Order of operations, fractions, standard form

Answer: 5/4 (that is 1¼)

1. Convert to a common denominator of 12: 8/12 + 9/12 − 2/12
2. Add and subtract the numerators: 15/12
3. Cancel to lowest terms: 5/4

Examiner technique: Three fractions in one line is a denominator question, not a fraction question. Find the lowest common multiple once, convert once, then work in a single line so a slip costs one mark instead of three.

Answer: 4.2 × 10⁻⁴

1. Move the point four places to get 4.2
2. Smaller than one, so the index is negative

• A. 4.2 × 10⁻⁴ — Correct: the decimal point moves four places, and the number is smaller than 1 so the index is negative.
• B. 42 × 10⁻⁵ — The value is right but the form is wrong: standard form requires a number between 1 and 10 before the power.
• C. 4.2 × 10⁻⁵ — One place out. Count the moves again: 0.00042 → 0.0042 → 0.042 → 0.42 → 4.2 is four moves.
• D. 0.42 × 10⁻³ — Also an incorrect first factor, and the same one-place error.

Examiner technique: Two things are marked here: the number in front must be between 1 and 10, and the index sign follows the direction you moved the point.