Grade 10 — Term 3

Rate

What you must know

• The average speed trap: Average speed is NEVER the simple arithmetic mean of two speeds; it must always be calculated as (Total Distance) / (Total Time).
• Unit compatibility: If speed is in km/h and time is in minutes, convert time to hours (e.g., 45 minutes = 45/60 = 0.75 hours) before multiplying.
• Tank filling/emptying problems: If pipe A fills a tank in 3 hours (rate = 1/3 tank/h) and pipe B empties in 4 hours (rate = 1/4 tank/h), net filling rate = 1/3 - 1/4 = 1/12 tank/h.

Try one question

Water flows into an empty rectangular water tank of base area 2.5 m² at a uniform rate of 150 litres per minute. By how many centimetres does the water level rise in 20 minutes?

1. A. 12 cm
2. B. 150 cm
3. C. 120 cm
4. D. 60 cm

Show the answer

Answer: C. 120 cm. Total volume in 20 min = 150 L/min × 20 min = 3000 L = 3 m³ (since 1000 L = 1 m³). Height = Volume / Base Area = 3 m³ / 2.5 m² = 1.2 m = 120 cm.

A model question written by Idasara on the exam pattern. It is not from a past paper.

Formulae

What you must know

• Clearing fractions first: When a formula contains fractions, multiply every term on both sides by the Lowest Common Multiple (LCM) of all denominators before rearranging.
• Target variable under radical/fraction: If target variable x is under a square root (e.g., T = 2π√(L/g)), isolate radical first, then square both sides: T² = 4π²(L/g) => g = (4π²L) / T².
• Target variable in denominator: Cross-multiply to bring the target variable to the numerator; NEVER leave the isolated subject in the denominator.

Try one question

Make 'r' the subject of the formula: A = 4πr² (where r > 0).

1. A. r = (A / 4π)²
2. B. r = A / (4π)
3. C. r = √(4πA)
4. D. r = √(A / (4π))

Show the answer

Answer: D. r = √(A / (4π)). Divide both sides by 4π: r² = A / (4π). Taking positive square root since r > 0: r = √(A / (4π)).

A model question written by Idasara on the exam pattern. It is not from a past paper.

Triangle Angle Theorems

What you must know

• Parallel lines requirement: Alternate and corresponding angles are ONLY equal when the lines are strictly parallel; always confirm parallel markings (arrows) before equating.
• Angle theorem abbreviation standards: In Paper 1 Part A, write recognized reasons: 'alt. ∠s, AB // CD', 'corr. ∠s, PQ // RS', 'vert. opp. ∠s'.
• Constructing auxiliary parallel lines: In stepped zig-zag lines between parallel boundaries, draw an auxiliary parallel line through the vertex to decompose the angle.

Try one question

In right-angled triangle ABC, angle B = 90°. If angle A = 2x and angle C = 3x, find the value of x.

1. A. 20°
2. B. 36°
3. C. 15°
4. D. 18°

Show the answer

Answer: D. 18°. The acute angles of a right-angled triangle sum to 90°: angle A + angle C = 90° → 2x + 3x = 90° → 5x = 90° → x = 18°.

A model question written by Idasara on the exam pattern. It is not from a past paper.

Linear Inequalities

What you must know

• The forgotten sign reversal trap: Forgetting to flip the inequality sign when dividing by a negative coefficient (e.g., writing -x > 4 ⟹ x > -4 instead of x < -4) is the most frequent blunder in Paper 1 Part A.
• Open vs closed circle on number lines: Drawing a solid dot for < or an open dot for ≤ loses plotting marks.
• Positive integer requirements: When questions ask for 'positive integer solutions', exclude 0 and all negative values.

Try one question

Find the set of all integer values of x that satisfy the inequality: 3x - 5 < 7 and x ≥ 1.

1. A. {2, 3}
2. B. {1, 2, 3, 4}
3. C. {0, 1, 2, 3}
4. D. {1, 2, 3}

Show the answer

Answer: D. {1, 2, 3}. 3x - 5 < 7 → 3x < 12 → x < 4. Combined with x ≥ 1, the range is 1 ≤ x < 4. The integers in this interval are 1, 2, and 3.

A model question written by Idasara on the exam pattern. It is not from a past paper.

Frequency Distributions

What you must know

• Assumed mean selection: Always choose A from the mid-values (x) column, ideally near the center with a high frequency; NEVER choose A from the frequency column.
• Deviation sign discipline: d = x - A; deviations below A are negative, deviations above A are positive; sum Σ fd algebraically taking signs into account.
• Stating the mean: Ensure the final calculated mean carries the problem's physical units (e.g., kg, hours, Rs.) and is rounded to specified decimal places.

Try one question

In a grouped frequency distribution, a class interval is given as 20 - 30. What is the class mark (mid-value) of this class interval?

1. A. 10
2. B. 24.5
3. C. 25.5
4. D. 25

Show the answer

Answer: D. 25. The class mark (mid-value) of a class interval is the average of its limits: (lower limit + upper limit) / 2 = (20 + 30) / 2 = 25.

A model question written by Idasara on the exam pattern. It is not from a past paper.

Chord-Centre Theorem

What you must know

• Radius as hypotenuse: In the right-angled triangle formed by the radius, half-chord, and perpendicular distance, the RADIUS (r) is always the hypotenuse opposite the right angle.
• Diameter vs radius trap: If diameter is given in the problem, divide by 2 to obtain radius r before applying Pythagoras' theorem.
• Distance between parallel chords: For two parallel chords on OPPOSITE sides of the centre, sum their distances (d₁ + d₂); for chords on the SAME side of the centre, subtract their distances (|d₁ - d₂|).

Try one question

A chord of length 16 cm is drawn in a circle of radius 10 cm. Find the perpendicular distance from the centre of the circle to the chord.

1. A. 6 cm
2. B. 5 cm
3. C. 8 cm
4. D. 7 cm

Show the answer

Answer: A. 6 cm. The perpendicular from the centre to a chord bisects the chord (half chord = 16/2 = 8 cm). By Pythagoras' theorem in the right triangle: d² + 8² = 10² → d² + 64 = 100 → d² = 36 → d = 6 cm.

A model question written by Idasara on the exam pattern. It is not from a past paper.

Constructions

What you must know

• Never erase construction arcs: Erasing construction arcs forfeits all method marks in Paper 2 Part B geometric construction questions.
• Compass sharpness: Ensure compass pencil is razor-sharp; double-lines, fuzzy arcs, or blunt impressions incur accuracy penalties.
• Measurements validation: Measure the constructed lengths and angles with ruler/protractor and write the values down clearly when requested in sub-questions.

Try one question

Using a straightedge and compasses only, which of the following angles can be constructed directly by bisecting a 60° angle?

1. A. 45°
2. B. 15°
3. C. 30°
4. D. 75°

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Answer: C. 30°. Bisecting a 60° angle (which is constructed as an angle of an equilateral triangle) yields exactly 30° (60° / 2 = 30°).

A model question written by Idasara on the exam pattern. It is not from a past paper.

Surface Area and Volume

What you must know

• Slant height vs vertical height in cone: In curved surface area πrl, use SLANT height l; in volume (1/3)πr²h, use VERTICAL perpendicular height h.
• Solid hemisphere total area: Total surface area of a SOLID hemisphere includes the flat circular base: 2πr² + πr² = 3πr², NOT 2πr².
• Volume-capacity liquid conversion: 1 litre = 1000 cm³; 1 m³ = 1000 litres; master these conversion factors for water tank problems.

Try one question

A solid metal cuboid of dimensions 10 cm × 8 cm × 5 cm is melted and recast into small cubes of edge 2 cm. How many small cubes can be formed without any loss of metal?

1. A. 25
2. B. 40
3. C. 100
4. D. 50

Show the answer

Answer: D. 50. Volume of cuboid = 10 × 8 × 5 = 400 cm³. Volume of one small cube = 2³ = 8 cm³. Number of small cubes = 400 / 8 = 50 cubes.

A model question written by Idasara on the exam pattern. It is not from a past paper.

Probability

What you must know

• With replacement vs Without replacement: In drawing problems, 'without replacement' reduces both the numerator and the denominator of the total items on the second draw.
• Branch probability sum: The sum of probabilities emanating from any single node on a tree diagram MUST always equal 1.
• 'At least one' shortcut: Calculate P(at least one success) = 1 - P(no successes) to save extensive branch additions.