HPC Chapter 6 and 7 Review

Vectors

100

Component form of vector with initial point (-3, 5) and terminal point (4, -2).

<7, -7>

200

Given: u = <5, -7> and v = <-1, 3>

Find  u - v

<6, -10>

300

Find the magnitude and direction of the vector <43, 61>. Round to the nearest tenth.

magnitude ~ 74.6 units

direction ~ 54.8 degrees

400

Given: u = <5, -7> and v = <-1, 3>

Find  u * v             (* is the dot product)

-26

500

Find the magnitude and direction of a plane flying 400 km/hr due North with a 45 km/hr crosswind blowing due East. Round to the nearest tenth.

402.5 km/hr 6.4 degrees East of North

Systems of Equations

100

The solution to the system:

y - 3x = 3
y = 3x - 2

no solution

200

The solution to the system:

8a + 5b = 9
2a - 5b = -4

(0.5, 1)

300

The solution to the system:

y = 3x - 1
7x + 2y = 37

(3, 8)

400

The solution to the system

x - 2y + x = 15

2x + 3y - 3z = 1

4x + 10y - 5z = -3

(8, -2, 3)

500

The solution to the system

9x² + y² = 9

y = 3x - 3

(0, -3) and (1, 0)

Systems of Inequalities

100

Graph the inequality

y > 2x - 4

slope 2

y-int (0, -4)

dotted, shade above

200

How you determine which side of the "line" is your solution region (where you shade).

y> shade above

y< shade below

300

How you determine whether to connect points with a solid or a dashed "line".

<, > dashed

<=, >= solid

400

Shade the solution region of the system

y > 1/3 x - 2

x <= 5

graph

500

Graph the inequality

y < x² + 6x -7

vertex (-3, -16)

roots (-7, 0) and (1, 0)

shade below

Areas of Obliques

100

In triangle ABC, A = 130 degrees, a = 49 ft, and c = 30 ft. Find the measure of angle C to the nearest integer.

C = 28 degrees

200

In triangle ABC, a = 13 yd, c = 22 yd, and B = 37 degrees. Find the length of side b. Round to the nearest tenth.

14 yd

300

In triangle ABC, A = 33 degrees, B = 105 degrees, and b = 37.9. Find the measure of side c. Round to the nearest tenth.

c ~ 26.3

400

Find the area of triangle ABC given B = 137 degrees, a = 5.9 mi, and C = 28 degrees. Round to the nearest tenth.

21.5 mi²

500

Find the area of triangle ABC given a = 4.3 in, b = 14 in, and c = 13 in. Round to the nearest tenth.

27.9 in²

Partial Fractions

100

The partial fraction decomposition of

2/(x²+4x+3)

1/(x+1) - 1/(x+3)

200

The partial fraction decomposition of

(3x+5) / (x-3)(2x+1)

2/(x-3) - 1/(2x+1)

300

Partial fraction decomposition of

(10x + 9) / [(x-4)(x+3)²]

1/(x-4) - 1/(x+3) + 3/(x+3)²

400

The partial fraction decomposition of

(3x + 10)/(x² + 9x + 20)

-2/(x+4) + 5/(x+5)

500

The partial fraction decomposition of

(3x+1) / (x-1)²(x+2)

5/[9(x-1)] + 4/([3(x-1)²] - 5/[9(x+2)]