Name________________ Midterm Practice Honors Algebra 2 Spring 2007 Caraco 1. Label the following diagram with the appropriate number set.

Integer Irrational Natural Rational Real Whole Matching 1. Slope of 0 a. b.

2. Undefined Slope 3. Negative Slope c. d. 4. Positive Slope 5. By which of the following means could you NOT determine the slope of a line?

a. find the change in y and x using 2 points, then divide b. measure the rise and the run between points of intersection then divide c. solve the equation for y, then take the coefficient of your independent variable d. in the form ax + by = c, take a ÷ b

Match such that each expression is paired with one of its factors 34. x3 + 216 a) x - 6 35. x4 – 10x2 + 9 b) x + 6 36. x2 – 5x – 6 c) x + 3 37. x2 + 6x – 27 d) x + 9

Determine the equations in y=m⋅x + b form and make a quick sketch. Label the x-intercept, y-intercept and slope. 17. 7x + 2y = 14 18. (-3, 2) and (3, 7)

Complete the table:

Standard Form Slope-intercept Form x-intercept y-intercept Slope

7. 2 6 12x y+ =

8. 2 4y x= −

9. x = -2 y = -1

10. y = 2 m = 1

11. x = 3 m =2

12. Ax + By = C

13. y = ax + b

24. Dr. Mildred Trotter (1899-1991), a physical anthropologist, was well known for her work

in the area of height prediction based on the length of the long bones in the arms and legs. One relationship proposed by Dr. Trotter suggested that H = 2.38F + 61.41 where H is the person’s height (in cm) and F is the length of the femur (in cm). Suppose, for most adults, femurs range in size from about 38 cm to 55 cm. According to Dr. Trotter’s formula, what is the range of height for most people?

My femur is 49 cm long. My dad’s femur is only 46 cm long. Based on Dr. Trotter’s formula, predict my and my dad’s height.

Complete the table Graph Slope-Intercept Form Standard Form 14.

15.

y = 2x + 3

16.

2x - 4y = 4

20. Match the scatter plot with an appropriate correlation coefficient. r = 0.9 _____ a) b) r = - 0.9 _____

r = 0.5 _____ c) d)

r = - 0.5 _____

25. The following set of data was gathered that compared the height of one of my former

classes with an estimation of the area of their hands. (a) Create a scatter plot that represents this data.

Area of hands (in cm2) 10.3 10.7 11.1 12.0 12.6 12.7 13.0 13.5 13.7 14.0 14.2 15.8

Height (in cm) 162.6 168.9 160.0 174.0 177.8 167.6 182.9 170.2 180.3 166.4 190.5 195.6

(b) Sketch a line of best fit. (c) Define the regression equation that you created.

(d) Describe, in your own words, what concept or attribute is represented by the slope and by

the y-intercept. 13. Find the determinant of each of the following.

E= ⎥⎦

⎤⎢⎣

⎡− 34

23

1 0 01 1 23 0 1

M⎡ ⎤⎢ ⎥= −⎢ ⎥⎢ ⎥⎣ ⎦

Solve the following systems using the defined method 1. 3x + 2y = 14 (linear combination)

-2x + 4y =-12

2. x + 3y = 8 (graphing)

2x + y = 4

3. x – 2y = 2 (substitution) 4x - 3y = 13

5. Graph the solution for each of the following: a) 1 5x− ≥

b) 9 3 15x− > 6. Manipulate if needed and then state each of the following as a distance problem:

a) 2 5x + <

b) 2 8 10x− ≤ 7. Graph the solution for each of the following:

a) 2 4x − =

b) 3 9 12x+ =

c) 1 43x − ≤

8. Given the following graphical solution, state an absolute value equation or inequality

a) -3 -2 -1 0 1 2 3 4

b) -3 -2 -1 0 1 2 3 4

9. A fruit grower has 150 acres of land available to raise two crops, A and B. It takes 1 day to trim an acre of crop A and 2 days to trim an acre of crop B, and there are 240 days per year available for trimming. It takes 0.3 day to pick an acre of crop A and 0.1 day to pick an acre of crop B, and there are 30 days available for picking. The profits are $140 per acre for crop A and $235 per acre for crop B.

a) Write the set of constraints. b) Write the profit formula

c) Graph the set of constraints.

d) Find the number of acres of each fruit that should be planted to maximize profit. e) What is the maximum profit?

10. Identify the order of each of the following matrices.

A=

2 31 1⎡ ⎤⎢ ⎥−⎣ ⎦ B=

312

⎡ ⎤⎢ ⎥−⎢ ⎥⎢ ⎥⎣ ⎦

C= D=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−

041

315

_________ ________ _________ _________ 11. Given matrices A, B, C, and D from problem #10, perform the following operations. a. 3A b. C - [ ]0 2 1− c. C • D 12. Given matrices A, B, C and D from problem #10, write P (possible) or NP (not possible).

If possible, state the order of the result. (e.g. A • B – P 2x1 ) a) A • C - ______ ___________

b) B • B - ______ ___________

c) A • D - ______ ___________

d) C • B - ______ ___________

14. Which of the following would NOT have an inverse? Explain your answer.

1 0 22 0 53 0 1

A⎡ ⎤⎢ ⎥= −⎢ ⎥⎢ ⎥⎣ ⎦

1 0 01 1 23 0 1

B⎡ ⎤⎢ ⎥= −⎢ ⎥⎢ ⎥⎣ ⎦

2 3 11 0 4

−⎡ ⎤⎢ ⎥⎣ ⎦

15. Fill in each of the 4 blank lines:

2 1 ___ ___ 1 05 3 ___ ___ 0 1

−⎡ ⎤ ⎡ ⎤ ⎡ ⎤• =⎢ ⎥ ⎢ ⎥ ⎢ ⎥−⎣ ⎦ ⎣ ⎦ ⎣ ⎦

16. Use determinants to find the area of the given triangle (I’ve configured the triangle so

that you can verify your answer if you’d like, but you will not receive ANY credit if you do NOT use a matrix/determinant).

(1,4) (-3,0) (4,0)

17. Use inverse matrices to solve the system:

3x + 4y = 10

2x + 3y = 7

18. Use Cramer’s Rule to solve for x in the linear system.

x – y = 1 x + y = 5

True or False 55. When employed correctly, the order of operations ensures that you

ALWAYS do multiplication before division. 56. I am more than 1 million seconds old. 57. In y = mx + b form, 7x + 2y = 14 would be y = 7 – 7x.

58. Given the following absolute value inequality, |x – 8| < 12, the solution would be -4< x <20.

59. Given the inequality, 4x - 2y > 6, the solution would be y < 2x – 3. 60. To express y = 3(2x – 8)2+ 5 graphically, shift the parent function 5 units up. 61. The y-intercept in the graph of –1.3x2 + 0.6x + 3= 0.2 would be 2.8. 62. In the expression x2 + 2 = 6, x = 2 is the only solution.

63. The determinant of ⎥⎦

⎤⎢⎣

⎡0123 would be 2.

Part 3 Multiple Choice 69. In the following expression, what would you do first?

24 ÷ 3 - 5 • (2+1) a) add b) subtract c) multiply d) divide 70. By which of the following means could you NOT determine the slope of a

line? a) find the change in y and x using 2 points, then divide b) solve the equation for y, then take the coefficient of your independent

variable c) in the form ax + by = c, take a ÷ b d) measure the rise and the run between points of intersection then divide

71. (3i - 2) • 2i would simplify as a) -6 – 4i b) -6 + 4i c) 6 – 4i d) 6 + 4i 74. If z = a + bi, y = a – bi, (where a & b are Real Number), then z•y=? a) z b) z2 c) a2 + b2 d) a2 - b2

76. For what values of k does the equation x2+ kx + 16 = 0 have two complex roots?

a) k > 8 b) |k| > 8 c) -8 < k < 8 d) all real k

82. If = , which of the following could be a value of x?

a) -7 b) -4 c) 28 d) 7

83. If b=3, then = ?

a) 24 b) 8 c) 6 d) 4

85. If = 7x, what is the value of x?

a) 0 b) 1 c) 2 d) 3 86. Which of the following represent f(x) = 3x2 + 2x –6 in completed square form?

a) 3( )2 – 6 b) 3( )2 –

c) ( )2 – d) ( )2 –

87. x2 – 16x + 64 would factor as the following: a) (x - 8) 2 b) (x – 16)(x - 4) c) (x - 12)(x - 4) d) prime 88. x2 – x + 1 would factor as the following: a) (x - 1) 2 b) (x – 2)(x + 1) c) (x + 2)(x - 1) d) prime 89. 2x2 + 5x – 3 would factor as the following: a) (2x - 3) 2 b) (2x – 1)(x + 3) c) (2x + 3)(x - 1) d) prime

90. Identify the order of the matrix B=

1

7 a) 2 x 1 b) 1 x 2 c) 2 x 2 d) 3 x 1

91. What would be the determinant of matrix A? A=

a) 29 b) 1 c) -1 d) -29

3 4x

3 x4

b3 b2 b

73 72

6

x13

x13

193

x13

193

x13

193

2

3

5

7

92. What would be the determinant of matrix A? A=

a) 29 b) 1 c) -1 d) -29

93. Matrix A could NOT be which of the following?

[A] •

a) 2 x 2 b) 1 x 2 c) 1 x 3 d) 3 x 2 94. What is the average of the even integers between 3 and 13? a) 4 b) 6 c) 8 d) 10 95. What is the units digit of 39 • 47 • 106 • 14? a) 2 b) 3 c) 4 d) 6 96. If a # b = a(a + b), then 2 # (3 # 4) = a) 23 b) 24 c) 32 d) 46 97. If 2100 – 299 = 2x, then x = a) 0 b) 1 c) 2 d) 99 98. What would be the sum of a number, a and it’s opposite? a) 0 b) 2a c) a2 d) a/2 100. The first row of the augmented matrix for the following

2x + 4y + 5z = 5 x + 3y + 3z = 2 2x + 4y + 4z = 2 would be: a) 2 4 5 5 b) 2 1 2 c) 2 4 5 d) none of the above

2

3

5

7

1

4

2

1

3

2