MAT 1275 Final Exam Review Problems

Final Exam Review Problems Summary

Key Evaluation Problems

• Problem 1: Evaluate expressions and plot on a number line:

  • (a) $- rac{−2−4 + 30}{− rac{2}{3}}−1$

  • (b) $5 imes rac{3}{−3(7 − 9)} − 27 imes rac{2}{3}$

  • (c) $7 − 4(5 − 6) − 9 rac{3}{2}$

Algebraic Simplifications

• Problem 2: Simplify $rac{9x^4y^3 − 12x^2y^4 + 3xy^3}{3xy^3}$.

Solving Equations

• Problem 3: Solve equations:

  • (a) $−2(x − 1) − (4 − 3x) = −2(−1 + x) − 7 + x − 3$

  • (b) $3(x − 2) − 7(x + 3) = −2(x + 6) + x$

• Problem 4: Solve and simplify:

  • (a) $6x^2 − 2x − 3 = 0$

  • (b) $−2x^2 + 4x − 5 = 0$

  • (c) $2x^2 + 2x = −3$

Quadratic and Graphing Problems

• Problem 6: Quadratic characteristics:

  • (a) $y = x^2 − 2x − 3$: Vertex (1,-4), intercepts (3,0), (-1,0)

  • (b) $y = x^2 + 2x$: Vertex (-1,-1), intercepts (0,0), (-2,0)

Complex Fractions and Logarithms

• Problem 7: Simplify complex fractions:

  • (a) $rac{2y^2 + 1}{y} imes rac{4y^2 − 1}{y}$

  • (b) $rac{2x + 1}{y} imes rac{3y − 4x}{1}$

• Problem 18: Evaluate logarithms without calculator.

Systems and Trig Calculations

• Problem 12: Solve systems of equations:

  • (a) $3x + y = 4$ and $x^2 − 3y = −32$

• Problem 13: Trig ratios and calculations, finding quadrants and reference angles:

  • (a) $tan(−135°)$: Quadrant III, Reference angle 45°, Exact value 1.

Trigonometric Ratios and Circle Equations

• Problem 14: Determine other trig ratios from given values.

• Problem 10: Circle equations in standard form; find centers and radii.

Miscellaneous Problems

• Problem 16: Solve trigonometric equations for precise solutions:

  • (a) $4sin(x) + 2 = 0$

Polynomials and Geometry

• Problem 20: Write cubic expression with specific roots:

  • Roots: 0, -2, 7

• Problem 26: Analyze a parabolic graph and find solutions based on given conditions.