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Mixed Deck — All NBT Topics Flashcards

100 cards from real NBT practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. A circle with equation x² + y² − 6x + 4y − 3 = 0 is reflected across the line y = x. What is the equation of the reflected circle?

    Answer: x² + y² + 4x − 6y − 3 = 0

    Complete the square: (x−3)² + (y+2)² = 16, so centre (3, −2), radius 4. Reflecting across y = x swaps x and y coordinates: new centre is (−2, 3). The reflected circle equation is (x+2)² + (y−3)² = 16. Expanding: x²+4x+4 + y²−6y+9 = 16 → x²+y²+4x−6y−3 = 0. This matches answer A.

  2. A cumulative frequency table shows that 48 out of 80 learners scored below 60%. What percentage scored 60% or above?

    Answer: 40%

    Scored 60% or above = 80 − 48 = 32; percentage = 32/80 × 100% = 40%.

  3. A triangle has angles measuring 30°, 60°, and 90°. What is the measure of the largest angle?

    Answer: 90°

    Explanation: In a triangle, the sum of all angles is always 180°. So, 180° - 30° - 60° = 90°.

  4. A store marks up an item by 40% and then discounts it by 40%. The final price compared to the original is:

    Answer: 16% less

    1.4 × 0.6 = 0.84, which is 16% less than the original price.

  5. An academic abstract states: 'This paper examines the extent to which socioeconomic factors influence educational outcomes in post-apartheid South Africa.' The author's attitude toward the topic is:

    Answer: Objective and inquiring — presenting a research focus without personal bias

    Passive, neutral language ('examines', 'extent to which') signals an objective, inquiring academic stance without advocating a position.

  6. An argument claims: "Smoking should be banned because it is bad for health." Which critical thinking concept is missing to make this a stronger argument?

    Answer: Empirical evidence supporting the health claim

    A strong argument requires empirical evidence — data, studies, or statistics — to substantiate the claim that smoking is bad for health. Unsupported assertions are weak arguments.

  7. How should a writer best integrate a direct quotation into a body paragraph?

    Answer: Introduce the quotation, present it, and then analyze its relevance to the argument

    Effective quotation integration uses the 'introduce, quote, analyze' (or 'sandwich') method to show how the evidence supports the argument.

  8. Read the sentence: "He nodded slowly when she announced her promotion, then turned to refill his coffee cup, which was already full." What does this passage imply about the man's reaction?

    Answer: He is concealing a negative emotional response — possibly resentment or disappointment — behind a mundane action.

    The key detail is that the coffee cup was *already full* — the action is irrational as a practical act, which means it functions as a displacement behaviour. He performs a mundane gesture to avoid engaging with her news. Combined with the 'slow nod' (minimal, non-committal acknowledgement), the passage implies a suppressed negative emotion. Option A is undermined by the full cup; option C contradicts the emotional flatness of the nod; option D requires external context not provided.

  9. Which logical structure correctly represents a valid modus tollens argument?

    Answer: If P then Q; Q is false; therefore P is false

    Modus tollens denies the consequent (Q is false) to validly conclude the antecedent (P) must also be false.

  10. The graph of y = (1/2)^x compared to y = 2^x is:

    Answer: A reflection of y = 2^x in the y-axis

    (1/2)^x = 2^(−x), which is y = 2^x reflected in the y-axis.

  11. "The professor's lecture was so **abstruse** that even doctoral students struggled to follow the argument." 'Abstruse' in this context means:

    Answer: extremely difficult to understand

    'Abstruse' means difficult to understand; the context of doctoral students struggling confirms this meaning.

  12. Which strategy most effectively strengthens an argumentative claim in an essay?

    Answer: Providing specific, credible evidence and explaining how it supports the claim

    Claims are strongest when supported by specific, credible evidence that is explicitly connected to the argument being made.

  13. Two lines are perpendicular. One has slope 2/3. What is the slope of the other?

    Answer: −3/2

    Perpendicular slopes are negative reciprocals: −1 ÷ (2/3) = −3/2.

  14. A scientist models the cooling of a substance with T(t) = 20 + 80e^(−0.5t), where T is temperature (°C) and t is time (hours). What is the temperature at t = 0?

    Answer: 100°C

    At t = 0, e^0 = 1, so T(0) = 20 + 80(1) = 100°C.

  15. Two workers, P and Q, are paid in the ratio of their work rates. P completes a job in 8 days and Q completes the same job in 12 days. They work together for 3 days, after which P leaves. How many more days does Q need to finish the job alone?

    Answer: 4.5 days

    P's rate = 1/8 per day; Q's rate = 1/12 per day. Together in 3 days they complete 3 × (1/8 + 1/12) = 3 × (3/24 + 2/24) = 3 × 5/24 = 15/24 = 5/8 of the job. Remaining work = 1 − 5/8 = 3/8. Q alone takes (3/8) ÷ (1/12) = (3/8) × 12 = 4.5 days.

  16. The function f(x) = log₃(x² − 5x + 6) has a domain restricted to where the argument is positive. Which of the following is the correct domain?

    Answer: x 3

    The argument x² − 5x + 6 = (x − 2)(x − 3) must be strictly positive. This product is positive when both factors are positive (x > 3) or both are negative (x 3.

  17. A scientist writes in a funding proposal: 'While preliminary results remain inconclusive, they do not contradict the central hypothesis.' What can be most accurately inferred about the state of the research?

    Answer: The evidence gathered so far is neutral — neither supporting nor refuting the hypothesis

    'Inconclusive' means the results do not point clearly in any direction. The phrase 'do not contradict' is a carefully hedged double negative — it means the hypothesis is still standing, not that it is confirmed. This is neutral ground. Option A overclaims, B overstates proof, and D is not supported by anything in the text.

  18. What should be included in a conclusion paragraph?

    Answer: Summarize key points and restate the thesis.

    A conclusion paragraph serves to bring the essay to a satisfying close. It effectively summarizes the main arguments presented throughout the body of the essay. Additionally, it restates the thesis statement in a new way, reinforcing the central idea and leaving the reader with a clear understanding of the essay's overall message.

  19. A cyclist completes a 90 km route in 3.5 hours. For the first 60 km they averaged 30 km/h. At what average speed did they cover the remaining 30 km?

    Answer: 20 km/h

    Time for 60 km at 30 km/h = 2 h; remaining time = 3.5 − 2 = 1.5 h; speed = 30/1.5 = 20 km/h.

  20. Exchange rates: 1 USD = 18.5 ZAR and 1 USD = 0.93 EUR. How many ZAR equals 200 EUR (rounded to the nearest whole number)?

    Answer: 3,978 ZAR

    200 EUR ÷ 0.93 ≈ 215.05 USD; 215.05 × 18.5 ≈ 3,978 ZAR.