C897 Mathematics: Content Knowledge

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Access and unlock Multiple Practice Question for C897 Mathematics: Content Knowledge to help you Pass at ease.

Free C897 Mathematics: Content Knowledge Questions

1.

Simplify the expression: (2⁻¹ × 3²) / (6⁻¹).

  • 9

  • 3

  • 27

  • 1

Explanation

Explanation:

Step 1: Rewrite using the negative exponent rule:

Correct Answer

27


2.

Evaluate sin(π/3) + cos(π/6).

  • √3

  • 1 + √3

  • (√3/2) + (1/2)

  • √3/2

Explanation

Explanation:

Step 1: Recall the exact trigonometric values:

sinπ/3=32, cosπ6=32

Step 2: Add the values:

sinπ3+cosπ6=32+32=232=3

Step 3: Therefore, the sum of trigonometric values is 3

Correct Answer:

3


3.

What is the domain of f(x) = √(4 - x²)?

  • x ≥ 0

  • All real x

  • x ≤ 4

  • -2 ≤ x ≤ 2

Explanation


4.

A teacher explores the foundations of probability with Kolmogorov’s axioms. Which axiom ensures that the probability of the entire sample space is 1?

  • Normalization axiom

  • Non-negativity axiom

  • Countable additivity axiom

  • Finite additivity axiom

Explanation

Explanation:

Step 1: Kolmogorov’s axioms formalize probability theory.

Step 2: The normalization axiom states that the probability of the entire sample space (S) is 1:

P(S) = 1

Step 3: This ensures that probabilities are properly scaled, providing a total measure of certainty over all possible outcomes.

Step 4: Therefore, the axiom that guarantees P(S) = 1 is the normalization axiom.

Correct Answer:

Normalization axiom


5.

In a geometry class, students prove triangle congruence. Which justifies SSS congruence?

  • All corresponding sides equal

  • Two sides and included angle

  • Two angles and non-included side

  • Hypotenuse and leg

Explanation

Explanation:

Step 1: Recall the SSS (Side-Side-Side) congruence criterion for triangles.

Step 2: SSS states that if all three sides of one triangle are equal in length to all three sides of another triangle, then the triangles are congruent.

Step 3: This means the corresponding angles are automatically equal, and the triangles are identical in shape and size.

Correct Answer:

All corresponding sides equal


6.

Factor completely: 4x² - 12x + 9.

  • (4x - 3)(x - 3)

  • (2x + 3)²

  • (2x - 3)²

  • Prime

Explanation

Explanation:


7.

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


8.

Which of the following is the correct simplification of √(50) + √(18) - √(8)?

  • 5√2

  • 7√2

  • 5√2 + 3√2 - 2√2

  • 3√2

Explanation

Explanation:

To simplify the expression, first break each square root into its prime factors: √(50) = √(25×2) = 5√2, √(18) = √(9×2) = 3√2, and √(8) = √(4×2) = 2√2. Then combine like terms: 5√2 + 3√2 - 2√2 = (5 + 3 - 2)√2 = 6√2. Note that none of the provided options match 6√2 exactly, but the intended approach is to combine coefficients of √2.

Correct Answer:

5√2 + 3√2 - 2√2


9.

Solve the inequality |x - 3| > 5.

  • x < -2 or x > 8

  • -2 < x < 8

  • x < 8

  • x > -2

Explanation

Explanation:


10.

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


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