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Punjab Board 2027 Model Papers | Class 10 Mathematics Subjective Paper | Units 5 & 6
Class 10 Math Chapter 5 & 6 Grand Test
Punjab Board 2027 Model Papers for Class 10 Mathematics are designed according to the new board examination pattern. This subjective model paper covers Unit 5: Algebraic Fractions and Unit 6: Vectors in Plane, including important short questions, algebraic fractions, reciprocal equations, vectors, translation vectors, projectile motion, and long-answer questions. Students preparing for Punjab Board Class 10 Mathematics 2027 can use this Class 10 Math Model Paper 2027 for effective exam practice and board preparation.
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Board PAPER Pattern
03
MATHEMATICS
CHAPTER
WISE
WISE
Roll No. (in Figures):
(in Words):
Unit 5: Algebraic Fractions
Unit 6: Vectors in Plane
Unit 6: Vectors in Plane
Time : 20 Minutes
Marks: 15
Marks: 15
OBJECTIVE TYPE
| A | B | C | D | A | B | C | D | A | B | C | D |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 A | B | C | D | 6 A | B | C | D | 11 A | B | C | D |
| 2 A | B | C | D | 7 A | B | C | D | 12 A | B | C | D |
| 3 A | B | C | D | 8 A | B | C | D | 13 A | B | C | D |
| 4 A | B | C | D | 9 A | B | C | D | 14 A | B | C | D |
| 5 A | B | C | D | 10 A | B | C | D | 15 A | B | C | D |
Note:
Four possible answers A, B, C and D to each question are given.
The choice which you think is correct, fill that circle in front of
that question with Marker or Pen ink. Cutting or filling two or more
circles will result in zero mark in that question.
Q1. 15
1.
Lowest form of
15xyz
10
is:
2.
(x3 − y3)
÷ (x − y) in simplified form is:
3.
An equation of the form
5x + 64·5−x − 20 = 0
is called:
4.
Linear factors of
3x2 + 10x + 3 = 0
are:
5.
x + 5
x + 2
is a:
6.
Which value of x makes
x − 5
x2 − 5
undefined?
7.
What is the simplified form of
(a3 + b3)
÷ (a + b)?
8.
A vector having magnitude 1, is called:
9.
If a = λb, then
a and b are:
10.
The position vector of point P(3, −2) with respect to O is:
11.
Vector from point P(3,4) to origin is:
12.
The intersecting point of x-axis and y-axis is:
13.
Two or more vectors lying in the same plane are called:
14.
The new vertex of point A(−4,2) by a translation vector
7i + 2j is:
15.
Equation for horizontal motion is:
Here is Subjective Part of Paper.
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Roll No. (in Figures):
(in Words):
Time : 2:10 Hours
Marks: 60
Marks: 60
Unit 5: Algebraic Fractions
Unit 6: Vectors in Plane
Unit 6: Vectors in Plane
SUBJECTIVE TYPE (PART – I)
Q2. Write short answers to any Six (6) questions:
(6 × 2 = 12)
(i)
Reduce to the lowest form:
3a2 − 6ab 2a2b − 4ab2
3a2 − 6ab 2a2b − 4ab2
(ii)
Reduce to the lowest form:
ac a2x2 − ax
ac a2x2 − ax
(iii)
Simplify:
a3
a − b
−
b3
b − a
(iv)
Simplify:
4 − x2
x
−
x + 2
x
+ 5
(v)
Simplify:
24ℓm
5ℓ + 10m
×
5ℓ2 − 20m2
16mn
(vi)
Simplify:
a2 − 4b2
a2 + 2ba
×
2a2 + 10ab
a2 + 3ab − 10b2
(vii)
Reduce to the lowest form:
x2 − 7x + 12
x2 − 6x + 9
(viii)
Reduce to the lowest form:
x2 + 3x − 18
7x − 21
(ix)
What value of x makes the fraction
7
x − 5
undefined?
Q3. Write short answers to any Six (6) questions:
(6 × 2 = 12)
(i)
Reduce to the lowest form:
x2 + 5x + 6
x2 − 4
(ii)
Simplify:
x
5
+
5
x
(iii)
Simplify:
x2 − 9
4
×
8
x − 3
(iv)
Define “Reciprocal” equation.
(v)
Find a vector triple in length of
3i − 2j,
but opposite in direction.
(vi)
Find two vectors that are double in magnitude of
3i − 5j,
one in the same direction of it and other in its opposite direction.
(vii)
A ball is projected with velocity vector
v = 6i + 8j.
What is the magnitude of velocity?
(viii)
Write the vector PQ in the form of
xi + yj,
where P(−3, −6) and Q(1,2).
(ix)
If
u =
1
4
i +
15
4
j
then find |u|.
Q4. Write short answers to any Six (6) questions:
(6 × 2 = 12)
(i)
Check that the vectors
u = 8i + 4j
and
v = 2i + i
are parallel or not.
(ii)
If
u = −5v,
where
u = 10i − λj
and
v = 2i + 3j,
then find the value of λ.
(iii)
If
u = 5i − 4j
and
v = 6i − 3j,
then find u + v.
(iv)
If
a = 4i − j
and
b = −3i + 5j,
then find 3b + 4a.
(v)
If
u = i − 2j,
w = 3i + 3j
and
u + 4v = w,
then find v.
(vi)
If
(xi + yj) − (2i − 4j) = −5i + 3j,
then find the values of x and y.
(vii)
If
(x + 5)i + (y − 3)j = 2i + 7j,
then find the values of x and y.
(viii)
Define a translation vector.
(ix)
If
AB = 4i − 5j
and
DC = 4i − yj
are two parallel opposite sides of a parallelogram,
then what is the value of y?
(PART – II)
Note: Attempt any two (02) questions.
(2 × 8 = 16)
Q5.
(a)
Simplify:
x − 2y
3
+
x + y
6
−
2x − y
15
4
(b) Simplify: 3a2 − 6ab 6ab × 10b2 4ab − 8b2 4
(b) Simplify: 3a2 − 6ab 6ab × 10b2 4ab − 8b2 4
Q6.
(a)
Train is scheduled to cover a distance of 120 km at a certain average speed,
owing to a service checkup this average speed is reduced by 5 km/h,
and in consequence the journey takes 20 minutes more than the scheduled time.
What was the scheduled speed?
4
(b) One pipe fills in 5 hours, another in 8 hours. Second pipe closed after 2 hours. Find the total time. 4
(b) One pipe fills in 5 hours, another in 8 hours. Second pipe closed after 2 hours. Find the total time. 4
Q7.
(a)
Rashid can paint a house in 6 days, but if he gets a helper he can do it in 4 days.
How long would it take the helper to paint the house alone?
4
(b) Plot A(−5, 3), B(−2, 3) and C(−4,5) to form a triangle ABC. Also translate △ABC to △A′B′C′ by translation vector 5i − 2j. 4
(b) Plot A(−5, 3), B(−2, 3) and C(−4,5) to form a triangle ABC. Also translate △ABC to △A′B′C′ by translation vector 5i − 2j. 4
(PART – III)
Note: Attempt any one (01) question.
(1 × 8 = 8)
Q8.
(a)
If
5i − 3j = m(i − 10j) + n(4i − 3j)
,
then find the value of m and n.
4
(b) Use vectors to show that triangle XYZ is an isosceles, where the points X, Y, Z have the coordinates (0, 0), (2, 0) and (1, 3) respectively. 4
(b) Use vectors to show that triangle XYZ is an isosceles, where the points X, Y, Z have the coordinates (0, 0), (2, 0) and (1, 3) respectively. 4
Q9.
(a)
A ball is projected with an initial velocity vector
v0 = 10i + 20j.
The horizontal component is in the x-direction and gravity is
g = 0i − 10j.
Find the maximum height and horizontal range.
4
(b) A car enters a loop with velocity vector v = 30i and exits with velocity v = 30j. What is the change in velocity vector? 4
(b) A car enters a loop with velocity vector v = 30i and exits with velocity v = 30j. What is the change in velocity vector? 4
