C897 Mathematics: Content Knowledge

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Free C897 Mathematics: Content Knowledge Questions

1.

A classroom activity involves geometric sequences. First term 4, ratio 1/2, what is the 5th term?

  • 1/2

  • 1/4

  • 1

  • 1/8

Explanation


2.

Simplify the expression (3x2 - 2x + 1) - (2x2 + 4x - 3).

  • x2 - 6x + 4

  • 5x2 - 2x - 2

  • x2 - 6x - 4

  • 5x2 + 6x - 4

Explanation

Explanation:

Step 1: Write the expression with parentheses:

(3x² - 2x + 1) - (2x² + 4x - 3)

Step 2: Distribute the negative sign to the second polynomial:

3x² - 2x + 1 - 2x² - 4x + 3

Step 3: Combine like terms:

x² terms: 3x² - 2x² = x²

x terms: -2x - 4x = -6x

constants: 1 + 3 = 4

Step 4: Write the simplified expression:

x² - 6x + 4

Correct Answer:

x2 - 6x + 4


3.

Factor: 2x² + 7x + 3.

  • (2x + 1)(x + 3)

  • (2x + 3)(x + 1)

  • (x + 1)(2x + 3)

  • Prime

Explanation


4.

During a seminar on computability, students encounter the halting problem. Which theoretical construct proves its undecidability?

  • Diagonalization argument

  • Reduction to the Post correspondence problem

  • Rice’s theorem

  • All of the above

Explanation

Explanation:

Step 1: The halting problem asks whether an algorithm can decide, for any program and input, whether the program halts or runs forever.

Step 2: The standard proof of undecidability uses a diagonalization argument, constructing a program that leads to a contradiction if a halting-decider exists.

Step 3: Alternative approaches include reductions from known undecidable problems like the Post correspondence problem, and Rice’s theorem generalizes undecidability to any nontrivial property of programs.

Step 4: Therefore, all these constructs are used to demonstrate the undecidability of the halting problem.

Correct Answer:

All of the above


5.

When teaching systems of inequalities, a teacher uses the scenario of budgeting for a school trip. If the constraints are x + y ≤ 10 and x ≥ 2, y ≥ 3, which region correctly represents the feasible solutions?

  • The area above both lines

  • The shaded polygon formed by the intersection

  • Only the points on the lines

  • The unbounded region to the right

Explanation

Explanation:

The feasible region for a system of inequalities is where all conditions are satisfied simultaneously. Here, x + y ≤ 10 represents all points below or on the line x + y = 10, while x ≥ 2 and y ≥ 3 represent all points to the right of x = 2 and above y = 3. The intersection of these constraints forms a polygon where all three conditions overlap. This polygon represents all possible solutions that satisfy the system of inequalities, including points on the boundaries.

Correct Answer:

The shaded polygon formed by the intersection


6.

A teacher uses vectors in navigation. If a plane flies 300 km east and 400 km north, what is the displacement?

  • 500 km at 53° north of east

  • 700 km

  • 500 km at 37° north of east

  • 400 km

Explanation


7.

In a probability lesson, a bag has 3 red, 4 blue, 2 green balls. P(not blue)?

  • 5/9

  • 4/9

  • 7/9

  • 3/9

Explanation


8.

Convert 5π/6 to degrees.

  • 150°

  • 120°

  • 135°

  • 180°

Explanation


9.

For a lesson on polynomials, factor x2 + 6x + 8.

  • (x + 4)(x + 2)

  • (x + 4)(x - 2)

  • (x - 4)(x + 2)

  • (x - 4)(x - 2)

Explanation

Explanation:

Step 1: Identify two numbers that multiply to 8 (constant term) and add to 6 (coefficient of x). These numbers are 2 and 4.

Step 2: Write the factored form using these numbers:

    x2+6x+8=(x+4)(x+2)

Step 3: Optionally, verify by expanding:

      x+4x+2=x2+2x+4x+8=x2+6x+8

Correct Answer

x+4x+2


10.

Solve the system: 2x + y = 7, x - y = 2.

  • (1, 5)

  • (2, 3)

  • (3, 1)

  • (4, -1)

Explanation

Explanation:


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