NBT flashcards
NBT · Build recall with a focused review session.
32 cards. Read the term and the definition here. The deck at the top of this page is optional.
- Percentage change formula
- Percentage change equals the new value minus the original value, divided by the original value, then multiplied by 100.
- Dividing in a given ratio
- Add the ratio parts to get the total number of parts, divide the quantity by that total, then multiply by each part separately.
- Average speed
- Average speed is the total distance travelled divided by the total time taken; it is not the average of the separate speeds.
- Compound interest formula
- A = P(1 + r)ⁿ, where P is the principal, r the interest rate per period written as a decimal, and n the number of periods.
- Simple interest formula
- A = P(1 + rn), where P is the principal, r the rate per period as a decimal and n the number of periods; interest is not added to the balance.
- Finding the whole from a percentage
- If 15% of a number is 45, divide the part by the decimal percentage: 45 divided by 0.15 gives 300.
- Hectare in square metres
- One hectare equals 10 000 square metres, which is the area of a square measuring 100 metres by 100 metres.
- Valid inference rule
- A valid inference must follow necessarily from the information given; a statement that only could be true is not supported by the passage.
- Hedging versus absolute words
- Words such as may, suggests and appears weaken a claim and make it easier to defend, while always, never and all make it absolute and harder to support.
- Author's tone
- Tone is revealed through word choice: approving, critical, neutral or ironic adjectives signal the writer's attitude towards the subject being discussed.
- Gradient as rate of change
- On a graph the gradient of a line gives the rate of change, so a steeper line means the quantity is changing faster.
- Area under a rate graph
- The area under a graph of rate against time equals the total accumulated, for example distance from a speed–time graph.
- Reading tables: units and totals
- Check the unit given in each column heading and whether the figures are totals or averages before comparing rows or calculating differences.
- Quadratic formula
- x equals negative b plus or minus the square root of b squared minus 4ac, all divided by 2a, for ax² + bx + c = 0.
- Discriminant
- For ax² + bx + c = 0 the discriminant is b² − 4ac: positive gives two real roots, zero gives one repeated root, negative gives no real roots.
- Logarithm product law
- The logarithm of a product equals the sum of the logarithms: log(ab) = log a + log b, for any valid base with a and b positive.
- Logarithm power law
- log(aⁿ) = n log a; the exponent moves to the front as a multiplier, which is used to solve equations with an unknown exponent.
- Arithmetic sequence nth term
- Tₙ = a + (n − 1)d, where a is the first term and d is the constant difference between consecutive terms in the sequence.
- Geometric series sum
- Sₙ = a(1 − rⁿ) ÷ (1 − r), provided r is not equal to 1, where a is the first term and r the constant ratio.
- Sine rule
- In any triangle, a ÷ sin A = b ÷ sin B = c ÷ sin C, where each side is opposite the angle named with the same letter.
- Cosine rule
- a² = b² + c² − 2bc cos A, used when you know two sides and the included angle or all three sides of a triangle.
- Pythagorean identity
- sin²θ + cos²θ = 1 for every angle θ, and tan θ equals sin θ divided by cos θ wherever cos θ is not zero.
- Gradient between two points
- m = (y₂ − y₁) ÷ (x₂ − x₁) gives the gradient of the line through two points, and parallel lines have equal gradients.
- Perpendicular gradients
- Two lines are perpendicular when the product of their gradients equals −1, so one gradient is the negative reciprocal of the other.
- Circle area and circumference
- The area of a circle is πr² and its circumference is 2πr, where r is the radius of the circle.
- Power rule for derivatives
- The derivative of xⁿ is nxⁿ⁻¹; setting the derivative equal to zero locates the stationary points of a function.
- Chain rule
- The derivative of f(g(x)) is f′(g(x)) multiplied by g′(x); differentiate the outer function, then multiply by the inner derivative.
- Probability addition rule
- P(A or B) = P(A) + P(B) − P(A and B); subtract the overlap so outcomes belonging to both events are not counted twice.
- Independent events
- Events are independent when P(A and B) = P(A) × P(B); the outcome of one event does not change the probability of the other.
- Complementary probability
- P(not A) = 1 − P(A); the probabilities of all mutually exclusive outcomes in a sample space together add up to 1.
- Future value annuity
- FV = x[(1 + i)ⁿ − 1] ÷ i, where x is the regular payment, i the interest rate per period and n the number of payments made.
- Exponential decay formula
- A = P(1 − r)ⁿ models repeated percentage decrease, where r is the rate per period as a decimal and n the number of decreases.