Mathematics — BGCSE

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

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

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.

Answer: P5,291.52

1. Year one: 4800 × 1.06 = 5088
2. Year two: 5088 × 1.04 = 5291.52
3. Money to two decimal places: P5,291.52

Two separate percentage rises never add up to 10%. Use a multiplier for each year and keep every digit until the final rounding.

Answer: x = 4, y = 2

1. From the second equation: x = y + 2
2. Substitute: 3(y + 2) + 2y = 16
3. Expand: 5y + 6 = 16, so y = 2 and x = 4

Substitution is quicker than elimination when one equation already says x = something. Marks are given for the substitution step, so write it before you solve.

Answer: (a) 77 (b) No, because 4n − 3 = 100 gives n = 25.75, and n must be a whole number.

1. (a) 4 × 20 − 3 = 77
2. (b) Set 4n − 3 = 100
3. Solving: n = 25.75, which is not a whole number, so 100 is not in the sequence

Part (b) is an analysis mark, not a guess. Say what you solved and what the non-integer result means — the meaning is the mark.

Answer: x = 20°, largest angle = 80°

1. Angles in a triangle total 180°: 2x + 3x + 4x = 180
2. 9x = 180, so x = 20
3. Largest angle = 4 × 20 = 80°

Two marks are given here even if the arithmetic slips, provided the equation is right. Write the equation, then solve it.

Answer: 15 cm

1. Pythagoras: diagonal² = 9² + 12²
2. = 225
3. Diagonal = 15 cm

The 9-12-15 triangle is a scaled 3-4-5, which appears in papers again and again. Recognising it saves a minute you can spend on a harder question.

Answer: 8.67 bags (2 d.p.)

1. Midpoints: 2, 7, 12, 17
2. fx column: 12, 84, 96, 68 → total 260
3. Frequency total: 30 days
4. Mean = 260 ÷ 30 = 8.67

The midpoints are estimated, so the answer is an estimate — say so if asked to comment. The fx column is not optional: the division is a marked step, and two marks belong to it.

Answer: 1/36

1. Independent events multiply
2. P(6) × P(6) = 1/6 × 1/6 = 1/36

Ask whether the two events are joined by "and" or "or". And multiplies; or adds, after you check nothing overlaps.

Answer: 2x² + 7x − 15

1. Four products: 2x·x, 2x·5, −3·x, −3·5
2. 2x² + 10x − 3x − 15
3. Collect: 2x² + 7x − 15

Write all four products before collecting. Skipping a term is the single most common error in this question type, and it costs the whole mark rather than part of it.

Answer: 3n + 2

1. Common difference = 3, so the rule starts 3n
2. n = 1 gives 3, but the first term is 5, so add 2

One mark, five seconds of checking: substitute n = 1 and n = 2 into your own rule. It is the cheapest verification in the whole paper.

Answer: 5

1. Order the list: 2, 3, 4, 5, 7, 7, 9
2. Seven values, so the median is the 4th
3. Median = 5

Order first, always. With an even count, take the mean of the two middle values — that is where 5.5 style answers come from.