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# Equations, Formulas, And Vectors for Physics Practice Test

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## Equations, Formulas, And Vectors Practice Test

1. The equation ( x − 4)( x + 5)( x − 1) = 0 is an example of

(a) a first-order equation.

(b) a second-order equation.

(c) a third-order equation.

(d) a fourth-order equation.

2. The real-number solutions to the equation in problem 1 are

(a) −4, 5, and − 1.

(b) 4, −5, and 1.

(c) There are no real-number solutions to this equation.

(d) There is not enough information to tell.

3. Suppose that there are two vectors in the xy plane as follows:

a = ( x a , y a ) = (3, 0)

b = ( x b , y b ) = (0, 4)

What is the length of the sum of these vectors?

(a) 5 units

(b) 7 units

(c) 12 units

(d) There is not enough information to tell.

4. Consider two vectors a and b , where a points east and b points north. In what direction does a · b point?

(a) Northeast

(b) Straight up

(c) Straight down

(d) Irrelevant question! The dot product is not a vector.

5. Consider the two vectors a and b of problem 4. In what direction does a × b point?

(a) Northeast

(b) Straight up

(c) Straight down

(d) Irrelevant question! The cross product is not a vector.

6. When dividing each side of an equation by a quantity, what must you be careful to avoid?

(a) Dividing by a constant

(b) Dividing by a variable

(c) Dividing by anything that can attain a value of zero

(d) Dividing each side by the same quantity

7. Consider a second-order equation of the form ax 2 + bx + c = 0 in which the coefficients have these values:

a = 2

b = 0

c = 8

What can be said about the solutions to this equation?

(a) They are real numbers.

(b) They are pure imaginary numbers.

(c) They are complex numbers.

(d) There are no solutions to this equation.

8. Consider the equation 4 x + 5 = 0. What would be a logical first step in the process of solving this equation?

(a) Subtract 5 from each side.

(b) Divide each side by x .

(c) Multiply each side by x .

(d) Multiply each side by 0.

9. When two vectors a and b are added together, which of the following statements holds true in all situations?

(a) The composite is always longer than either a or b .

(b) The composite points in a direction midway between a and b .

(c) The composite is perpendicular to the plane containing a and b .

(d) None of the above.

10. An equation with a variable all by itself on the left-hand side of the equals sign and having an expression not containing that variable on the right-hand side of the equals sign and that is used to determine a physical quantity is

(a) a formula.

(b) a first-order equation.

(c) a coefficient.

(d) a constant.

1. c

2. b

3. a

4. d

5. b

6. c

7. b

8. a

9. d

10. a

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