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. The gradient of the tangent to f(x) = x³ at x = 2 is: → 12
2. A dataset of five values is 4, 6, 6, 8, 11. What is the mean (average)? → 7
3. Which set of ordered pairs represents a function? → {(1,2),(2,3),(3,4)}
4. A survey of 200 students shows 30% prefer online classes. How many students prefer online classes? → 60
5. Two friends share R450 in the ratio 5:4. How much does the friend with the larger share receive? → R250
6. Read this sentence: 'The study's findings were tentative and should not be generalised.' What does 'tentative' most nearly mean here? → Provisional and uncertain
7. A class has 18 girls and 12 boys. What is the ratio of girls to boys in simplest form? → 3:2
8. The y-intercept of f(x) = 3x² − 5x + 2 is: → 2
9. The circumference of a circle is given by which formula (r = radius)? → 2 pi r
10. If a passage describes a plan as 'feasible', the writer believes the plan is: → Capable of being done successfully
11. A bar graph shows monthly rainfall in Cape Town: Jan 15mm, Feb 17mm, Jun 93mm, Jul 82mm. Which month had the highest rainfall? → June
12. What is the area of a rectangle that is 8m long and 5m wide? → 40 m^2
13. What is the domain of f(x) = √(4 − x)? → x ≤ 4
14. A learner scored 36 out of 45 on a test. What is this as a percentage? → 80%
15. Solve the inequality: x - 6 < 2. → x < 8
16. In a right-angled triangle, sin(theta) is defined as: → opposite / hypotenuse
17. For f(x) = x³ − 3x, the x-values of the turning points are: → x = ±1
18. If f(x) = 2x - 5, what is f(4)? → 3
19. What is lim(x→2) [(x² − 4) / (x − 2)]? → 4
20. A reading passage uses the word 'consequently' to begin a sentence. What relationship does this signpost word indicate? → Cause and effect
21. If f′(c) = 0 and f″(c) > 0, the point x = c is: → A local minimum
22. What is the value of cos(60 degrees)? → 0.5
23. A passage concludes: 'The evidence, while compelling, is far from conclusive.' What is the author's overall stance toward the evidence? → The evidence is strong but not yet decisive
24. Simplify: 2(x + 4) + 3x. → 5x + 8
25. A pie chart shows a household budget: Rent 40%, Food 25%, Transport 20%, Other 15%. If the total monthly income is R12 000, how much is spent on rent? → R4 800
26. In academic reading, a 'main idea' of a paragraph is best described as: → The central point the paragraph develops
27. What is the maximum value of f(x) = −2x² + 8x − 3? → 5
28. Solve for x: 3x + 7 = 22. → x = 5
29. An author writes that survey results were 'skewed' by a small sample. The word 'skewed' implies the results were: → Distorted or biased
30. Expand: (x + 2)(x + 3). → x^2 + 5x + 6