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WorksheetsSAT - Category 1 Heart of Algebra
Total questions: 50
Worksheet time: 25mins
If a = b = - 1, what is the value of (a - b)(a + b)?
-1
0
1
2
If x = 102, what is the value of (4 + x)(4 - x)(1/x)?
168.1
-99.84
-159
152
If a/b = k and ab ≠ 0, then (a + b)/a is equal to
k/(k + 1)
(k + 1)/(k - 1)
(k + 1)/k
k + 1
If a = 3, b = - 5, and c = 3, what is the value of (a + b)c?
5
8
-6
-8
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?
d/x
(x - d)/d
(x - d)/x
(d - x)x
When twice the sum of - 4x + 6 and 6x - 4 is subtractd from 8x + 6, the result is
12x + 10
-4x - 2
4x + 2
4x + 8
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?
3000p dollars
6000p dollars
(3000 +2c)p dollars
(6000 - c)p dollars
If 3/x - 2 = 2/x, what is the value of x?
-5/2
-1/2
1/2
5/2
If 5x + 3 = 23, then x - 1/2 =
3.5
4
4.5
7
If 3x - 7 = 5, then 9x - 21 =
3
4
10
15
For what value of x is 2(x + 3) + 4x equal to 3(2x + 1)?
Inifinately many values exist
No such value exists
2
0
Given (x + 3)/2 + 2x = 3/2 - (x - 27)/5, what is the value of x?
2
3/2
-2
1
If k + m2 = k + n2, then what is the value of m?
n only
-n only
n or -n
0
If D - m = mrx, then m =
(rx)/D
D/(rx)
D/(2rx)
D/(1 + rx)
Solve for x: 1/a - 1/x = 1/b
a - b
(ab)/(b - a)
(b - a)/(ab)
(-ab)/(b - a)
If |121 - g| = 6, what is on possible value of (g + 1)/2?
58
63
60
56
Solve for x: 2x - |x + 2| = 11
-3
13
-3 and 13
3 and 13
If - 2x > - x + 10, which of the following numbers is not a solution?
-24
-22
-12
-5
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
None
I only
I and II only
III only
If - 17 ≤ 3a - 5 < 16, what is the greatest possible integer value of 2a + 3?
16
-1
15
0
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?
6
4
8
10
Which of the following is equivalent to |x - 7| < 5
x < 12
2 < x < 12
x < - 2 or x > 12
-12 < x < 2
Which of the following is equivalent to |8 - 6m| > 4
m < 2/3 or m > 2
m > 2/3 or m > 2
m < 2 or m > 2/3
-2/3 < m < 2
The design for various city sewer pipes allows for pipes of diameter d, ranging from 24 to 32 inches. Any pipes more or less than these diameters are rejected. Which of the following represents the correct inequality by which a pipe is judged to be acceptable?
|d - 28| ≤ 4
|d - 4| ≤ 28
|d + 4| ≤ 32
|d + 24| ≤ 32
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.
f(m) = 25 + 50m
f(m) = 50 + 25m
f(m) = 75
f(m) = 25m - 50
If f(x) = 2x + 3, for what value of a is it true that 3f(a) = f(4a)?
1.5
2
3
4.5
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?
The song's point rating fell by 2 points every week after it was released
The point rating for the song increased by 2 points every week after it was released
The song had a point rating of - 2 three weeks after it was released
Not very many people liked the song 5 weeks after it was released
If g(x) = (1/3)x + 16, what is the value of x when g(x) = 19?
6
7
8
9
The line y = mx + 10, where m is a constant, is graphed in the xy-plane. If the line contains the point (a, b), where a ≠ 0 and b ≠ 0, what is the slope of the line in terms of a and b?
(b + 10/a
(b - 10)/a
(a - b)/10
(a + 10)/b
Which of the following represents a line that is perpendicular to the line with equation y = - 2x + 5?
2y - x = 12
y = - 2x + 9
2y - (1/2)x = 6
2x + 2y = 12
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?
(0, 4)
(1, 4)
(4, 1)
(8, 3)
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?
The slope of line p is undefined
The slope of line p is positive
The slope of line p is negative
The slope of line p is 0.
The graph of a linear function f has intercepts at (c, 0) and (0, d) in the xy-plane. If c + d = 0 and c ≠ d, which of the following is true about the slope of the graph of f?
It is positive
It equals 0
It is undefined
It is negative
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?
4
5.5
1
7
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
54
6
-6
1/6
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?
4 tens and 8 twenties
6 tens and 6 twenties
7 tens and 5 twenties
8 tens and 4 twenties
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
1/4
4
2
1
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?
4
13
9
5
Graphite tennis racquets can be bought for $150 and aluminum tennis racquets for $100. The specialty store Point-Set-Match wants to order no more than $900 worth of tennis racquets, and plans to order more aluminum racquets than graphite ones. Which of the following systems of inequalities can represent the possible combinations of graphite racquets (x) and aluminum racquets (y) that can be ordered?
y > x
150x + 100y < 900
y > x
150x + 100y ≤ 900
y < x
150x + 100y ≥ 900
y ≥ x
150x + 100y ≤ 900
In the system of inequalities y ≥ 2x + 1 and y ≤ 2x are graphed in the xy-plane, which quadrant contains no solutions to the system?
Quadrant I
Quadrant II
There are solutions in all four quadrants
There are no solutions in any of the four quadrants
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?
48.9 feet
65 feet
90 feet
100 feet
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?
45
5
9
3
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?
2
4
6
8
What is the product of the coordinates of the midpoint of the line segment with endpoints (1, 3) and (- 5, - 4)?
1
-1
2
-2
What is the slope of the line segment with endpoints (1, 3) and (- 5, - 4)?
7/6
6/7
-7/6
-6/7
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?
(4, 9)
(13, 11)
(9, 17)
(7, 15)
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)
8y = 5x + 1
8x - 5y = 1
5y = - 8x + 1
1 = 8x + 5y
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?
The initial cost of renting the bicycle
The total number of bicycles rented on any given day.
The average number of hours a person rents a bicycle.
The increase in the cost to rent the bicycle per hour of rental.
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?
h = 5T
T = 2.50h + 8
T = (5/8)h + 8
h = (8/5)T + 8
Which of the following graphs shows a one-to-one function?
