Grade 10 — Term 1

Perimeter

What you must know

• The missing radius trap: The perimeter of a sector is the arc length plus both radii — leave out +2r and the figure you have given is the arc alone.
• Compound shape internal lines: Shaded or dashed internal boundaries must strictly be excluded from perimeter calculations.
• Value of π: Use π = 22/7 when radius or diameter is a multiple of 7; otherwise use the specified value and state exact units (cm, m).

Square Root

What you must know

• Digit pairing rule: Grouping MUST start from the decimal point: whole numbers paired right-to-left (e.g., 1,44.00), decimals paired left-to-right (e.g., 0.05,20).
• Decimal place precision: To find square root correct to 2 decimal places, continue division until 3 decimal digits are obtained, then round appropriately.
• Square root of fractions: √(a/b) = √a / √b; if denominator is not a perfect square, rationalize denominator first: √(a/b) = √(ab) / b.

Try one question

Find the square root of 53 to the first decimal place by division or approximation method.

1. A. 7.5
2. B. 7.3
3. C. 7.7
4. D. 7.1

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

Fractions

What you must know

• The 'remaining' fraction trap in Paper 2 Part A: If 1/4 is spent, the remainder is 3/4; spending 1/3 OF THE REMAINDER equals (1/3) × (3/4) = 1/4, NOT 1/3 of the total.
• Reciprocal in division: Never invert the dividend (the first fraction); strictly invert the divisor (the second fraction).
• Mixed numbers conversion: Always convert mixed numbers to improper fractions before performing multiplication or division.

Try one question

Simplify: $\left(\frac{3}{4} + \frac{1}{6}\right) \div \left(\frac{5}{8} - \frac{1}{4}\right)$

1. A. $2\frac{4}{5}$
2. B. $1\frac{4}{9}$
3. C. $2\frac{2}{9}$
4. D. $2\frac{4}{9}$

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

Binomial Expressions

What you must know

• The dropped middle term trap: Writing (a + b)² = a² + b² or (a - b)² = a² - b² is a severe algebraic blunder; never omit the middle term ±2ab.
• Sign rule for (a - b)²: The final term +b² is ALWAYS positive because (-b)² = +b²; only the middle term -2ab is negative.
• Mental arithmetic evaluation: Use algebraic identities for rapid numerical calculations, such as 102² = (100 + 2)² = 10000 + 400 + 4 = 10404.

Try one question

Expand and simplify the algebraic product: (2x - 3)(3x + 4).

1. A. 6x² - 12
2. B. 6x² - x - 12
3. C. 6x² - 5x - 12
4. D. 6x² + x - 12

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

Congruence of Triangles

What you must know

• The non-included angle trap in SAS: The angle MUST be between the two equal sides; SSA (Side-Side-Angle) is NOT a valid congruence criterion.
• State reasons for every statement: In formal geometric proofs (Paper 2 Part B), every stated equality must cite a valid geometric reason (e.g., 'common side', 'vertically opposite angles', 'radii of same circle').
• Deductions from congruence: Once triangles are proven congruent, state corresponding elements clearly (e.g., 'AB = XY (corresponding sides of congruent triangles)').

Try one question

In triangles ABC and PQR, AB = PQ, BC = QR, and angle B = angle Q. Under which geometric congruence condition are triangles ABC and PQR congruent?

1. A. Side-Angle-Side (SAS)
2. B. Side-Side-Side (SSS)
3. C. Angle-Side-Angle (ASA)
4. D. Right angle-Hypotenuse-Side (RHS)

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

Area

What you must know

• Perpendicular height requirement: In triangles, parallelograms, and trapeziums, ALWAYS use the vertical perpendicular height (h), NEVER the slanted edge length.
• Area units: State final answers in square units (cm², m²); never write linear units (cm, m) for area.
• Shaded area problems (Paper 1 & Paper 2): Clearly state the outer shape formula minus the inner cutout formula before substituting numerical values.

Try one question

A trapezium has parallel sides of lengths 12 cm and 18 cm. If the perpendicular distance between the parallel sides is 8 cm, what is the area of the trapezium?

1. A. 120 cm²
2. B. 96 cm²
3. C. 144 cm²
4. D. 240 cm²

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

Factors of Quadratic Expressions

What you must know

• Sign errors in middle-term splitting: If c is positive, both p and q share the sign of b; if c is negative, p and q have opposite signs, with the larger magnitude matching the sign of b.
• Incomplete factorisation penalty: Expressions like 2x² - 8 must be factored completely as 2(x² - 4) = 2(x - 2)(x + 2); leaving 2(x² - 4) forfeits full marks.
• Negative leading coefficient: When factoring -x² + bx + c, extract -1 first: -(x² - bx - c).

Triangles

What you must know

• Exterior angle misidentification trap: The exterior angle is formed between the produced line and the adjacent side, NOT the reflex angle or vertical opposite angle.
• Proof justification in angle-chasing problems: In Paper 1 Part A, always cite geometric theorems concisely (e.g., 'ext. angle of △', 'angles on a straight line = 180°', 'angles opposite equal sides').
• Triangle existence check: To verify if side lengths (a, b, c) can form a triangle, verify that the sum of the two smaller sides exceeds the longest side.

Try one question

In triangle ABC, the side BC is produced to D. If angle ABC = 55° and angle BAC = 65°, find the magnitude of the exterior angle ACD.

1. A. 60°
2. B. 110°
3. C. 120°
4. D. 130°

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

Inverse Proportion

What you must know

• Direct vs Inverse proportion trap: In direct proportion y/x = constant (cross-multiply); in inverse proportion x × y = constant (multiply across rows).
• Added workers problem: If 6 workers take 10 days, total = 60 man-days; to finish in 4 days requires 60 / 4 = 15 workers; the ADDED workers needed = 15 - 6 = 9 workers.
• Units in rates: Ensure time units (hours, days, weeks) are consistent across all terms before equating products.

Try one question

6 workers take 12 days to complete constructing a boundary wall. How many days will it take for 9 workers working at the same rate to complete the same wall?

1. A. 6 days
2. B. 9 days
3. C. 10 days
4. D. 8 days

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

Data Representation

What you must know

• The 360° total validation: The sum of all calculated sector angles in a pie chart MUST equal exactly 360°; check your angle arithmetic before drawing.
• Protractor precision in Paper 1 Part B & Paper 2: Align the protractor origin precisely with the circle centre and baseline; inaccurate angles lose plotting marks.
• Label every sector: Every sector in a pie chart must clearly display its category name and calculated angle or frequency.

Try one question

In a pie chart representing the preferred subjects of 720 students, the sector angle for Mathematics is 80°. How many students prefer Mathematics?

1. A. 200
2. B. 180
3. C. 140
4. D. 160

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