Roll No: Answer Sheet No: ______________

Sig. of Candidate: _____________ Sig. of Invigilator: ______________

Federal Board SSC-II Examinations

Model Question Paper Mathematics
(Science Group) (Curriculum 2006)

SECTION – A
Time allowed: 20 minutes Marks: 15
Note: Section-A is compulsory. All parts of this section are to be answered on the separately
provided OMR Answer Sheet and should be completed in the first 20 minutes and
handed over to the Centre Superintendent. Do not use lead pencil.

Q.1 Choose the correct answer by filling the relevant bubble for each question on the
OMR Answer Sheet according to the instructions given there.
Each part carries one mark.
(1) Which of the following types represents (𝑥 − 3)(𝑥 + 3) = 0 ?
A. Quadratic equation B. Linear equation
C. Cubic equation D. Pure quadratic equation
(2) For what value of k, 2𝑥 2 + 𝑘𝑥 + 3 = 0 has equal roots?
A. 2√6 B. 24
C. ±2√6 D. ±6√2
(3) If 𝑧 ∝ (𝑤 + 3) and 𝑤 = 3, 𝑧 = 6. What is value of 2𝑧 when 𝑤 = 9 ?
A. 12 B. 24
C. 6 D. 4.5
(4) If 𝛼 and 𝛽 are the roots of 2𝑥 2 − 6𝑥 − 4 = 0. What is value of 𝛼 2 𝛽 3 + 𝛼 3 𝛽 2 ?
A. −12 B. 12
C. 6 D. −6
𝑥3
(5) Which of the following are the partial fractions of ?
𝑥 3 +1
𝐴𝑥 3 𝐵𝑥+𝐶 𝐴 𝐵𝑥+𝐶
A. + 𝑥 2 −𝑥+1 B. 1 + 𝑥−1 + 𝑥 2 +𝑥+1
𝑥+1
𝐴 𝐵𝑥+𝐶 𝐴 𝐵𝑥+𝐶
C. 1 + 𝑥+1 + 𝑥 2 −𝑥−1 D. 1 + 𝑥+1 + 𝑥 2 −𝑥+1

(6) Which of the expressions shows the shaded region?

A. 𝐴 ∩ 𝐵′
B. 𝐴′ ∩ 𝐵
C. 𝐴 ∪ 𝐵′
D. 𝐴′ ∪ 𝐵
𝑈
(7) If 𝒙 = 7, ∑ 𝑓 = 30 and ∑ 𝑓𝑥 = 120 + 3𝑘 then value of k is
A. 30 B. −30
C. −11 D. 11
4 5
(8) If 𝑠𝑖𝑛𝜃 = 5 and 𝑠𝑒𝑐𝜃 = 3 then what is value of 𝑡𝑎𝑛𝜃 ?
2√3 √34
A. B.
5 3
4 3
C. D.
3 4
1
(9) What is the radius of circle if an arc of 10cm subtends an angle of 60° ?
30 𝜋
A. cm B. cm
𝜋 30
10800 1
C. cm D. cm
𝜋 6
𝑜
(10) What is the value of 𝑚∠𝐴𝑂𝐵 in the adjoining figure
of a hexagon?
A. 360° ÷ 45° 𝐴
B. 360° ÷ 60°
C. 360° ÷ 30° 𝐵
D. 360° − 60°
(11) What is the elevation of Sun if a pole of 6m high casts a shadow of 2√3𝑚 ?
A. 30° B. 45°
C. 60° D. 90°
(12) ̅̅̅̅ = 𝑚𝐶𝐷
What is the value of x if 𝑚𝐴𝐵 ̅̅̅̅ = 6𝑐𝑚, 𝑚𝑂𝐸̅̅̅̅ = 2𝑥 and 𝑚𝑂𝐹
̅̅̅̅ = 3𝑥 − 1?

E
A. 1 A B

B. −1 2x
7 O
C. 3 3x-1
D. 3
C F D

(13) In the adjoining figure, 𝑚∠𝑃𝑄𝑅 = 30°. What is the value of 𝑚∠𝑃𝑂𝑅 ?
P
A. 130°
B. 150° O 30° Q
C. 60°
D. 75° R

D
(14) In the drawn figure, what is value of 𝑚∠𝐵𝐶𝐷 ? C

A. 165° B. 155°
C. 80° D. 130° O

50°
A B
(15) If 𝑓: 𝐵 → 𝐴, then which of the following represents a/an ?
f
A. Onto function A 𝐵
B. Bijective function
C. Injective function 1 a
2
D. Into function 3
b
4 c

2
 Federal Board SSC-II Examination
Mathematics Model Question Paper
(Science Group) (Curriculum 2006)

Time allowed: 2.40 hours Total Marks: 60

Note: Sections ‘B’ and ‘C’ comprise pages 1-2 and questions therein are to be answered on
the separately provided Answer Book. Write your answers neatly and legibly.

SECTION – B (Marks 36)

Q.2 Attempt ALL parts. Each part carries (04) marks.
i. Solve the equation 3𝑥 2 + 4𝑥 − 5 = 5𝑥 2 + 2𝑥 + 1.
ii. Show that the equation 𝑥 2 + (𝑚𝑥 + 𝑐)2 = 𝑎2 has equal roots if 𝑐 2 = 𝑎2 (1 + 𝑚2 )
OR
If 𝜃 and 𝜑 are the roots of 𝑦 2 − 7𝑦 + 9 = 0, then form an equation whose roots
are 2𝜃 and 2𝜑.
iii. P is directly proportional to Q and 𝑃 = 12 when 𝑄 = 4. Write an equation
connecting P and Q and find the value of P, when 𝑄 = 8.
iv. If 𝑈 = {1, 2, 3, . . . . . , 10}, 𝐴 = {2, 4, 6} and 𝐵 = {1, 3, 5}, then verify that
(𝐴 ∩ 𝐵)’ = 𝐴’ 𝑈 𝐵’
OR
If 𝐴 = {1, 2, 3} and 𝐵 = {2, 4, 6}, then find domain and range of
𝑅 = {(𝑥, 𝑦)|𝑦 = 2𝑥}
v. The table shows the number of goals scored by a soccer team in 10 matches:

4 1 2 1 0 0 3 2 3 3

Find values of Mean, Median and Mode.

OR
The salaries of seven employees in rupees are as follows:
43500, 46400, 50000, 48500, 44200, 47700, 41900
Find standard deviation and variance of the salaries.
4
vi. If 𝑡𝑎𝑛 𝜃 = 3 and 𝑠𝑖𝑛 𝜃 < 0. Find values of 𝑠𝑒𝑐 𝜃 and 𝑐𝑜𝑠𝑒𝑐𝜃 and
show that 1 + 𝑐𝑜𝑡 2 𝜃 = 𝑐𝑜𝑠𝑒𝑐 2 𝜃.
OR
𝑠𝑖𝑛 𝜃
Prove that + 𝑐𝑜𝑡 𝜃 = 𝑐𝑜𝑠𝑒𝑐 𝜃.
1+𝑐𝑜𝑠 𝜃

vii. In ∆𝑃𝑄𝑅, 𝑚𝑄𝑅 = 6𝑐𝑚, 𝑚𝑃𝑅 = 2√2𝑐𝑚 and ∠𝑃𝑅𝑄 = 135˚. Draw perpendicular
from P to 𝑄𝑅, to meet 𝑄𝑅 produced at S and find the numeric value of 𝑚𝑅𝑆.
Moreover, by using (𝑚𝑃𝑄)2 = (𝑚𝑄𝑅)2 + (𝑚𝑃𝑅)2 + 2(𝑚𝑄𝑅)(𝑚𝑅𝑆) find the
numeric value of 𝑚𝑃𝑄.

3
 viii. ̅̅̅̅ = 8𝑐𝑚 and 𝑚∠𝑂𝐶𝐵 = 30°.
In the figure, given that 𝑂𝐴 𝑨
̅̅̅̅
Find the numeric values of 𝑚∠𝐴𝑂𝐵 and 𝑚𝐴𝐶

𝑪 𝐎
30°
OR

A, B, C and P are four points on a circle with centre O. P

Given that POC is a diameter of the circle.
𝒙
30°
Find the numeric values of 𝑥, 𝑦 and 𝑚∠𝐴𝑂𝐵
O
with reasons to justify your steps.
A B

C
ix. Prove that if a line is drawn perpendicular to a radial segment of a circle at its
outer end point, it is tangent to the circle at that point.
OR
̅̅̅̅ = 6𝑐𝑚, 𝐵𝐶
Circumscribe a circle about a triangle ABC with sides 𝐴𝐵 ̅̅̅̅ = 4𝑐𝑚,
̅̅̅̅
𝐴𝐶 = 4𝑐𝑚 and measure its radius.

SECTION – C (Marks 24)

Note: Attempt ALL questions. Each question carries (08) marks.

Q.3 The area of a rectangle is 48cm2. If length and width of each are increased by 4cm. the
area of larger rectangle is increased by 12cm2. Find the length and width of the original
rectangle.
OR
𝑥2
Resolve into partial fractions.
(1−x)(1+𝑥 2 )
𝑥−6𝑎 𝑥+6𝑏 12𝑎𝑏
Q.4 Using theorem of componendo-dividendo, find the value of − , if 𝑥 =
𝑥+6𝑎 𝑥−6𝑏 𝑎−𝑏

Q.5 Prove that if two arcs of a circle (or of congruent circles) are congruent then the
corresponding chords are equal.
OR
In a parallelogram ABCD, prove that (𝐴𝐶)2 + (𝐵𝐷)2 = 2[(𝐴𝐵)2 + (𝐵𝐶)2 ]

4
 Federal Board of Intermediate and Secondary Education
SSC-II Examinations
Model Question Paper Mathematics
(Curriculum 2006)
Alignment of Questions with Student Learning Outcomes

Cognitive Allocated
Sec-A Q 1 Contents and Scope Student Learning Outcomes *
Level ** Marks
8.1 Quadratic Equation Define quadratic equation.
i K 1
9.3 Nature of Roots of a iii) Discuss the nature of roots of
ii Quadratic Equation a quadratic equation through K 1
discriminant.
10.1 Ratio, Proportions and i) Define ratio, proportions and
iii Variations. variations U 1
(direct and inverse)
9.4 Symmetric Functions of ii) Evaluate a symmetric Function
Roots of a Quadratic of the roots of a quadratic
iv equation in terms of its U 1
Equation.
coefficients.
11.2 Resolution of Fraction Resolve an algebraic fraction
into Partial Fractions. into partial fractions when its
v U 1
denominator consists of non-
repeated linear factors.
12.1.3 Venn Diagram i) Use Venn diagram to
represent
vi • union and intersection of U 1
sets,
• complement of a set.
13.3 Measures of Central i) Calculate the arithmetic mean by
vii U 1
Tendency definition (for ungrouped data)
16.3 Trigonometric Ratios vi) Find the values of remaining
viii trigonometric ratios if one K 1
trigonometric ratio is given.
16.2 Sector of a circle i) Establish the rule 𝑙 = 𝑟𝜃 ,
where 𝑟 is the radius of the
ix circle, 𝑙 the length of circular U 1
arc and 𝜃 the central angle
measured in radians.
 30.2 Circles attached to Circumscribe a regular hexagon
polygons about a given circle.
x U 1

16.5 Angle of elevation and ii) Solve real life problems

xi Depression. involving angle of elevation U 1
and depression
25.1 Chords of a Circle Apply the theorem stated as:
iv) If two chords of a circle are
xii congruent then they will be A 1
equidistant from the centre.

26.1 Tangent to a Circle Apply the theorem stated as:

iii) “The two tangents drawn to a
xiii circle from a point outside it, A 1
are equal in length”
to solve appropriate problems.

28.1 Angle in a Segment of Apply the theorem stated as:

a Circle i) “The measure of a central
angle of a minor arc of a circle,
xiv is double that of the angle A 1
subtended by the corresponding
major arc”
to solve appropriate problems.

12.3 Function ii) To demonstrate the following:

• Into function
• One-one function
xv • Injective function K 1
• Surjective function
• Bijective function
8.2 Solution of Quadratic i) Solve a quadratic equation in
Equations one variable by
Q2 i U 4
• Factorization,
• Completing square
9.1 Nature of the Roots of aiv) Determine the nature of
Quadratic Equation roots of a given quadratic
ii U 4
equation and verify the result
by solving the equation.
9.5 Formation of Quadratic Establish the formula,
Equation 𝑥 2 − (𝑆𝑢𝑚 𝑜𝑓 𝑟𝑜𝑜𝑡𝑠)𝑥 +
ii (𝑃𝑟𝑜𝑑𝑢𝑐𝑡 𝑜𝑓 𝑟𝑜𝑜𝑡𝑠) = 0 , U 4
to find a quadratic equation from
the given roots.
 10.1 Ratio, Proportion and i) Define ratio, proportions and
Variation. variations (direct and inverse)
iii U 4

12.1.2 Properties of Union iv) De Morgan’s Laws

iv K 4
and Intersection
12.3 Function Define function and identify its
iv K 4
domain, co-domain and range.
13.3 Measures of Central i) Calculate mean, median and
v Tendency mode for ungrouped data. U 4

13.4 Measures of Dispersion Measure range, variance and

v standard deviation. U 4

16.3 Trigonometric Ratios v) Recognize the signs of

trigonometric ratios in different
quadrants
vi 4
vi) Find the values of remaining U
trigonometric ratios if one
trigonometric ratio is given.
16.4 Trigonometric Prove the trigonometric identities
Identities and apply them to show different
trigonometric relations.
vi U 4

24.1 Projection of a Side of a Prove the following theorem

Triangle along with corollaries and apply it
to solve the appropriate problems.
i) In an obtuse-angled triangle,
the square on the side opposite to
vii the obtuse angle is equal to the A 4
sum of the squares on the sides
containing the obtuse angle
together with twice the rectangle
contained by one of the sides, and
the projection on it of the other.
26.1 Tangent to a Circle Apply the theorem stated as:
iii) “The two tangents drawn to a
circle from a point outside it,
viii are equal in length” A 4
to solve appropriate problems.
 27.1 Chords and arcs Apply the theorem stated as:
“The measure of a central angle
of a minor arc of a circle, is
viii double that of the angle A 4
subtended by the corresponding
major arc” to solve appropriate
problems.
26.1 Tangent to a Circle i) If a line is drawn perpendicular
to a radial segment of a circle at
ix K 4
its outer end point, it is tangent
to the circle at that point.
30.2 Circles attached to i) Circumscribe a circle about a
ix K 4
Polygons given triangle.
9.7 Simultaneous Equations Solve the real life problems
Q3 U 8
leading to quadratic equations.
11.2 Resolution of Fraction Resolve an algebraic fraction
into Partial Fractions into partial fractions when its
Q3 U 8
denominator consists of non-
repeated quadratic factors.
10.2 Theorems on Proportion Apply theorem of componendo-
Q4 A 8
dividendo to find proportions.
27.1 Chords and Arcs i) If two arcs of a circle (or of
congruent circles) are congruent
Q5 K 8
then the corresponding chords
are equal.
24.1 Projection of a Side of a iii) In any triangle, the sum of the
Triangle squares on any two sides is
equal to twice the square on
Q5 half the third side together with K 8
twice the square on the median
which bisects the third side
(Apollonius’ Theorem).
 Federal Board of Intermediate and Secondary Education
ASSESSMENT GRID FOR MODEL QUESTION PAPER
Level: SSC-II Subject: Mathematics Curriculum: 2006 Examination: Annual 2024
Units

8. Quadratic Equations

Equations
9. Theory of Quadratic

10. Variations

11. Partial Fractions

12. Sets and Functions

13. Basic Statistics

Trigonometry
16. Introduction to

of a Triangle
24. Projection of a Side

25. Chords of a Circle

26. Tangent to a Circle

27. Chords and Arcs

of a Circle
28. Angle in a Segment

Geometry-Circles
30. Practical

assessment objective
Total marks for each
Knowledge 2 iv (4)
1 i (1) 1 ii (1) 35
based 2 iv (4) 1 viii (1) 5 (8) 2 ix (4) 5 (8) 2 ix (4)
30%
Comprehension/ 1 ix (1)
Understanding 1 iv (1) 1 vii (1)
1 iii (1) 1 v (1) 1 xi (1) 1 xii (1) 57
based 2 i (4) 2 ii (4) 1 vi (1) 2 v (4) 1 x (1)
2 iii (4) 3 (8) 2 vi (4) 50%
2 ii (4) 2 v (4)
2 vi (4)
3 (8)
Application 1 xiii (1) 23
based 4 (8) 1 xv (1) 2 vii (4) 2 viii (4) 1 xiv (1)
2 viii (4) 20%
Total marks
for each unit 05 18 13 09 10 09 11 04 09 09 12 01 05 115

 1, 2, 3 etc. stands for question numbers

 i, ii, iii etc. stands for part of question numbers
 (1), (2), (3) etc. stands for marks of question papers