National Benchmark Test (NBT) – South Africa — Questions and Answers

Question 1: An author writes that survey results were 'skewed' by a small sample. The word 'skewed' implies the results were:

Translated incorrectly
Doubled in size
Perfectly balanced
Distorted or biased (Correct answer)

Correct answer: Distorted or biased

'Skewed' means distorted away from a true or balanced value, here because of the small sample.

Question 2: If f′(c) = 0 and f″(c) > 0, the point x = c is:

An asymptote
A local minimum (Correct answer)
A local maximum
A point of inflection

Correct answer: A local minimum

By the second derivative test, f′(c) = 0 with f″(c) > 0 indicates the curve is concave up at c, confirming a local minimum.

Question 3: A R1 200 deposit earns 8% simple interest in one year. How much interest is earned?

R960
R96 (Correct answer)
R80
R120

Correct answer: R96

8% of R1 200 = 0.08 x 1 200 = R96 interest.

Question 4: Simplify: 2(x + 4) + 3x.

5x + 8 (Correct answer)
2x + 7
6x + 8
5x + 4

Correct answer: 5x + 8

Expand: 2x + 8 + 3x. Combine like terms: 5x + 8.

Question 5: A table lists test scores: 60, 72, 72, 80, 96. What is the mode of these scores?

72 (Correct answer)
80
96
60

Correct answer: 72

The mode is the most frequent value. 72 appears twice while all others appear once, so the mode is 72.

Question 6: Which set of ordered pairs represents a function?

{(1,2),(2,3),(3,4)} (Correct answer)
{(2,1),(2,2),(3,4)}
{(1,2),(1,3),(2,4)}
{(1,2),(3,2),(1,5)}

Correct answer: {(1,2),(2,3),(3,4)}

A function requires each x-value to map to exactly one y-value; only {(1,2),(2,3),(3,4)} satisfies this.

Question 7: What is the derivative of f(x) = sin(x)?

cos(x) (Correct answer)
tan(x)
−cos(x)
−sin(x)

Correct answer: cos(x)

By the standard trigonometric derivative rule, d/dx[sin(x)] = cos(x).

Question 8: A class has 18 girls and 12 boys. What is the ratio of girls to boys in simplest form?

3:2 (Correct answer)
6:4
18:12
2:3

Correct answer: 3:2

18:12 divides by 6 to give 3:2, the simplest form of the ratio of girls to boys.

Question 9: When an academic writer uses the phrase 'it is widely assumed that', they are most likely about to:

State a proven fact they fully accept
Quote a dictionary definition
End the essay
Introduce a common belief they may then question (Correct answer)

Correct answer: Introduce a common belief they may then question

Phrases like 'it is widely assumed' often set up a common belief that the writer will examine or challenge, signalling possible disagreement.

Question 10: A passage says a policy was 'implemented incrementally'. What can you infer about how the policy was introduced?

Only on paper, never in practice
Secretly and without notice
Gradually, in stages over time (Correct answer)
All at once on a single day

Correct answer: Gradually, in stages over time

'Incrementally' means in small steps or stages, so the policy was rolled out gradually rather than all at once.

Question 11: A text states: 'Whereas urban schools reported improvements, rural schools saw little change.' The word 'whereas' signals:

Agreement between the two groups
A cause of the change
A contrast between the two groups (Correct answer)
A chronological order

Correct answer: A contrast between the two groups

'Whereas' is a contrast connector, here highlighting the difference between urban and rural school outcomes.

Question 12: The gradient of the tangent to f(x) = x³ at x = 2 is:

3
8
12 (Correct answer)
6

Correct answer: 12

f′(x) = 3x², so f′(2) = 3(4) = 12.

Question 13: Solve the inequality: x - 6 < 2.

x > -4
x < 8 (Correct answer)
x > 8
x < 4

Correct answer: x < 8

Add 6 to both sides: x < 8.

Question 14: In the sentence 'The minister's response was evasive,' the word 'evasive' suggests the minister:

Refused to speak at all
Avoided giving a straight answer (Correct answer)
Answered directly and clearly
Gave a written report

Correct answer: Avoided giving a straight answer

'Evasive' describes language that dodges or avoids the question, so the minister avoided a direct answer.

Question 15: A reading passage uses the word 'consequently' to begin a sentence. What relationship does this signpost word indicate?

Sequence in time only
Cause and effect (Correct answer)
Comparison
Contrast

Correct answer: Cause and effect

'Consequently' introduces a result or effect that follows from a previously stated cause, making it a cause-and-effect connector.

Question 16: An academic text refers to 'the latter' when discussing two methods. If the methods mentioned are 'observation and experimentation', what does 'the latter' refer to?

Observation
Experimentation (Correct answer)
Both methods equally
Neither method

Correct answer: Experimentation

'The latter' always refers to the second of two items mentioned. Here the second item is 'experimentation'.

Question 17: A recipe uses flour and sugar in the ratio 3:1. If you use 600g of flour, how much sugar do you need?

100g
600g
200g (Correct answer)
300g

Correct answer: 200g

The ratio 3:1 means sugar is one third of the flour. 600 / 3 = 200g of sugar.

Question 18: Make y the subject: 2y + x = 10.

y = (x - 10)/2
y = 10 - 2x
y = (10 - x)/2 (Correct answer)
y = 10 - x

Correct answer: y = (10 - x)/2

Subtract x: 2y = 10 - x. Divide by 2: y = (10 - x)/2.

Question 19: What is lim(x→2) [(x² − 4) / (x − 2)]?

Undefined
2
4 (Correct answer)
0

Correct answer: 4

Factoring gives (x+2)(x−2)/(x−2) = x+2; substituting x=2 yields 4.

Question 20: What is the area of a rectangle that is 8m long and 5m wide?

40 m^2 (Correct answer)
13 m^2
45 m^2
26 m^2

Correct answer: 40 m^2

Area of a rectangle = length x width = 8 x 5 = 40 m^2.

Question 21: If 60% of a number is 90, what is the number?

150 (Correct answer)
54
120
180

Correct answer: 150

If 60% = 90, then 1% = 1.5, so 100% = 150. The number is 150.

Question 22: Two data sets have the same mean but Set A's values are tightly clustered while Set B's are widely spread. Which set has the greater range?

Range cannot relate to spread
They are equal
Set A
Set B (Correct answer)

Correct answer: Set B

Range measures spread (highest minus lowest). The more widely spread Set B has the larger range.

Question 23: Two angles are complementary and one is 35 degrees. What is the other angle?

145 degrees
325 degrees
55 degrees (Correct answer)
45 degrees

Correct answer: 55 degrees

Complementary angles add to 90 degrees. 90 - 35 = 55 degrees.

Question 24: In academic reading, a 'main idea' of a paragraph is best described as:

The central point the paragraph develops (Correct answer)
The first word of the paragraph
A single supporting example
An unrelated side comment

Correct answer: The central point the paragraph develops

The main idea is the central point a paragraph develops; supporting details and examples explain or back it up.

Question 25: A learner scored 36 out of 45 on a test. What is this as a percentage?

75%
85%
72%
80% (Correct answer)

Correct answer: 80%

36 / 45 = 0.8, which is 80%.

Question 26: If f(x) = eˣ, then f′(x) equals:

x · eˣ⁻¹
eˣ (Correct answer)
ln(x)
e

Correct answer: eˣ

The exponential function eˣ is its own derivative: d/dx[eˣ] = eˣ.

Question 27: A jacket costs R800 and is discounted by 25%. What is the sale price?

R775
R600 (Correct answer)
R750
R200

Correct answer: R600

25% of R800 = R200 discount. Sale price = 800 - 200 = R600.

Question 28: The area under f(x) = 2x from x = 0 to x = 3 is:

3
18
6
9 (Correct answer)

Correct answer: 9

∫₀³ 2x dx = [x²]₀³ = 9 − 0 = 9.

Question 29: A bar graph shows monthly rainfall in Cape Town: Jan 15mm, Feb 17mm, Jun 93mm, Jul 82mm. Which month had the highest rainfall?

February
July
June (Correct answer)
January

Correct answer: June

June recorded 93mm, the largest value shown, so it is the wettest month in the data.

Question 30: Which of the following equals ∫4x³ dx?

4x⁴ + C
x⁴/4 + C
x⁴ + C (Correct answer)
12x² + C

Correct answer: x⁴ + C

∫4x³ dx = 4 · x⁴/4 + C = x⁴ + C by the power rule for integration.

National Benchmark Test (NBT) – South Africa

The NBT assesses the academic readiness of South African school leavers for higher education across Academic Literacy and Mathematics, helping universities determine admission and support needs.

Questions

35 min

Time Limit

70%

To Pass

Checking for saved progress...

Exam Rules

You can skip questions and return to them later
Flag questions for review before submitting
No feedback shown until you submit the entire exam
Unanswered questions count as wrong — answer everything
10 pretest questions are mixed in and don't affect your score
Timer auto-submits when time runs out
Your progress is auto-saved every 30 seconds