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9th Class Mathematics Board Pattern Paper 2026

9th Class · Mathematics · Federal (FBISE)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 75Time: 3 hours (Section A: 1 hour 10 minutes)

Q1. Multiple choice questions (Attempt all · 48 × 0.75 = 36)

x² − 9 can be factorized as:
1. (x − 3)(x + 3)
2. (x − 9)(x + 1)
3. (x − 3)²
4. (x + 3)²
If a.b = 1, what is be called?
1. multiplicative inverse of a
2. additive identiy
3. multiplicative identity
4. self-multiplicative inverse
Mid-point of ( c , d ) and ( - d , c ) is.
1. $\left(\frac{c-d}{2},\frac{c+d}{2}\right)$
2. $\left(\frac{-c-d}{2},\frac{d-c}{2}\right)$
3. $\left(\frac{-d+c}{2},\frac{c-d}{2}\right)$
4. ( c - d , - d + c )
Which of the following is measure of central tendency?
1. variance
2. standard deviation
3. range
4. arithmetic mean
For three sets, the central region of a Venn diagram represents:
1. A ∪ B ∪ C
2. A ∩ B ∩ C
3. A − B
4. A′
If a tower is 100 m high and tan θ = 1, horizontal distance from tower is:
1. 50 m
2. 100 m
3. 150 m
4. 200 m
If slopes of two lines are m₁ and m₂, then tan θ is:
1. (m₂−m₁)/(1+m₁m₂)
2. (m₁+m₂)/(1−m₁m₂)
3. m₁m₂
4. m₂/m₁
In the figure, AB = 21 cm and P divides AB in the ratio 3 : 4. What is length of $\overline{AP}$ ?
1. 8 cm
2. 10 cm
3. 12 cm
4. 9 cm
log 125 can be written as:
1. log 5
2. 2 log 5
3. 3 log 5
4. 5 log 3
Which one is the standard form of linear equation?
1. $ax^2 + b = 0$
2. ax + b = -c
3. ax + b > 0
4. ax + b = 0
If LM = 4 cm, MN = 4.7 cm and ∠M = 120°, the given angle lies between:
1. LM and MN
2. LM and LN
3. MN and LN
4. None
a/b + c/b equals:
1. (a + c)/b
2. (a + c)/2b
3. ac/b
4. a+c
Which of the following sets have the closure propetry w.r.t. multiplication?
1. { -1 , -2 }
2. { 0 , -1 }
3. { 0 , 1 }
4. ${ 1 , \sqrt{2} }$
( 5 , 2 ) , ( 7 , 0 ) , ( 1 , - 2 ) and ( -1 , 0 ) are the vertices of a
1. parallelogram
2. square
3. trapezium
4. kite
For class interval 31–40, the class mark is:
1. 35
2. 35.5
3. 36
4. 40.5
An ordered pair is written as:
1. {a, b}
2. (a, b)
3. [a, b]
4. a + b
To convert degrees into radians, multiply by:
1. π/180
2. 180/π
3. 60
4. 360
Slope of the line joining (−2, 4) and (1, −3) is:
1. $-\frac{7}{3}$
2. $\frac{7}{2}$
3. $-\frac{3}{7}$
4. $\frac{1}{7}$
A regular polygon has exterior angle 15°. Number of sides is:
1. 20
2. 21
3. 24
4. 25
5 log 2 - 2 log 5 is
1. $\frac{(\log 2)^5}{(\log 5)^2}$
2. $\frac{\log 2^5}{\log 5^2}$
3. $\frac{\log 2^2}{\log 5^5}$
4. $\frac{5}{2}log\frac{2}{5}$
The symbol “>” means:
1. Less than
2. Greater than
3. Equal to
4. Not equal to only
Which instrument is used to draw an arc of a specified radius?
1. Protractor
2. Compass
3. Set square
4. Scale only
√(x²) is:
1. x only
2. ±x
3. x²
4. 2x
A person walks 3.5 km/h for 12 hours. The total distance is:
1. 36 km
2. 40 km
3. 42 km
4. 45 km
The mid point of the hypotenuse of a right triangle with vertices ( 4 , 0 ) , ( 2 , 1 ) and ( - 1 , - 5 ) is.
1. $\left(2,\frac{1}{2}\right)$
2. $\left(\frac{1}{2},-2\right)$
3. $\left(\frac{3}{2},-\frac{5}{2}\right)$
4. $\left(\frac{3}{2},\frac{5}{2}\right)$
An event which can never happen is called.
1. sure event
2. certain event
3. possible event
4. impossible event
The Venn diagram is used to represent:
1. Numbers only
2. Relations between sets
3. Equations only
4. Angles
Bearing of South is:
1. 090°
2. 180°
3. 270°
4. 360°
A constant rate of change in a situation is represented graphically by a:
1. Circle
2. Straight line
3. Parabola
4. Triangle
For similar figures, ratio of their areas is equal to:
1. Ratio of corresponding sides
2. Square of ratio of corresponding sides
3. Cube of ratio of sides
4. Sum of sides
Logarithmic methods are especially useful when numbers are:
1. Very small or very large
2. Equal to zero only
3. Negative only
4. Whole numbers only
Solve: 2 < x < 6
1. x < 2 or x > 6
2. 2 < x < 6
3. x ≤ 2
4. x ≥ 6
The sum of interior angles of a triangle is:
1. 90°
2. 180°
3. 270°
4. 360°
The HCF–LCM relation is useful for finding:
1. An unknown polynomial
2. Angles only
3. Logarithms only
4. Coordinates only
$\sqrt[m]{\sqrt[n]{a}} = \ldots\ldots$
1. $\sqrt[mn]{a}$
2. $\sqrt[m+n]{a}$
3. $\sqrt[m-n]{a}$
4. $\sqrt[n]{\sqrt[m]{a}}$
If AB + BC = AC, then points A, B and C are:
1. Non-collinear
2. Collinear with B between A and C
3. Vertices of a square
4. Vertices of a circle
A wheel has 8 equal sectors. Probability of stopping at one specified sector is:
1. '1/4
2. '1/6
3. '1/8
4. '1/10
If 52 people speak Arabic and 112 speak French, those who speak both are represented by:
1. A ∪ F
2. A ∩ F
3. A − F
4. F′
A bearing of 050° means:
1. 50° clockwise from north
2. 50° clockwise from south
3. 50° anticlockwise from east
4. 50° clockwise from west
The equation 5x − 6 = 0 represents a line parallel to the:
1. x-axis
2. y-axis
3. Line y = x
4. Origin
A square has perimeter 48 ft. Its side is:
1. 8 ft
2. 10 ft
3. 12 ft
4. 16 ft
Scientific notation of 6.25 is:
1. 6.25 × 10⁰
2. 0.625 × 10¹
3. 62.5 × 10⁻¹
4. All represent same value, but standard form is A
Which one is the solution of $2(x + 6) \leq 3 (x + 4)$ ?
1. $x \leq 0$
2. $x \geq 0$
3. $x \leq 24$
4. $x \geq 24$
If two given sides are 5.7 cm and 7.5 cm and the angle 105° is opposite the 7.5 cm side, the construction involves:
1. An oblique triangle case
2. Only an equilateral triangle
3. A square
4. A circle only
x (2a + 3b + 7) + x (2a + 3b + 5) equals
1. 2 x (2a + 3b + 6)
2. 4 x (2a + 3b + 6)
3. x (2a + 3b + 7)(2a + 3b + 5)
4. (x + x) (2a + 3b + 12)
The expression $a^{1/2}$ is equivalent to:
1. a²
2. √a
3. 1/a
4. 2a
If all four sides of a quadrilateral are equal and its diagonals bisect each other at right angles, it can be a:
1. Rectangle only
2. Rhombus
3. Trapezium
4. Scalene triangle
If a coin is tossed 10 times and head occurs 6 times, relative frequency of head is:
1. 0.4
2. 0.5
3. 0.6
4. 0.8

Q2. Short questions (Attempt all. Each question has an OR choice · 7 × 3 = 21)

A decagonal die labelled 4 , 4 , 4 , 4 , 5 , 5 , 6 , 7 , 8 , 8 is rolled once. Find the probability of getting. $\text { LCM of } 4 \text { and } 8$
OR
Represent the following on a number line. x < 0
Convert in radian. Use π= 3.1416. $60^\circ$
OR
Given that D = {a, e, i}, E = {a, c}, F = {b, c}. Find $D \times (E \cap F )$
Factorize the following polynomial. $2x^2y^3 - 6x^2y^2 + 2xy^3$
OR
Which of the following are axioms? How many of the axioms are postulates? When we add three consecutive even numbers, their sum is even.
Define orthocentre.
OR
Check whether the given value of each variable satisfies the inequality. $4 - 2x \leq 9; x = -3$
Find the distance between pair of points. $(\frac{1}{2},2) \text { and }( -2 , 1 )$
OR
Reduce the equation 6x + 8y - 11 = 0 into. $point - slope form$
If log b 2 = 0.3010 m log b 3 = 0.4771 log b 5 = 0.6990 , then evaluate $\log_b 0.0036$
OR
Find the median for the following data. 0 , 1 , - 2 , - 3 , 4 , 5 , 6 , 3
Write exponential expression as an equivalent radical expression and simplify if possible. $(29)^\frac{1}{2}$
OR
Find value of θ for the following question in the interval $0 \leq θ \leq \frac {\pi}{2}$ . ${\sec^2\theta - 2\tan^2\theta} = 0$

Q3. Long questions (Attempt all. Each question has an OR choice · 3 × 6 = 18)

Find the number of sides in a regular polygon when the measure of each exterior angle is 72⁰.
OR
Show that altitude of the following triangle are concurrent. $\Delta PQR \text{ when } PQ = 4.6 \, \text{cm}, \,QR = 6.5 \, \text{cm}, \, \angle P = 90^\circ$
Find the HCF of the following by division method. $2x^3 + 6x^2 + x + 3, 3x^3 + 9x^2 - 2x - 6, x^3 + 3x^2 + 2x + 6$
OR
Solve the following. $\frac{\sqrt{5x - 4} - 4}{10}$
The area of a right triangle is 50 cm². One of its angles is 45⁰. Find the lengths of the sides and hypotenuse of the triangle.
OR
Lines $\overline{OC} \text { and } \overline {AB}$ are shown in the graph. (i) Coordinates of end points of $\overline{OC} \text { and }AB$ . ( ii ) Slopes of both lines. ( ii ) Equations of both lines. ( iv ) Coordinates of point of intersection of both lines.