MAT 1275 Final Exam Review Problems

These flashcards review key concepts and problems from the MAT 1275 final exam on various mathematical topics including algebra, geometry, trigonometry, and calculus.

What is the solution to the equation −2(x − 1) − (4 − 3x) = −2(−1 + x) − 7 + x − 3?

x = −3

What is the polynomial simplified from 9x^4y^3 − 12x^2y^4 + 3xy^3 ?

3x^3 − 4xy + 1

What are the x-intercepts of the quadratic equation y = x^2 − 2x − 3?

(3, 0) and (−1, 0)

What is the vertex of the quadratic equation y = x^2 + 2x?

Vertex: (−1, −1)

How do you express the operation (−2 + 3i)(5 − 7i) in the form a + bi?

Result: 11 + 29i

What is the center of the circle given by the equation x^2 + y^2 − 6x + 4y − 4 = 0?

Center: (3, −2)

What is the radius of the circle x^2 + y^2 + 8x − 2y − 8 = 0?

Radius: r = 5

Where is the terminal side of the angle for tan(−135◦) located?

Quadrant III.

What is the exact value of cos(240◦)?

−1/2

What is the relationship defined by the Law of Sines?

sin A/a = sin B/b = sin C/c

How can you express the line y − 3 = 2(x + 4) in slope-intercept form?

y = 2x + 11

What are the solutions for the equation 4 sin x + 2 = 0?

x = 7π/6 and 11π/6.

What is the general approach for solving the system of equations 3x + y = 4 and x^2 − 3y = −32?

Substitution or elimination method.

What is the exponent rule for simplifying expressions with powers?

a^m * a^n = a^(m+n) and a^m / a^n = a^(m-n).

What is the simplified form for the complex fraction 2/(y^2 + 1)/(y)/(4y^2 − 1)?

Simplified: 2 + y/4 - y.