MATH 1051 Exam 1 (Final Review)

Factoring

100

16x² - 49

(4x - 7)(4x + 7)

200

x² + 16x + 60

(x + 6)(x + 10) 

300

x³ - 2x² + 5x - 10 

(x² + 5)(x - 2) 

400

12x² - 38x - 14

(3x + 5)(4x - 1) 

500

108x² - 93x - 168

3(9x + 8)(4x - 7) 

Linear Equations

100

Find the equation for the line through the points (-6,4) and (2,1) 

y = (-3/8)x + 7/4 

or 

y - 4 = (-3/8)(x + 6) 

or

y - 1 = (-3/8)(x - 2) 

200

Find the equation of the line in slope-intercept form parallel to the line y = 5x - 2 that passes through the point (4,3) 

y = 5x - 17

300

Find the equation of the line in point-slope form perpendicular to the line -4x + 2y = 8 that passes through the point (-3,5). 

y = (-1/2)x + 13/2

400

Find the point(s) of intersection for the two lines with the equations 2x - 4y = 8 and x = 5y + 2

(16/3, 2/3) 

500

A pine tree was 27 feet tall in 2004. By 2010, it had grown to 30 feet. If the function which expresses the height of the tree over time is a straight line, how tall will the tree be in 2019? 

y = 0.5x + 27 (equation) 

answer: 34.5 ft 

Simplifying Rational Exp.

100

Simplify (x² - 4)/(x² - x - 2) 

(x + 2)/(x + 1) 

200

x²/(x-3) + (x-12)/(x-3) 

x + 4

300

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

(-2x²-15x-4)/(3x²-6x)

or 

(-2x²-15x-4)/[(3x)(x-2)]

400

[(6x+2)/x + (x-4)/(x+2)]/(x+1)

(7x²+10x+4)/(x³+3x²+2x)

or 

(7x²+10x+4)/[(x²+2x)(x+1)]

500

[(x-2)/4x]/[(x²-4x+4)/12x]

3/(x-2)

Solving for x

100

8(x+4) + 4 = 4x + 1

x = -35/4

200

-4(-x+2) + 10 = 3 + 10x + 4(x+1)

x = -1/2

300

8 + 3|4x - 7| >= 17

(-infinity, 1] U [5/2, infinity)

400

8 - 3 |4x + 7| = -19 

x = 1/2, -4

500

| |2x + 5| - 3 | = 8

x = -8, 3

Quadratic Equations/Parabolas

100

Complete the square to find the vertex of x²+5x+4

vertex: (-5/2, -9/4) 

200

Find the vertex of 3x²-12x+9

vertex: (2,-3) 

300

Consider the following function: y = -4x²+8x+16

(a) Find its vertex 

(b) Does the function have a maximum or a minimum point? 

(a) vertex: (1,20) 

(b) vertex is a maximum 

400

(a) Find the general equation for the parabola that goes through the vertex (2,1) and passes through the point (3,5)

(b) Is the vertex a maximum or a minimum? 

(a) vertex form: y = 4(x-2)²+1 and general form: y = 4x^2-16x+17

(b) vertex is maximum 

500

(a) Find the vertex form of the parabola with vertex (-3/2,-49) passing through point (1/2, -33)

(b) Find its x-intercept(s) 

(c) Find its y-intercept

(a) y = 4(x+3/2)²-49

(b) x-ints: (-5,0), (2,0) 

(c) y-int: (0,-40)