Florida Algebra 1 End-of-Course Assessment Item Bank, Polk County School District

Transcription

1 Benchmark: MA.912.A.2.3; Describe the concept of a function, use function notation, determine whether a given relation is a function, and link equations to functions. Also assesses MA.912.A.2.13; Solve real-world problems involving relations and functions. Problem 1: Problem 2:

2 Problem 3: What equation models the data in the table if d = number of days and c = cost? Days Cost A. d = 22c B. c = 22d C. c = d + 22d D. c = d + 22 Problem 4: You can use the formula to convert temperature in degrees Fahrenheit, F, to temperature in degrees Celsius, C. What is 62 F in degrees Celsius? Round your answer to the nearest tenth. A. 30 degrees Celsius B degrees Celsius C degrees Celsius D. 2.4 degrees Celsius Problem 5: If

3 Benchmark: MA.912.A.2.4; Determine the domain and range of a relation. Also assesses MA.912.A.2.13 Solve real-world problems involving relations and functions. Problem 1: Problem 2:

4 Problem 3: Problem 4: Problem 5:

5 Benchmark: MA.912.A.3.1; Solve linear equations in one variable that include simplifying algebraic expressions. Also assesses MA.912.A.3.2; Indentify and apply the distributive associative, and commutative properties of real numbers and the properties of equality. Problem 1: Problem 2: Problem 3: Solve the problem. 3x 1 = 5 (x 1) 2 (7 2x) A. 3 B. 0 C. -9 D. -10

6 Problem 4: Problem 5:

7 Benchmark: MA.912.A.3.3; Solve literal equations for a specified variable. Problem 1: Problem 2: Problem 3:

8 Problem 4: Problem 5: A. p = (1/4) (q + 11) B. p = q/ C. p = (q-11)/4 D. p = q/4-11

9 Benchmark: MA.912.A.3.4; Solve and graph simple and compound inequalities in one variable and be able to justify each step in a solution. Problem 1: Problem 2: Problem 3:

10 Problem 4: Problem 5: Solve the inequality for x: (3/5)x 10 + (1/5)x A. x 25 B. x 4 C. x 25 D. x 4

11 Benchmark: MA.912.A.3.5; Symbolically represent and solve multi-step and real-world applications that involve linear equations and inequalities. Problem 1: Problem 2:

12 Problem 3: Problem 4: A. 4 = (r + c) 1.5 B. 4 = (r - c) 1.5 C. 1.5 = (r + c) 4 D. 1.5 = (r - c)4 Problem 5: Working together, Paul and Daniel can pick forty bushels of apples in 4.95 hours. Had he done it alone, it would have taken Daniel 9 hours. Find how long it would take Paul to do it alone.

13 Benchmark: MA.912.A.3.8; Graph a line given any of the following information: a table of values, the x- and y-intercepts, two points, the slope and a point, the equation of the line in slope-intercept form, standard form, or point-slope form. Also assesses MA.912.A.3.12; Graph a linear equation or inequality in two variables with and without graphing technology. Write an equation or inequality represented by a given graph. Problem 1:

14 Problem 2: Problem 3:

15 Problem 4: Which of the following is a graph of the equation 2x + y = 4? A. B. C. D.

16 Problem 5:

17 Benchmark: MA.912.A.3.9; Determine the slope, x-intercept, and y-intercept of a line given its graph, its equation, or two points on the line. Also assesses MA.912.A.3.12; Graph a linear equation or inequality in two variables with and without graphing technology. Write an equation or inequality represented by a given graph. Problem 1: Problem 2:

18 Problem 3: Determine the slope of the given line. A. -1/2 B. 2/1 C. -2/1 D. 1/2 Problem 4: Problem 5:

19 Benchmark: MA.912.A.3.10; Write an equation of a line given any of the following information: two points on the line, its slope and one point on the line, or its graph. Also, find an equation of a new line parallel to a given line, or perpendicular to a given line, through a given point on the new line. Also assesses Problem 1: MA.912.A.3.7; Rewrite equations of a line into slope-intercept form and standard form. MA.912.A.3.12; Graph a linear equation or inequality in two variables with and without graphing technology. Write an equation of inequality represented by a given graph. MA.912.A.G.1.4; Use coordinate geometry to find slopes, parallel lines, perpendicular lines and equations of lines

20 Problem 2: Problem 3: What is the slope-intercept form of the line that passes through (6,-7) and is perpendicular to the line shown? A. y = 2x + 3 B. y = 4x -1.5 C. y = (1/2) x + 4 D. y = (-1/2) x - 4

21 Problem 4:. A. y = -2x + 12 B. y = 2x - 8 C. y = 8x - 2 D. y = - 2x + 8 Problem 5: A. y = 3x B. y = -3x C. y = (1/3)x D. y = (-1/3)x

22 Benchmark: MA.912.A.3.11; Write an equation of a line that models a data set, and use the equation or the graph to make predictions. Describe the slope of the line in terms of the data, recognizing that the slope is the rate of change. Also assesses MA.912.A.3.12; Graph a linear equation or inequality in two variables with and without graphing technology. Write an equation or inequality represented by a given graph. Problem 1: Problem 2:

23 Problem 3: Problem 4:

24 Problem 5:

25 Benchmark: MA.912.A.3.14; Solve systems of linear equations and inequalities in two and three variables using graphical, substitution, and elimination methods. Also assesses MA.912.A.3.13; Use a graph to approximate the solution of a system of linear equations or inequalities in two variables with and without technology. MA.912.A. 3.15; Solve real-world problems involving systems of linear equations and inequalities in two and three variables. Problem 1: Problem 2: Problem 3:

26 Problem 4: Problem 5: What is the value of y in the ordered pair that is the solution for the system?

27 Benchmark: MA.912.A.4.1; Simplify monomials and monomial expressions using the laws of integral exponents. Problem 1: Problem 2: Problem 3: Problem 4: What is the coefficient of the simplified expression below?

28 Problem 5: Simplify. Write the exponent of the y in the simplified answer. A. 7 B. 3 C. 1 D. -3

29 Benchmark: MA.912.A.4.2; Add, subtract, and multiply polynomials. Problem 1: Problem 2:

30 Problem 3: Problem 4: Problem 5: A. 5x 2-3x - 3 B. 3x 2-3x - 3 C. 3x 2-11x + 7 D. 4x 2-11x + 7

31 Benchmark: MA.912.A.4.3; Factor polynomial expressions. Also assesses MA.912.A.5.1; Simplify algebraic ratios. Problem 1: Problem 2: Problem 3:

32 Problem 4: Problem 5: A. (2x + 5)(2x + 5) B. (2x + 5)(2x - 5) C. (2x - 5)(2x - 5) D. (4x -1)(x + 25)

33 Benchmark: MA.912.A.4.4; Divide polynomials by monomials and polynomials with various techniques, including synthetic division. Problem 1: Problem 2: Problem 3: The area of the rectangle below can be shown by the expression (16x + 4y) square feet. If the width of the rectangle is 4 feet, what is the length of the rectangle? A. (12x + 1y) B. (4x + y) C.4x + 4y D. 16x + 1y

34 Problem 4: The perimeter of the square below can be show by the expression below. What is the length of each side of the square? A. 3x 2 + 6x B. 8x x C. 3x x D. 12x 2 + 6x Problem 5: A contractor built a basement for a new home. The volume of the rectangular basement shown at the right is represented by the expression 3x 3 + 6x 2-30x. If the height of the basement is 3x, what is the area of the base? A. x 3 + 2x 2-10 B. x 4 +2x 3-10 C. x 2 + 2x -10 D. 9x x 3-90x 2

35 Benchmark: MA.912.A.5.4; Solve algebraic proportions. Problem 1: Problem 2:

36 Problem 3: Problem 4:

37 Problem 5: Solve. A.1.5 B C. 3 D. 4

38 Benchmark: MA.912.A.6.2; Add, subtract, multiply, and divide radical expressions (square roots and higher). Also assesses MA.912.A.6.1; Simplify radical expressions. Problem 1: Problem 2: Problem 3:

39 Problem 4: Problem 5:

40 Benchmark: MA.912.A.7.1; Graph quadratic equations with and without graphing technology. Also assesses MA.912.A.7.8; Use quadratic equations to solve real-world problems. Problem 1: Problem 2:

41 Problem 3: Problem 4: Problem 5: Match the graph with its equation. y = 2x A. B. C. D.

42 Benchmark: MA.912.A.7.2; Solve quadratic equations over the real numbers by factoring and by using the quadratic formula. Also assesses Problem 1: MA ; Use the zero product property of real numbers in a variety of contexts to identify solutions to equations. MA.912.A.7.8; Use quadratic equations to solve real-world problems. Problem 2:

43 Problem 3: Problem 4: Problem 5: A. x = 2 or x = 1 B. x = -2 or x = -1 C. x = -2 or x = 1 D. x = 2 or x = -1

44 Benchmark: MA.912.D.7.1; Perform set operations such as union and intersection, complement, and cross product. Problem 1: Problem 2: Problem 3:

45 Problem 4: Problem 5:

46 Benchmark: MA.912.D.7.2; Use Venn diagrams to explore relationships and patterns and to make arguments about relationships between sets. Problem 1: Problem 2:

47 Problem 3: Problem 4:

48 Problem 5: Eight boxes of juice are organic and 11 are unsweetened. Five of the boxes of juice are both organic and unsweetened. How many boxes of juice are there?