LINEAR
QUADRATIC
SYSTEMS
GRAPHS
OTHERS
100
What value of x is the solution of the equation.
(3x-7)/5=x+1?
–6
100
Consider the function ƒ(x) = x2 + bx – 16,
where b is a constant. If the function has an
axis of symmetry at x = 5, what is the value of b?
–10
100
The functions ƒ and g are defined as follows.
ƒ(x) = –x + 2 and. g(x) = x2 – 1
The point (b, c) is on both the graph of ƒ and the graph of g in the xy-plane. Which of the following inequalities must be true?
A. b > 0 C. c > 0
B. b < 0 D. c < 0
C
100
The graph of y = ƒ(x) is shown in the xy-plane. Which equation defines function ƒ?
A
100
The value, V, of an investment is given by the function V(t), where t is the number of years since 1995 and V is measured in thousands of dollars. Which equation indicates that the investment had a value of $8,000 in 2005?
A. V(8) = 10 B. V(10) = 8
C. V(8,000) = 2005 D. V(2005) = 8,000
D
200
Samantha has $35 in her savings account. At the end of each week, she will add $20 to the account. Which equation describes the total amount S, in dollars, that Samantha will have in her account at the end of week w?
A. S = 15w C. S = 20 + 35w
B. S = 55w D. S = 35 + 20w
D
200
Choose the expressions that are equivalent to
x2 + 4x + 3. Select all that apply
A. (x + 2)2 – 1 C. (x – 1)(x – 3)
B. (x + 2)2 + 1 D. (x + 1)(x + 3)
E. (x – 1)(x + 4)
A, and D
200
A small company manufactures a certain item and sells it online. The company has a business model where the cost C, in dollars, to make x items is given by the equation C = 20/3x+50 and the revenue R, in dollars, made by selling x items is given by the equation R = 10x. The break-even point is the point where the cost and revenue intersect. How many items must the company sell to break even?
15
200
The graphs of ƒ(x) = –x3 – 4 and
g(x) = 0.5x2 + x + 4 are given. Use the graphs to
find the solution to the equation –x3 – 4 = 0.5x2 + x + 4.
(–2, 4)
200
A sequence is defined by
a1 = –5 + (n – 1)14, where n is a positive integer. What is the value of a10?
121
300
A student claims that if an equation has no exponente greater than 1, then the equation is linear. Which equation can be used to show that the student's claim is false?
A. y = x. C. x + y = 1
B. y = |x| D. y – x2 = 1
B
300
The equation x2 – 8x – 5 = 0 can be transformed into the equation
(x – p)2 = q, where p and q are real numbers.
What is the value of q?
21
300
A system of equation is given. y = 9x - 1 and
y = 2x + 3. What is the value of x in the solution
(x, y) to the system?
4/7
300
The graph of the function ƒ is given below. What function rule best describe the graph?
ƒ(x) = 2x – 3
300
The function ƒ is defined as
ƒ(x) = x(x2 – 4) – 3x(x – 2). An equivalent form of ƒ
is given as ƒ(x) = x(x – 2)(x – a), where a is a
constant. What is the value of a?
1
400
A student read a 303-page book in 7 days. The table shows the total number of pages the student had read at the end of each day for the 7 days. What was the average number of pages the student read per day from the end of day 2 to the end of day 6?
45. 5 pages
400
Which of the following expressions can be written as
(ax+ b)(ax – b), where a and b are integers?
Select ALL that apply.
A. x2 – 9 B. x2 – 11
C. 4x2 – 1 D. 4x2 – 2
E. 9x2 – 4
A, C, and E
400
The system of equations shown is graphed in the xy-plane. x + y = 1 and
2x – 3y = 17. Determine the coordinates of the solutions of the system
(4, –3)
400
A quadratic function ƒ(x) is graphed in the xy-coordinate plane. In which quadrant would the vertex of
ƒ(x + 3) + 2 be located?
quadrant 2
400
What are the zeros of the function
ƒ(x) = x(x2 – 4) – 3x(x – 2)?
0, 1 and 2
500
A student is saving money in a bank account to buy a computer. The function ƒ(w) = 35w + 10 represents the total amount of money, ƒ, in dollars, in the student's account w weeks after the student started saving for the computer. What does the number 10 in the function represent in the context?
The starting amount in the student's savings account.
500
Consider the function ƒ(x) = x2 + bx – 16,
where b is a constant. If b = –6,
what are the zero(s) of the function?
–2 and 8
500
The figure shows a graph of the function of ƒ(x) in the xy-coordinate plane, with the vertex at (1, 9) and the zeros at –2 and 4.
The function g is defined by g(x) = –3x + 2. Which statements are true? Select ALL that apply.
A. ƒ(–2)>g(–2) B. ƒ(–1)<g(–1) C. ƒ(0)>g(0)
D. ƒ(1)<g(1) E. ƒ(2)>g(2)
C and E
500
Two functions, ƒ and g, are graphed in the xy-plane shown.
In what interval(s) do the solutions of the equation ƒ(x) = g(x) exist?
between x = –1 and x = 0, and
between x = 4 and x = 5
500
The diagram represents a right rectangular prism with dimensions labeled as algebraic expressions.
Which of these expressions represents the volume of the prism? Select ALL that apply.
A. 7x D. 3x(4x2 – 25)
B. 4x2 – 25 E. (2x + 5)(6x2 – 15x)
C. 12x3 – 75x F. 12x3 + 60x2 + 75x
C, D and E