Mixed Deck — All TMUA Topics Flashcards
100 cards from real TMUA practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 20 Mixed Deck — All TMUA Topics flashcards as text
In a proof by contradiction that √3 is irrational, after assuming √3 = p/q in lowest terms and squaring, one deduces 3q² = p². This implies:
Answer: p is divisible by 3
3 | p² implies 3 | p (since 3 is prime), so p = 3k for some integer k.
When conducting a risk assessment for TMUA operations, which factor should receive the HIGHEST priority?
Answer: Probability and severity of potential harm
The probability and severity of potential harm are the primary factors in risk assessment. While cost and convenience are considerations, they should never override the assessment of how likely an incident is and how severe its consequences could be.
What is the relationship between a percentage and its decimal equivalent?
Answer: Divide the percentage by 100 to get the decimal
A percentage is converted to its decimal equivalent by dividing by 100. For example, 75% becomes 0.75.
A uniform beam of length 4 m and weight 200 N is supported at both ends. A 100 N load is placed 1 m from the left end. What is the reaction at the left support?
Answer: 175 N
Taking moments about the right support: R_L × 4 = 200 × 2 + 100 × 3 = 700, so R_L = 175 N.
What is the relationship between a percentage and its decimal equivalent?
Answer: Divide the percentage by 100 to get the decimal
A percentage is converted to its decimal equivalent by dividing by 100. For example, 75% becomes 0.75.
In TMUA test preparation, what is the best approach to estimation problems?
Answer: Round to manageable numbers and calculate approximate answers
Rounding to manageable numbers allows quick approximate calculations that can verify reasonableness of answers or eliminate incorrect choices.
To prove ∑_{k=1}^{n} k = n(n+1)/2 by induction, the base case checks:
Answer: n = 1: 1 = 1(2)/2 ✓
The standard base case is n = 1: the left side is 1 and the right side is 1(2)/2 = 1, which checks out.
Which measure of spread is most resistant to extreme outliers?
Answer: Interquartile range
The IQR uses only the middle 50% of data and is unaffected by extreme outliers.
What role does collaboration play in proof techniques for TMUA professionals?
Answer: It enhances outcomes through diverse perspectives and shared expertise
Collaboration leverages diverse perspectives and combined expertise to achieve better outcomes than any individual could alone.
Prove by contradiction: if n² is even, then n is even. Which step is essential?
Answer: Assuming n is odd and showing n² is odd
For contradiction, assume n is odd (n = 2k+1), then n² = 4k²+4k+1 is odd — contradicting n² being even.
A TMUA certified professional is asked to provide services outside their scope of competence. The CORRECT ethical response is to:
Answer: Decline and refer to a qualified professional
Ethical practice requires professionals to work within their scope of competence. Accepting work beyond one's qualifications can lead to substandard results and potential harm. Referring to qualified professionals ensures proper service delivery.
Using the pigeonhole principle, what is the minimum number of students needed to guarantee that at least 3 share the same birth month?
Answer: 25
With 12 months, distributing 24 students allows 2 per month; the 25th guarantees a third in some month.
An isosceles trapezoid has parallel sides of 6 cm and 10 cm, and legs of 5 cm each. What is its area?
Answer: 8√21 cm²
Each leg projects 2 cm horizontally; h = √(25−4) = √21; area = ½(6+10)·√21 = 8√21 cm².
How does the TMUA body of knowledge relate to daily professional practice?
Answer: It provides the foundational framework that guides decision-making and standard practices
The body of knowledge provides the foundational framework of principles, standards, and best practices that professionals use to guide their daily decision-making, ensure consistent quality, and maintain alignment with industry standards.
The area enclosed between y = x² and y = x over [0, 1] is:
Answer: 1/6
∫₀¹ (x − x²) dx = [x²/2 − x³/3]₀¹ = 1/2 − 1/3 = 1/6.
A data set consists of values 3, 7, 7, 9, 12, 15, 15, 15, 20. What is the mode?
Answer: 15
The mode is the value that appears most frequently; 15 appears three times, more than any other value.
A cumulative frequency graph (ogive) shows that the 60th percentile is 74. What does this mean?
Answer: 60% of values are below 74
The 60th percentile means 60% of data values fall at or below 74.
Which statement is logically equivalent to 'If A, then B'?
Answer: If not B, then not A
This is the definition of a contrapositive. A conditional statement 'If A, then B' is logically equivalent to its contrapositive 'If not B, then not A.' This means that if one statement is true, the other must also be true, and vice-versa.
A function satisfies f(x) = f(−x) for all x. What type of symmetry does its graph have?
Answer: Symmetry about the y-axis
f(x) = f(−x) defines an even function, which is symmetric about the y-axis.
Simplify (√5 + 2)(√5 − 2).
Answer: 1
Using the difference of two squares: (√5)² − 2² = 5 − 4 = 1.