Linear Algebra And Differential Calculus Of Several Variables (MATH 51)

In the equation A = p + prt, t is equivalent to
(1) A-pr d
(2) A-p pr
(3) A pr-p
(4) A p-pr d

Which is an irrational number?
(1) 0
(3)- 1 3
(2) π
(4) √9

What are the factors of x² - 10x - 24?
(1) (x-4)(x + 6)
(2) (x-4)(x-6)
(3) (x - 12)(x + 2)
(4) (x + 12)(x – 2) -

4. The expression 4x² - 25 is equivalent to
(1) (4x5)(x + 5)
(3) (2x + 5)(2x - 5)
(2) (4x + 5)(x - 5)
(4) (2x-5) (2x - 5)

5. If the function f(x) = x² has the domain {0, 1, 4, 9}, what is its range?
(1) {0, 1, 2, 3}
(2) {0, 1, 16, 81}
(3) {0, -1, 1, -2, 2, -3, 3}
(4) {0, 1, 1, -16, 16, 81, 81}

6. The formula for the volume of a right circular cylinder is V = πr²h. The value of h can be expressed as
(3) πν 2 V
(1) V2 r π
V
(2)
πγ2
(4) V – πr²

The accompanying box-and-whisker plot represents the scores earned on a science test.
55
60
65
70
75
80
85
90
95
100
What is the median score?
(1) 70
(2) 75
(3) 77
(4) 85

4. The expression 4x² - 25 is equivalent to
(1) (4x5)(x + 5)
(3) (2x + 5)(2x - 5)
(2) (4x + 5)(x - 5)
(4) (2x-5) (2x - 5)

5. If the function f(x) = x² has the domain {0, 1, 4, 9}, what is its range?
(1) {0, 1, 2, 3}
(2) {0, 1, 16, 81}
(3) {0, -1, 1, -2, 2, -3, 3}
(4) {0, 1, 1, -16, 16, 81, 81}

1. Boyle's Law involves the pressure and volume of gas in a container. It can be represented by the formula P₁V₁ = P2V2. When the formula is solved for P2, the result is
   (3) P1V1 V2
   (4) P1V2 V₁ 1
   (1) P1V1V2
   (2) V2 P1V1

2. David correctly factored the expression m² 12m 64. 2 Which expression did he write?
(1) (m-8)(m - 8)
(2) (m-8)(m + 8)
(3) (m-16)(m + 4)
(4) (m + 16)(m - 4)

3. Compared to the graph of f(x) = x², the graph of g(x) = (x - 2)2 + 3 is the result of translating f(x)
(1) 2 units up and 3 units right
(2) 2 units down and 3 units up
(3) 2 units right and 3 units up
(4) 2 units left and 3 units right

Analysis of data from a statistical study shows a linear relationship in the data with a correlation coefficient of -0.524. Which statement best summarizes this result?
(1) There is a strong positive correlation between the variables.
(2) There is a strong negative correlation between the variables.
(3) There is a moderate positive correlation between the variables.
(4) There is a moderate negative correlation between the variables.

Analyze the product: x² - x - (m + 1) (m + 2)