FTCE Math 6-12 Exam Overview

Exam Format

• Purpose: Assess skills and knowledge of prospective math teachers for grades 6-12 in Florida.
• Structure: 70 multiple-choice questions, computer-administered.
• Duration: 2 hours and 30 minutes.
• Location: Administered via Pearson Professional testing centers.

Exam Content

• Question Types: Word problems, graphics, direct questions, command, sentence completion, and selection.
• Competencies Covered:
  • Algebra (13%): Covers ratio, proportions, linear equations, quadratic solutions, graphing.
  • Advanced Algebra (12%): Polynomial equations, complex numbers, sequences, logarithms, matrices.
  • Functions (8%): Identifying functions, domain/range, graph/equations transformations.
  • Geometry (15%): Theorems, formulas, constructions, Pythagorean theorem, special triangles.
  • Coordinate Geometry (6%): Parabolas, circles, transformations on a plane.
  • Trigonometry (7%): Right triangle problems, trigonometric functions, laws of sines and cosines.
  • Statistics and Probability (10%): Data analysis, laws of probability, experimental interpretation.
  • Calculus (9%): Derivatives, integrals, tangents, related rates.
  • Mathematical Reasoning (5%): Inductive/deductive reasoning, logic.
  • Instruction and Assessment (15%): Learning environments, assessments, instructional strategies.

Registration and Fees

• Process: Online registration through FTCE website.
• Fee: $150.
• Rescheduling: Must reschedule at least 24 hours in advance.
• Retake Policy: Wait 31 days after failing or 3 years after passing.
• Accommodations: Available for disabilities and nursing mothers.

Study Resources

• Study Guides: Available online for free or purchase.
• Practice Tests: Essential for gauging preparedness and identifying weak areas.
• Study Tips: Use study guides, take frequent practice tests, and create a balanced study plan.

Sample Practice Questions

1. Distance Question:

   • Correct answer: (5, -5), (- 1, - 5)

2. Line Segment Division:

   • Correct answer: 11

3. Graph of an Even Function:

   • Correct answer: Parabola at (h, k)

4. Matrix Inversion:

   • Correct answer: ( A^{-1} = \frac{1}{11}(3 8 2 5) )

5. Direct Proof:

   • Correct answer: Mathematical assertions are intermediate conclusions.

6. Matrix Addition:

   • Correct answer: (2, 14)

7. Inscribed Angle and Arc Measure:

   • Correct answer: 50

8. Derivative Calculation:

   • Correct answer: ( \text{Image 7} )

9. Product Calculation:

   • Correct answer: 8125

10. Reasoning Type:

    • Correct answer: Inductive reasoning

11. Rectangle Area Ratio:

    • Correct answer: 2:1

12. Equation Solutions:

    • Correct answer: ( x = 1 + 12i6 \text{ and } x = 1 - 12i6 )

13. Exterior Angle of Secants:

    • Correct answer: 120

14. Evaluate Piecewise Function:

    • Correct answer: 2

15. Reasoning Type:

    • Correct answer: Inductive reasoning

Conclusion

The FTCE Math 6-12 exam requires comprehensive preparation involving focused study on each competency, utilizing available resources like study guides and practice tests to ensure success.