NBT Cheat Sheet 2026

The 30 highest-yield NBT facts, distilled from real exam questions. Print it, save it as a PDF, or study it here — free, no sign-up.

1. Which word correctly completes this sentence? 'The professor asked students to _______ between the two competing theories before forming an opinion.' → differentiate
2. What is the approximate value of √50, rounded to the nearest integer? → 7
3. Water flows out of a tank at a rate of 15 litres per minute. How many litres will flow out in 1 hour and 20 minutes? → 1 200 litres
4. A farmer has both chickens and cows. He counts 20 heads and 56 legs. How many cows does he have? → 8
5. A car travels from City A to City B at 90 km/h and returns at 60 km/h. What is the average speed for the entire round trip? → 72 km/h
6. A function f satisfies f(x) + 2f(1/x) = 3x for all x ≠ 0. What is f(2)? → 7/3
7. Given f(x) = (2x + 1)/(x − 3) and g(x) = x² − 4, find the value(s) of x for which (f ∘ g)(x) is undefined. → x = ±2 and x = ±√7
8. On a graph, f(x) is a straight line that is neither increasing nor decreasing. Which type of function is this? → Constant function
9. Which sentence uses 'less' and 'fewer' correctly? → She has fewer worries and less stress now.
10. The volume of a cube with side length 4 cm is: → 64 cm³
11. A scatter plot shows a strong negative correlation. Which statement best describes this relationship? → As x increases, y decreases
12. The word 'reductive' in academic discourse typically means: → Oversimplified in a way that distorts complexity
13. What is the range of f(x) = −x² + 4? → (−∞, 4]
14. Which measure of central tendency is most affected by outliers? → Mean
15. Choose the sentence that uses the correct tense consistently: → They studied for the test and passed with distinction.
16. A city's municipal budget increased by 50% in Year 1, then decreased by 33⅓% in Year 2. After both changes, how does the budget compare to its original value? → It is exactly equal to the original value
17. A box contains 4 red, 3 blue, and 3 green balls. One ball is drawn at random. What is the probability of drawing a red ball? → 2/5
18. A school tuck shop buys cold drinks at R8.50 each and sells them at a mark-up of 40%. What is the selling price? → R11.90
19. The function g(x) = a · b^x passes through (0, 5) and (1, 15). What are a and b? → a = 5, b = 3
20. A hire-purchase agreement for R9 000 requires a 10% deposit and 18 monthly instalments of R480. What is the total amount paid? → R9 540
21. The function f(x) = 2x − 6. What is the x-intercept? → x = 3
22. "The **ubiquitous** presence of smartphones has fundamentally altered how young people consume information." 'Ubiquitous' most nearly means: → present everywhere
23. Simplify the expression: (2^(x+1) · 4^(x−1)) / 8^(x−1) → 4
24. The maximum value of y = 5sin(x) + 3 is: → 8
25. If 5x − 3 = 2x + 12, what is x? → 5
26. What is the key difference between a fact and an opinion in argumentative writing? → Facts can be verified through evidence; opinions express personal judgments or beliefs
27. A problem states: "It takes 3 workers 4 days to complete a task. How many days will 6 workers take to complete the same task?" → 2 days
28. The exterior angle of a regular polygon is 36°. How many sides does the polygon have? → 10
29. In triangle ABC, angle B = 90°, AB = 5 and BC = 12. What is sin A? → 12/13
30. Which sentence is grammatically correct? → The data clearly show that the hypothesis was correct.