Math Precalculus

MATH 130 (Precalculus) Spring 2020

Exam 2 Tuesday, April 7

• The exam should be submitted in full via Gradescope by 11:59PM on Tuesday, April 7. Make sure that for each n, your submission for Question n contains only the work and answers for Question n.

• While the use of notes is not permitted, the use of non-graphing calculators is permitted.

• All work must be shown, and must lead to your final answer, which must be specified by drawing a circle or box around it.

• All numerical answers must be exact. For instance, if 2/5 is correct then writing 0.4 is equally valid, but if 1/3 is correct then writing 0.3 or 0.33 is not. All fraction answers must be in lowest terms.

• All solution sets must be written out in suitable notation.

• Good luck!

Problem Value Points 1 8 2 8 3 10 4 8 5 10 6 8 7 8 8 8 9 8 10 8 11 8 12 8

Total 100

I pledge that I have neither given nor received assistance on this exam.

Name (Print) Signature

(1) (8 points) If θ is an angle satisfying the property that

cos θ = − 2

7

find the remaining five trigonometric functions of θ.

2

(2) (4 points each) In each case, find the point (x,y) on the unit circle that corresponds to the given angle.

(a) t = −3π 4

(b) t = 20π 3

3

(3) (a) (6 points) Write out the following quadratic function in standard form:

h(x) = 2x2 + 8x − 1

(b) (4 points) Find the vertex and the axis of symmetry for the graph of the function in part (a).

4

(4) (4 points each) Use the One-to-One property to solve the each of the following equations:

(a) 3t+4 = 81 (b) e3x−1 = e8

5

(5) (10 points) Solve the following logarithmic equation algebraically:

ln(x − 2) = ln(x + 6) − ln(x − 3)

6

(6) (4 points each) For each of the angles below, give two angles which are coterminal, one positive and the other negative. (If the angle is given in degrees, your answers should be in degrees, and if it is given in radians, your answers should be in radians.)

(a) 65◦ (b) −3π 4

7

(7) (a) (3 points) Find the domain of the following logarithmic function in interval notation:

f(x) = − log2(x) + 3

(b) (4 points) Find the x−intercept of the graph of the function in part (a). (Your answer must be an ordered pair for full credit.)

(c) (3 points) Find the vertical asymptote of the graph of the function in part (a).

8

(8) (8 points) Solve the following exponential equation algebraically:

e2x + 6ex − 7 = 0

9

(9) (8 points) Condense the expression to the logarithm of a single quantity:

log10 r + 4 log10 s − 3 log10 t

10

(10) (8 points) Find the standard form for the quadratic function whose graph passes through (0, 13) and has the vertex (3,−5).

11

(11) (8 points) Use the properties of logarithms to expand the expression as a sum, difference and/or constant multiple of logarithms. (Assume all variables are positive.)

ln

( u3 √

v

w5

)

12

(12) (4 points) Find the reference angle θ′ for the angle θ = 11π 6 .

(b) (4 points) Sketch θ and θ′ from part (a) in standard position.

13