer

6000p dollars

Answer

(6000 - c)p dollars

Question 7

If 3/x - 2 = 2/x, what is the value of x?

Accepted Answer

1/2

Answer

-5/2

Answer

-1/2

Answer

5/2

Question 8

If 5x + 3 = 23, then x - 1/2 =

Accepted Answer

3.5

Answer

4

Answer

4.5

Answer

7

Question 9

If 3x - 7 = 5, then 9x - 21 =

Accepted Answer

15

Answer

3

Answer

4

Answer

10

Question 10

For what value of x is 2(x + 3) + 4x equal to 3(2x + 1)?

Accepted Answer

No such value exists

Answer

Inifinately many values exist

Answer

2

Answer

0

Question 11

Given (x + 3)/2 + 2x = 3/2 - (x - 27)/5, what is the value of x?

Accepted Answer

2

Answer

3/2

Answer

-2

Answer

1

Question 12

If k + m² = k + n², then what is the value of m?

Accepted Answer

n or -n

Answer

n only

Answer

-n only

Answer

0

Question 13

If D - m = mrx, then m =

Accepted Answer

D/(1 + rx)

Answer

(rx)/D

Answer

D/(rx)

Answer

D/(2rx)

Question 14

Solve for x: 1/a - 1/x = 1/b

Accepted Answer

(ab)/(b - a)

Answer

a - b

Answer

(b - a)/(ab)

Answer

(-ab)/(b - a)

Question 15

If |121 - g| = 6, what is on possible value of (g + 1)/2?

Accepted Answer

58

Answer

63

Answer

60

Answer

56

Question 16

Solve for x: 2x - |x + 2| = 11

Accepted Answer

13

Answer

-3

Answer

-3 and 13

Answer

3 and 13

Question 17

If - 2x > - x + 10, which of the following numbers is not a solution?

Accepted Answer

-5

Answer

-24

Answer

-22

Answer

-12

Question 18

Let a and b be positive integers. If a > b, which of the following expression(s) must be true?

I. a² > b²

II. a - b < 0

III. - 2a > - 2b

Accepted Answer

I only

Answer

None

Answer

I and II only

Answer

III only

Question 19

Pili is shipping boxes of chocolate to her customers. Each box of chocolate weighs 6.2 ounces, and the shipping box weights 10.5 ounces. Pili will pay $4.95 in shipping costs if the total weight of her package is 36 ounces or less. What is the maximum number of boxes of chocolate Pili can ship in one box without going over the weight limit?

Accepted Answer

4

Answer

6

Answer

8

Answer

10

Question 20

Which of the following is equivalent to |x - 7| < 5

Accepted Answer

2 < x < 12

Answer

x < 12

Answer

x < - 2 or x > 12

Answer

-12 < x < 2

Question 21

Which of the following is equivalent to |8 - 6m| > 4

Accepted Answer

m < 2/3 or m > 2

Answer

m > 2/3 or m > 2

Answer

m < 2 or m > 2/3

Answer

-2/3 < m < 2

Question 22

A local fitness club charges a $50 sign-up fee and then $25 per month. Express the cost of using the fitness club as a function of m, where m represents the number of months the member participates.

Accepted Answer

f(m) = 50 + 25m

Answer

f(m) = 25 + 50m

Answer

f(m) = 75

Answer

f(m) = 25m - 50

Question 23

If f(x) = 2x + 3, for what value of a is it true that 3f(a) = f(4a)?

Accepted Answer

3

Answer

1.5

Answer

2

Answer

4.5

Question 24

A newly released song had an original rating of 23 points on a musical survey chart. Each week after the song was released, its rating fell by the same number of points such that the equation that represents the song's point rating during any given week is h(w) = 23 - 2w, where w is the number of weeks since the song's release. Which of the following is the best interpretation of the term -2w?

Accepted Answer

The song's point rating fell by 2 points every week after it was released

Answer

The point rating for the song increased by 2 points every week after it was released

Answer

The song had a point rating of - 2 three weeks after it was released

Answer

Not very many people liked the song 5 weeks after it was released

Question 25

If g(x) = (1/3)x + 16, what is the value of x when g(x) = 19?

Accepted Answer

9

Answer

6

Answer

7

Answer

8

Question 26

Which of the following represents a line that is perpendicular to the line with equation y = - 2x + 5?

Accepted Answer

2y - x = 12

Answer

y = - 2x + 9

Answer

2y - (1/2)x = 6

Answer

2x + 2y = 12

Question 27

A line in the xy-plane passes through the origin and has slope m = 1/4. Which of the following points lies on the line?

Accepted Answer

(4, 1)

Answer

(0, 4)

Answer

(1, 4)

Answer

(8, 3)

Question 28

Line p in the xy-plane contains points from each of quadrants I, III, and IV, but no points from quadrant II. Which of the following must be true?

Accepted Answer

The slope of line p is positive

Answer

The slope of line p is undefined

Answer

The slope of line p is negative

Answer

The slope of line p is 0.

Question 29

The graph o a line in the xy-plane has slope m = - 1/2 and contains the point (0, 5). The graph of a second line in the same coordinate plane passes through the points (1, - 3) and (2, - 1). If the two lines intersect at the point (a, b), what is the value of a + b?

Accepted Answer

7

Answer

4

Answer

5.5

Answer

1

Question 30

In the system of equations below, a and b are constants. If the system has infinitely many solutions, what is the value of ab?

ax + by = 6

6x + 9y = 18

Accepted Answer

6

Answer

54

Answer

-6

Answer

1/6

Question 31

Alannis has twelve pieces of U.S. paper currency that is a mixture of tens and twenties. In total she has $200 in value. how may of each bill does she have?

Accepted Answer

4 tens and 8 twenties

Answer

6 tens and 6 twenties

Answer

7 tens and 5 twenties

Answer

8 tens and 4 twenties

Question 32

In the system of linear equations, c and d are constants. If the system has infinitely many solutions, what is the value of d/c?

3x + 12y = 18

cx + dy = 6

Accepted Answer

4

Answer

1/4

Answer

2

Answer

1

Question 33

A group of families is going to see a movie. The adult tickets cost $13.75 each and the children's tickets cost $9.50 each. If the total cost of the movie tickets was $161.75 for 13 people, how many adults were in the group?

Accepted Answer

9

Answer

4

Answer

13

Answer

5

Question 34

In a freshwater lake, the increase in water pressure varies directly with the increase in water depth. If a scuba diver feels 21.65 pounds per square inch of pressure at a depth of 50 feet, how deep is he when the pressure is 38.97 pounds per square inch?

Accepted Answer

90 feet

Answer

48.9 feet

Answer

65 feet

Answer

100 feet

Question 35

The number of days needed to complete a job varies inversely with the number of people working on the job if all the people work at the same rate. If 15 people can dig a trench in 3 days, how fast can 9 people dig the same-sized trench?

Accepted Answer

5

Answer

45

Answer

9

Answer

3

Question 36

If a varies inversely as the square of b and directly as c, and a = 4 when b = 4 and c = 8, then what is the value of a when c = 18 and b = 6?

Accepted Answer

4

Answer

2

Answer

6

Answer

8

Question 37

What is the product of the coordinates of the midpoint of the line segment with endpoints (1, 3) and (- 5, - 4)?

Accepted Answer

1

Answer

-1

Answer

2

Answer

-2

Question 38

What is the slope of the line segment with endpoints (1, 3) and (- 5, - 4)?

Accepted Answer

7/6

Answer

6/7

Answer

-7/6

Answer

-6/7

Question 39

Suppose that a line segment has endpoints A(1, 3) and B(x, y). If the midpoint M has coordinates of (x + 3A, y + 2A), what are the coordinates of B?

Accepted Answer

(13, 11)

Answer

(4, 9)

Answer

(9, 17)

Answer

(7, 15)

Question 40

Which of the following is the equation of the line that is perpendicular through the midpoint to the segment with endpoints (10, 2) and (- 6, - 8)

Accepted Answer

5y = - 8x + 1

Answer

8y = 5x + 1

Answer

8x - 5y = 1

Answer

1 = 8x + 5y

Question 41

The graph displays the total cost, T, in dollars, of renting a bicycle for h hours. What does the T-intercept represent in the graph?

Accepted Answer

The initial cost of renting the bicycle

Answer

The total number of bicycles rented on any given day.

Answer

The average number of hours a person rents a bicycle.

Answer

The increase in the cost to rent the bicycle per hour of rental.

Question 42

The graph displays the total cost, T, in dollars, of renting a bicycle for h hours. Which of the following represents the relationship between T and h?

Accepted Answer

T = 2.50h + 8

Answer

h = 5T

Answer

T = (5/8)h + 8

Answer

h = (8/5)T + 8

Question 43

Which of the following graphs shows a one-to-one function?

Accepted Answer

Option D is correct

Answer

A.

Answer

B.

Answer

C.

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