Live practice

Use the sequence definition or geometric-progression formula, keeping the first-term offset explicit.

The displayed substitutions cover every requested part and verify the result against the original data.

Apply (a+b)⁵ with a=1 and b=−2x.

Apply the multiplication principle to the hundreds, tens and units places.

Divide by the positive number 24, so the inequality sign is unchanged.

Multiply the factors and use i²=−1.

Use θ radians = θ° × π/180.

Equality of ordered pairs requires equality of corresponding coordinates.

1. A set: January, June and July are objectively determined.
2. Not a set: ‘most talented’ has no fixed criterion.
3. Not a set: ‘best’ depends on judgement.
4. A set: class membership is definite.
5. A set: the condition is precise.
6. A set: authorship is verifiable.
7. A set: evenness is a definite property.
8. A set: the chapter fixes the collection.
9. Not a set: ‘most dangerous’ is subjective.

Each step in a food chain, at which transfer of food and energy takes place, is called a trophic level.

• First trophic level: grass, the producer, fixes solar energy.
• Second trophic level: grasshopper, the primary consumer or herbivore.
• Third trophic level: frog, the secondary consumer.
• Fourth trophic level: snake, the tertiary consumer.

Only a small part of the energy at one level is available to the next level, so food chains usually contain only a few trophic levels.

A compass needle is itself a small magnet. The bar magnet creates a magnetic field at the compass. Opposite forces on the needle's poles form a torque that turns it until its north pole points along the local field direction.