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Section A: Non-Calculator (40 Points)

Instructions: Answer all questions in this section without the use of a calculator. Show all your work for free-response questions to receive full credit.

Solve for $x$ : $3x - 7 = 14$

(2 Points)

Select one option

$x = 3$

$x = 7$

$x = \frac{7}{3}$

$x = \frac{14}{3}$

Simplify the expression: $(x^4)(x^2)$

(2 Points)

Select one option

$x^6$

$x^8$

$2x^6$

$x^{16}$

If $f(x) = 2x + 5$ , what is $f(-3)$ ?

(2 Points)

Select one option

$-1$

$1$

$11$

$2$

Simplify: $(4x^2 - 3x + 1) + (x^2 + 5x - 2)$

(2 Points)

Select one option

$5x^2 + 2x - 1$

$5x^2 - 8x - 1$

$3x^2 + 2x - 1$

$5x^2 + 2x + 3$

What is the slope of the line represented by the equation $y = -3x + 4$ ?

(2 Points)

Select one option

$-3$

$4$

$\frac{1}{3}$

$-4$

Simplify: $5(2x - 3) - 4x$

(2 Points)

Select one option

$6x - 15$

$6x - 3$

$10x - 15 - 4x$

$14x - 15$

Which expression is equivalent to $(a^3 b^2)^3$ ?

(2 Points)

Select one option

$a^6 b^5$

$a^9 b^6$

$a^6 b^6$

$a^9 b^5$

Consider the system of equations: $y = x + 3$ and $y = -2x$ . What is the solution to this system?

(2 Points)

Select one option

$(1, 4)$

$(-1, 2)$

$(-3, 0)$

$(0, 3)$

10.

Solve for $x$ : $2(x - 4) + 5 = 3x - 1$

(5 Points)

11.

Simplify the expression: $\frac{12x^5 y^{-2}}{3x^2 y^3}$

(5 Points)

12.

Multiply and simplify: $(x - 5)(2x + 3)$

(6 Points)

13.

Solve the following system of equations using substitution or elimination: $2x + y = 7$ $x - y = 2$

(8 Points)

14.

Section B: Calculator Allowed (60 Points)

Instructions: Answer all questions in this section. You may use a calculator. Show all your work for free-response questions to receive full credit.

15.

A quadratic equation has a discriminant of $25$ . Which statement is true about its solutions?

(2 Points)

Select one option

It has no real solutions.

It has one real solution.

It has two distinct real solutions.

It has two complex solutions.

16.

Which of the following points is a solution to the inequality $y < -2x + 1$ ?

(2 Points)

Select one option

$(0, 2)$

$(-1, 3)$

$(1, -2)$

$(-2, 5)$

17.

A population of bacteria doubles every hour. If the initial population is $100$ , which equation models the population $P$ after $t$ hours?

(2 Points)

Select one option

$P = 100 + 2t$

$P = 100(2)^t$

$P = 2(100)^t$

$P = 100t^2$

18.

What is the equation of the axis of symmetry for the quadratic function $y = x^2 - 6x + 5$ ?

(2 Points)

Select one option

$x = -3$

$x = 3$

$y = 3$

$x = -6$

19.

The sum of two numbers is $20$ . Their difference is $4$ . Let $x$ and $y$ be the two numbers. Which system of equations represents this situation?

(2 Points)

Select one option

$x + y = 20$ \n $x + y = 4$

$x + y = 20$ \n $x - y = 4$

$x - y = 20$ \n $x + y = 4$

$xy = 20$ \n $x/y = 4$

20.

A function is graphed on a coordinate plane. If the graph extends infinitely to the left and right, and its lowest point is at $y = -5$ , what is the range of the function?

(2 Points)

Select one option

All real numbers

$y \ge -5$

$x \ge -5$

$y \le -5$

21.

A line passes through the points $(0, 2)$ and $(3, 8)$ . What is the equation of the line in slope-intercept form?

(2 Points)

Select one option

$y = 2x + 2$

$y = 3x + 2$

$y = \frac{1}{2}x + 2$

$y = 2x - 2$

22.

What are the solutions to the equation $x^2 + x - 12 = 0$ ?

(2 Points)

Select one option

$x = 3, x = 4$

$x = -3, x = 4$

$x = 3, x = -4$

$x = -3, x = -4$

23.

The cost $C$ (in dollars) of producing $n$ items is given by the equation $C = 5n + 50$ . What does the $50$ represent in this equation?

(2 Points)

Select one option

The cost per item

The number of items produced

The fixed cost of production

The total cost

24.

A car depreciates at a rate of $15\%$ per year. If its initial value is $20,000$ , what will its value be after $1$ year?

(2 Points)

Select one option

$3,000

$17,000

$23,000

$15,000

Coordinate Plane for Question 25

25.

Graph the linear equation $y = -\frac{2}{3}x + 4$ on the coordinate plane below. Label at least two points on the line.

(8 Points)

26.

Solve the quadratic equation $2x^2 + 5x - 3 = 0$ using the quadratic formula. Show all your work.

(8 Points)

27.

A local theater sold $250$ tickets for a total of $2200$ . Adult tickets cost $10$ each and student tickets cost $6$ each. How many adult tickets and how many student tickets were sold? Show all your work.

(8 Points)

Coordinate Plane for Question 28

28.

Consider the quadratic function $y = x^2 - 4x + 3$ . a) Find the vertex of the parabola. b) Find the equation of the axis of symmetry. c) Find the $y$ -intercept. d) Find the $x$ -intercepts (roots). e) Graph the parabola on the coordinate plane below, clearly labeling the vertex and intercepts.

(8 Points)

29.

A certain type of radioactive material decays at a rate of $8\%$ per hour. If you start with $500$ grams of the material, how much will be left after $3$ hours? Round your answer to two decimal places.

(8 Points)