Mixed Deck — All NBT Topics Flashcards

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

Answer: Distorted or biased

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

Expand: (x + 2)(x + 3).

Answer: x^2 + 5x + 6

FOIL: x^2 + 3x + 2x + 6 = x^2 + 5x + 6.

The circumference of a circle is given by which formula (r = radius)?

Answer: 2 pi r

Circumference = 2 pi r (or pi d). The area, by contrast, is pi r^2.

Solve the inequality: x - 6 < 2.

Answer: x < 8

Add 6 to both sides: x < 8.

The average rate of change of f(x) = x² from x = 1 to x = 3 is:

Answer: 4

[f(3) − f(1)] / (3 − 1) = (9 − 1) / 2 = 8/2 = 4.

Which of the following equals ∫4x³ dx?

Answer: x⁴ + C

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

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

Answer: 3:2

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

If f(x) = eˣ, then f′(x) equals:

Answer: eˣ

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

If a passage describes a plan as 'feasible', the writer believes the plan is:

Answer: Capable of being done successfully

'Feasible' means practical and capable of being done, so the writer thinks the plan can realistically be carried out.

The period of f(x) = sin(2x) is:

Answer: π

The period of sin(bx) is 2π/b; with b = 2 the period is 2π/2 = π.

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

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.

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

Answer: cos(x)

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

The range of f(x) = −x² + 3 is:

Answer: y ≤ 3

The parabola opens downward with vertex at (0, 3), so the maximum output is 3 and f(x) ≤ 3 for all x.

The transformation that maps f(x) to f(x + 2) − 3 is:

Answer: Shift left 2 and down 3

Replacing x with x+2 shifts the graph 2 units left; subtracting 3 outside shifts it 3 units down.

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

Answer: Avoided giving a straight answer

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

Petrol increases from R20 to R23 per litre. What is the percentage increase?

Answer: 15%

Increase = R3 on R20. 3 / 20 = 0.15 = 15% increase.

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?

Answer: Set B

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

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

Answer: June

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

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

Answer: 9

∫₀³ 2x dx = [x²]₀³ = 9 − 0 = 9.

In a right-angled triangle, sin(theta) is defined as:

Answer: opposite / hypotenuse

By definition, sin(theta) = opposite side / hypotenuse (the 'SOH' in SOH-CAH-TOA).