Number flashcards

Topic 1: Number

Prime number

A number with exactly two factors: 1 and itself. 1 is not prime (it has only one factor).

Rational and irrational numbers

Rational: can be written as a/b, where a and b are integers (b ≠ 0). Irrational: cannot be written as a fraction, for example π and √2.

How do you find the HCF and LCM of two numbers?

1. Write each number as a product of prime factors. 2. HCF: multiply the shared primes, each to its lowest power. 3. LCM: multiply every prime, each to its highest power. Example: 56 = 2³ × 7, 210 = 2 × 3 × 5 × 7, so HCF = 14 and LCM = 840.

Sets: formula for n(A ∪ B)

n(A ∪ B) = n(A) + n(B) − n(A ∩ B) n means "number of elements in". Subtract the overlap because it was counted twice.

Write 0.6̇3̇ (0.6363…) as a fraction

x = 0.6363…, so 100x = 63.6363… Subtract: 99x = 63 x = 63/99 = 7/11

Index rules for zero, negative and fractional powers

a⁰ = 1 a⁻ⁿ = 1/aⁿ a^(m/n) = (ⁿ√a)ᵐ: take the root first, then the power. Example: 64^(2/3) = 4² = 16.

Standard form

A × 10ⁿ, where 1 ≤ A < 10 and n is an integer. Examples: 45 000 000 = 4.5 × 10⁷; 0.00306 = 3.06 × 10⁻³. 30 × 10⁴ is not in standard form: write 3 × 10⁵.

A length is 847.6 m to 1 decimal place. Write its bounds.

847.55 ≤ l < 847.65 The bounds are half a unit (0.05) either side. For the largest a − b or a ÷ b, use the upper bound of a with the lower bound of b.

How do you share an amount in a ratio? (240 in the ratio 3 : 5)

1. Add the parts: 3 + 5 = 8. 2. One part = 240 ÷ 8 = 30. 3. Multiply: 3 × 30 = 90 and 5 × 30 = 150.

Reverse percentage: after a 20% discount a coat costs 1920 dollars. Find the original price.

The multiplier for a 20% decrease is 0.8. Original = 1920 ÷ 0.8 = 2400 dollars. Divide by the multiplier; do not take 20% of the new price.

Compound interest formula

Amount = P × (1 + r/100)ⁿ P = principal, r = rate per year (%), n = number of years. Subtract P to get the interest. Example: 480 dollars at 5% for 3 years: 480 × 1.05³ = 555.66 dollars.

How do you rationalise a denominator of the form a + √b?

Multiply top and bottom by a − √b. The denominator becomes a² − b. Example: 9/(4 + √7) = 9(4 − √7)/(16 − 7) = 4 − √7.