Class IX Mathematics Guess Paper 2026

Chapter 1: Real and Complex Numbers

Perform the following operations:

• (2, −3) + (−1, 7)
• (4, −5)(5, −4)
• (3, −7) ÷ (3, 2)
• (4, 5) ÷ (2, −3)
• (15, 12) − (10, −9)
• (0, −6)(8, 5)

Q1: If z₁ = −4 + 6i and z₂ = 4 − 2i, verify that:
(i) z₁ + z̅₂ = z̅₁ + z̅₂
(ii) z₁ − z̅₂ = z̅₁ − z̅₂

Q2: If z₁ = 2 − 7i and z₂ = −2 − 3i, verify that:
(i) z₁z̅₂ = z̅₁z̅₂
(ii) (z₁/z₂)̅ = z̅₁ / z̅₂

Chapter 2: Logarithm

Find values using logarithms:

• 25.753 × 0.5341 × 490.8
• 25.753 / 0.5341
• (239 × 20.45) / 19.12
• 99.87 / (8.369 × 0.785)
• ⁵√2.709 × ⁷√1.239
• (4308)³ × √80.06 / (0.3387)³

Chapter 3: Algebraic Expressions & Formulas

Using formulas:

• Find a − b if a + b = 9, ab = 20
• Find a² + b² and ab if a + b = 8, a − b = 6
• Find a² + b² + c² if a + b + c = 9, ab + bc + ac = 13
• Find a + b + c if ab + bc + ac = 0.8 and a² + b² + c² = 0.9
• Find a³ + b³ if a + b = 4, ab = 3
• Find ab if a³ + b³ = 5, a + b = 5
• Find 125x³ + y³ if 5x + y = 13, xy = 10
• Find 216x³ + y³ if 6x + y = 11, xy = 8
• Find x³ + 1/x³ if x + 1/x = 7
• Find y² + 1/y² if y + 1/y = 4
• Find x³ − 1/x³ if x − 1/x = 11

Simplify:

• √(81x⁻³z⁴⁴)
• √[(216)^(2/3) × (125)^(1/2) × (0.04)^(-3/4)]
• √(256a⁶b¹²c⁹³)

Find the value:

• If x = 8 − 3√7, find (x + 1/x)²
• If x = 3 − 2√2, find x² + 1/x²
• If x = 3 − 2√2, find x² − 1/x²
• If 1/x = 2√28 − 11, find x² + 1/x²
• If 1/y = 2 + √3, find y⁴ + 1/y⁴
• If x = √5 + 2, find x⁴ + 1/x⁴
• If 1/z = 7 − 4√3, find z² − z⁻²

Chapter 4: Factorization

(Exercise 4.6 – 4.8)

Remainder Theorem:

• x³ + 6x² + 11x + 8 ÷ (x + 1)
• (2y + 1)³ − 6(3 − 4y) − 10 ÷ (2y − 1)
• x³ − 3x² + 4x − 14 ÷ (x + 2)
• x⁴ + x²y² + y⁴ ÷ (2y − 1)

Find k if 4x³ − 7x² + 6x + 3k is divisible by (x + 2)

Find r if (y + 2) is factor of 3y² − 4xy − 4r²

Synthetic Division:

• x³ + 6x² + 11x − 6 ÷ (x − 2)
• x⁴ + x³ − x² + x − 1 ÷ (x − 1)
• 2x⁴ − 2x³ + 100x² − 168x + 95 ÷ (x − 2)

Find value of constants (k, m) for factors/zeros.

Factorization:

• x³ − 6x² + 11x − 6
• 6x³ + 7x² − x − 2
• x³ + 5x² − 4x − 20
• x³ + 12x² + 44x + 48

Chapter 5: Algebraic Manipulation

HCF (Division Method):

• 2x³ + 15x² + 31x + 12 and 3x³ + 23x² + 50x + 24
• x² + xy − 2y², x³ + 3y + 2y³, x³ + 3x²y + 2xy² + 2y³

HCF (Factorization Method):

• x² − 3x − 18 and x² + 5x + 6
• (2a² − 8b²), (4a² + 4ab − 24b²), (2a² − 12ab − 16b²)
• 4x² − 9 and 2x² − 5x + 3

LCM (Factorization Method):

• 2x² − 14x and 3x² − 5x + 2
• 6x² + 11x + 3, 2x² − 5x − 11, 3x² − 11x − 4
• x² + 11x + 28 and x² + x − 12

Chapter 6: Linear Equations & Inequalities

Solve:

• (2x − 4)/5 = (5x − 12)/4
• (12x − 3)/15 = (7x + 4)/10
• (1/4)x + x = −3 + (1/2)x
• 1/3 + 2m = m − 3/2

Square Root Equations:

• 6 + √x = 7
• √x + 9 = 7
• √(4x + 5) = √(3x − 7)
• √(25y − 25) = √(y − 2)

Absolute Value: Solve equations and inequalities.

Chapter 7: Linear Graphs

• 3x − 11 = y, x − 3y = 9
• 3x = 5y − 2, 3x + 5y = 8
• 3x − 2y = 1, 2x + 3y = 13

Chapter 8: Quadratic Equations

Factorization:

• x² + 5x + 6 = 0
• 12x² − 41x + 24 = 0
• (x − 5)² − 9 = 0
• (3x + 4)² − 16 = 0

Quadratic Formula:

• x² − 2x = 15
• 10x² + 19x − 15 = 0
• 9x² = 12x − 49

Chapter 9 – 15: Theorems

• Triangle congruency
• Parallelogram properties
• Angle bisectors
• Triangle inequalities
• Areas
• Apollonius theorem

Chapter 16: Coordinate Geometry

Distance Formula:

• (−4, 5) and (6, 6)
• (2, 2) and (2, 3)
• (0, 1) and (2, 3)
• (5, −1) and (2, −3)

Applications:

• Perimeter of triangle
• Collinearity
• Triangle types
• Square/rectangle verification
• Parallelogram proof

Midpoint Formula: Find midpoints of given pairs.

Circle Problems:

• Centre from diameter
• Radius calculation