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10th Class Mathematics Board Pattern Paper 2026

10th Class · Mathematics · Federal (FBISE)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 75Time: 3 hours

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

Which of the following is a quadratic equation?
1. ax + b = c
2. ax² + bx + c
3. ax² + bx + c = 0
4. ax² + bx + c = 0, a = 0
$\frac{2}{1 - i}$ =?
1. $\frac{1 + i}{2}$
2. $\frac{(1+i)^2}{2}$
3. $1 - i$
4. $1 + i$
An expression which is the ratio of two polynomials but the polynomial in denominator is non-zero is called.
1. polynomial
2. rational Expression
3. compound Expression
4. irrational Expression
Direct common tangents of equal circles are:
1. parallel
2. intersecting
3. converging
4. not parallel
If A and B are two matrices, conformable for the product AB then $(AB)^t =$
1. $A^tB^t$
2. $(BA)^t$
3. $B^tA^t$
4. AB
If $f(x) =\frac{1}{2} x$ , what is $f^2 (x)$ ?
1. $\frac{1}{4x}$
2. $\frac{1}{4} x$
3. 2x
4. $\frac{1}{4} x^2$
CV is given by the formula:
1. $\frac{\text{SD}}{\text{range}} \times 100$
2. $\frac{\text{mean}}{\text{SD}} \times 100$
3. $\frac{\text{100}}{\text{mean}} \times SD$
4. $\frac{\text{SD}}{\text{100}} \times \text { mean }$
Which of the following vectors represents a position vector?
1. $\overrightarrow{OP}$
2. $-\overrightarrow{OP}$
3. $\overrightarrow{PO}$
4. $\overrightarrow{PQ}$
If a circle is divided into ten equal arcs, then central angle of each arc is …………
1. 10°
2. 36°
3. 60°
4. 90°
Which ordered pair is a solution of the system 2x - y ≤ 5 and x + 2y > 2?
1. (1 , -1)
2. (4 , 1)
3. (2 , 0)
4. (3 , 2)
Angle subtended by an arc at centre of circle is called ………… angle.
1. reflex
2. inscribed
3. straight
4. central
In right △ABC, a = 2 cm , c = 4 cm, what is α?
1. 30°
2. 45°
3. 60°
4. 120°
Which of the following is a reciprocal equation?
1. $x^2 + 2x + 2 = 0$
2. $x^4 + x^3 + x^2 + x + 1 = 0$
3. $\sqrt{2x + 3}$
4. $x^4 + 2x^3 + x^2 + 4x = 0$
$1 + (i)^9$ = ?
1. $1 + i$
2. $1 +\sqrt{-1}$
3. $1 - i$
4. $-i$
Coefficients in the polynomial $\sqrt{16x^2y} - \frac{1}{2}y^3 + \frac{22}{7}z$ are the elements of the set of:
1. Integers
2. Irrational numbers
3. Odd numbers
4. Rational numbers

Q2. Short questions (Attempt any 9 of 12 · 9 × 4 = 36)

Find z . $\bar{z} : {z} = 14 - 7i$
In the figure, $\overline{AB} = 4 \overline{BC}$ and , ∠AOB find: ∠OAB + ∠ABC + ∠BCO + ∠COA
Find the values of unknown in the figure.
Sketch the graph of the quadratic function y = −x²− 4x. Will it open upward or downward?
Find all roots of 8x³− 7x³− 1 = 0
Raabi and Jerry are hoping on their play circles of four sectors each painted in red, green, yellow and blue colours. Find the probability that they will jump on: (1) At the same colour (2) At the different colours.
Draw a circle with the help of any round object, then find its centre.
Solve the inequalities, if possible, graph the solution. $\frac{2}{3}x - 4 ≥ 1$
Verify A(B + C) = AB + AC $A = \begin{bmatrix} 5 & 2 \end{bmatrix}, B = \begin{bmatrix} 6 \\ 4 \end{bmatrix} \text{ and } C = \begin{bmatrix} 1 \\ 2 \end{bmatrix}.$
Draw vectors $\vec{a}$ = 3 units west and $\vec{b}$ = 3 unit north on graph paper. Draw the following vector on the graph paper. $\vec{a} - 2\vec{b}$
Prove that $r_2 = 4R \cos \frac{\alpha}{2} \cos \frac{\gamma}{2} \sin \frac{\beta}{2}$
Simplify the following. $\frac{x^2 - 25}{5} - \frac{x}{4} \div \frac{3x}{20}$

Q3. Long questions (Attempt any 3 of 5 · 3 × 8 = 24)

A truck leaves dry port on a bearing of 30° and travels 15 km. It then turns due west and travels 8 km. How far is the truck from the dry port and what is its bearing?
Does the system of inequalities have any solution? x - y > 5 ; x - y < 1
If $g(x) = \frac{1}{2x^3} + \frac{x}{2} + 2, \, \text{find } g\left(-\frac{1}{3}\right).$
In the figure, AOB is equilateral triangle. Find the measures of ∠O and ∠C.
Two parallel chords of lengths 18 cm and 80 cm are drawn on the same side of a circle of radius 41 cm. Find the distance between the chords.