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Punjab (PTB) · 9th Class Mathematics paper scheme (Punjab boards) · Free

9th Class Mathematics Board Pattern Paper 2026

75 marks · About 2 hours 40 minutes · 47 questions. Covers: 13 chapters (UNIT 1: Real Number to UNIT 13: Probability).

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9th Class Mathematics Board Pattern Paper 2026

9th Class · Mathematics · Punjab (PTB)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 75Time: About 2 hours 40 minutes

Q1. Multiple choice questions (Attempt all · 15 × 1 = 15)

  1. Which one tells us how often a specific event occurs relative to the total number of frequency event or trials?

    1. Expected frequency

    2. Sum of relative frequency

    3. Relative frequency

    4. Frequency

  2. The inequality represents:

    1. A parabola 

    2. A straight line 

    3. A shaded region 

    4. A single point 

  3. What is the formula for the weighted mean? 

    1. Weighted=

    2. Weighted mean = ?(wx) × Ew

    3. Weighted mean = ?(wx) – S? 

    4. Weighted mean = ?(wx) + Ew

  4. The square root of  is:

  5. Convert  radians to degrees. 

  6. Example of equal set:

    1. {a,b,c}, {1,2,3}

    2. {1,2,3}, {2,1,3}

    3. Both a and b

    4. None of these

  7. Expand:

  8. In an equilateral triangle, what is the measure of each angle?

  9. In a reciprocal function  as x approaches zero, what happens to y? 

    1. It approaches infinity

    2. It approaches zero

    3. It becomes undefined

    4. It remains constant

  10. A line passing through points (1,2) and (4,5) is:

    1. y = x + 1

    2. y = 2x + 3

    3. y = 3x - 2

    4. y = x + 2

  11. What is the angle formed by two intersecting rays from a vertex in a triangle called? 

    1. Complementary angle

    2. Opposite angle

    3. Vertical angle

    4. Exterior angle

  12. A profit of 20% on cost price of Rs. 500 means the selling price is:

    1. Rs 600

    2. Rs 400

    3. Rs 550

    4. Rs 700

  13. The circumference of a circle with radius r is:

    4. None of these

  14. The relative frequency of selecting a red ball from 80 students is: 

    1. 0.29

    2. 0.19

    3. 0.31

    4. 0.12

  15. The intersection of two half-planes is known as: 

    1. A vertex 

    2. A feasible region 

    3. A line 

    4. A parabola 

Q2. Short questions (Attempt any 6 of 9 · 6 × 2 = 12)

  1. Solve following inequality and represent the solution on a real line:

  2. Insert two rational numbers between:  and 

  3. Is there any set which has no proper subset? if so, name that set.

  4. Find logarithm of the following number:

  5. Factorize:

  6. Solve the following linear inequalities in xy-plane.

  7. Represent on a number line.

  8. Let , ,  and  List the member of the following set: 

  9. Express the following in logarithmic form: 

Q3. Short questions (Attempt any 6 of 9 · 6 × 2 = 12)

  1. Formulate simple deductive proof's of the following algebraic expression, prove that L.H.S is equal to the R.H.S.

  2. A company manufactures school bags. The function of producing x bags is C(x)= 1200 + 800x and the revenue from selling x bags is R(x)=50x. Determine the profit or loss when 250 bags are sold.

  3. In a landscaping project, the path starts at (2,3) and ends at (10,7). Find the midpoint.

  4. A toy manufacturer produces model cars which are similar in every way to the actual cars. If the ratio of the door area of the model to the door area of the car is 1 cm to 2500 cm, find: the ratio of the capacities of their petrol tanks.

  5. Find in which quadrant the following angles lie. Write a co-terminal angle for the following:

  6. Define tautology.

  7. How do you identify an exponential function from a table of values?

  8. The points and are ends of a diameter of a circle. Find the centre and radius of the circle.

  9. Find the missing value in the following similar solid:

Q4. Short questions (Attempt any 6 of 9 · 6 × 2 = 12)

  1. The arithmetic mean of 45 numbers is 80. Find their sum.

  2. What is a favorable outcome?

  3. Construct the following triangles and find whether there exists any ambiguous case: and .

  4. Following are the number of telephone calls made in a week to 30 teachers of high school:

    5 8 11 25 13 16 20 17 15 16 30 21 14 18 19
    6 22 26 15 19 35 29 31 23 25 20 10 9 7 26

    Construct a frequency distribution with number of classes?

  5. What is the probability of rolling a double six with two dice?

  6. Construct with the given measurements and verify that the perpendicular bisectors of the triangle are concurrent: and

  7. Usman rolled a fair dice eight times. Each time their sum was recorded as 8,5,6,6,9,4,3,11. Find the median and mode of the sum.

  8. The probability that Ayesha will pass the examination is 0.85. What will be the probability that Ayesha will not pass the examination?

  9. What is an ambiguous case in triangle construction?

Q5. Long questions (Attempt any 3 of 5 · 3 × 8 = 24)

  1. Let, ,  and : Find

  2. The heights (in inches) of 200 students are recorded in the following frequency distribution. Find the mean height of the student by short formula:

    Height (x) (in inches) 51 52 53 54 55 56 57 58 59 60
    Frequency (f) 2 5 8 24 55 45 38 16 6 1

  3. A drone is flying from point (2,3) to point (10,15) on the grid. Calculate the gradient of the line along which the drone is flying and the total distance travelled.

  4. A tessellation is created by repeatedly reflecting a basic shape. The basic shape is a right-angled triangle with sides of lengths 3, 4 and 5 units. Find: The minimum number of reflections needed to create a tessellation that covers a square with an area of 3600 square units.

  5. Plot the graph of the following quadratic and cubic function: