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Class 10 Chapter 5 Full Unit Test 2027 | Mathematics Algebraic Fractions | Punjab Boards
Class 10 Math Chapter 5 full unit Test
Class 10 Chapter 5 Full Unit Test 2027 for Mathematics is designed according to the new Board Pattern 2027 for Punjab Boards. This Algebraic Fractions test provides objective and subjective questions for complete chapter preparation, including rational expressions, algebraic fractions, simplification, quadratic equations, exponential equations, reciprocal equations, and word problems. Students can use this Class 10 Mathematics Chapter 5 Test for board exam preparation, revision, practice, and self-assessment.
Full Unit Test
Unit 5: Algebraic Fractions
Board Paper Pattern
Objective Type
Time Allowed: 20 Min.
Max. Marks: 15
Note: Four possible answer 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 ink pen in the answer book. Cutting filling two
or more circles will result in zero mark in that question.
(i) Which of the following is a rational fraction?
(ii) The rational expression
x + y
x2 + y2
in lowest form is:
(iii) Simplifying
1
x
+
1
y
=
(iv)
3
x − y
−
1
y − x
=
(v) Reducing equation
x4 + 2x2 + 1 = 0
into a quadratic equation by letting
x2 = t to get:
(vi) What we need to substitute to convert the equation
(x2 +
1
x2
)
− 3(x +
1
x
)
+ 4 = 0
into a quadratic equation.
(vii) To convert
(x + 2)(x − 5)(x + 3)(x − 6) = 12
we need to suppose:
(viii) The equation
5x4 − 19x2 + 12 = 0
in reduced quadratic form is:
(ix) To reduce
(x + 1)(x − 4)(x + 2)(x − 5) = −8
into quadratic equation, we need to suppose:
(x) Solution of the equation
x +
1
x
= 2
is x =
(xi) To convert
9x − 2(3x) + 1 = 0
into quadratic equation, we need to suppose:
(xii) Solution of the equation
22x − 3 × 2x + 2 = 0
is x =
(xiii) To reduce the equation
x4 − 16x2 + 63 = 0
into a quadratic equation, we need to suppose that:
(xiv) Arshia and Ibrahim complete a job together in 4 hours.
If job rate of Arshia is x and of Ibrahim is y, then mathematical
equation in this scenario is:
(xv) Least common multiples of
x − y, x + y, x2 − y2
is:
Here is Subjective Part of Model Paper 2027.
Subjective Type
Time Allowed: 2:10 hours
(Part-I)
Max. Marks: 60
2. Write short answers to any six (06) questions:
(2 × 6 = 12)
(i) Reduce to lowest form:
6x2 − 8xy 9xy − 12y2
6x2 − 8xy 9xy − 12y2
(ii) Reduce the following rational expressions to lowest forms:
ac a2x2 − ax
ac a2x2 − ax
(iii) Reduce the following rational expressions to lowest forms:
x(2a2 − 3ax) a(4a2x − 9x3)
x(2a2 − 3ax) a(4a2x − 9x3)
(iv) Simplify:
x − 2y
4
+
x + y
6
−
2x − y
15
(v) Simplify:
4a
a2 − 1
−
a + 1
a − 1
(vi) Simplify:
x + y
12x − 6y
+
x − y
18x − 9y
(vii) Simplify:
3a2 − 6ab
6ab
×
10b2
4ab − 8b2
(viii) Simplify:
5a2
4a − 8
·
6a − 12
10a
(ix) Simplify:
24/m
5l + 10m
×
5l2 − 20m2
16mn
3. Write short answers to any six (06) questions:
(2 × 6 = 12)
(i) Solve:
2x4 − 11x2 + 12 = 0
(ii) Define Exponential Equation with example.
(iii) Define algebraic fraction.
(iv) Reduce the following rational expressions to lowest forms:
15a2b2c 100(a2 − a2b)
15a2b2c 100(a2 − a2b)
(v) Define rational expression.
(vi) Solve the following equations:
4x4 − 16x2 + 15 = 0
(vii) Solve the following equations:
4 · 22x+1 − 9 · 2x + 1 = 0
(viii) Define Irrational expression with example.
(ix) Solve the following equations:
3x + 33−x − 12 = 0
4. Write short answers to any six (06) questions:
(2 × 6 = 12)
(i) A tradesman buys a number of articles for Rs. 300.
Four of them are broken in transit but by selling the remaining
at a profit of Rs. 1.25 each, he gains Rs.350 altogether.
How many articles did he buy?
(ii) Arshia and Ibraheem complete a job together in 4 hours.
If Arshia takes 6 hours, then find how much time will Ibraheem take?
(iii) Solve the following equations:
x4 − 16x2 + 63 = 0
(iv) Simplify:
x3 − 27
x2 − 9
÷
x2 + 3x + 9
x2 + 6x + 9
(v) Reduce the following to the lowest form:
x2 − 7x + 12
x2 − 6x + 9
(vi) One pipe fills water in 5 hours, another in 8 hours.
Second pipe closed after 2 hours. Find the total time.
(vii) A tap can fill a tank in 6 hours. Another tap can fill it
in 9 hours. If both taps are opened together, how long will it
take to fill the empty tank?
(viii) Define Reciprocal Equation with example.
(ix) Ahmad takes 2 hours to paint 50 glasses. Faiza takes 2 hours
to paint 45 glasses. Working together, how long should it take
them to paint 150 glasses?
(Part-II) Note: Attempt any two (02) questions.
(2 × 8 = 16)
5:(a) Simplify:
1
x2 − 5x + 6
+
1
x2 − 3x + 2
−
1
x2 − 8x + 15
(b) Simplify:
x + 2
x2 − x − 12
−
x
x2 + 6x + 9
6:(a) Simplify:
x3 − a3
x2 − 2bx + b2
×
x2 − bx − cx + bc
ax − x2
÷
x2 − cx
x − b
(b) Solve the equation:
(
x2 +
1
x2
)
+ 2
(
x +
1
x
)
− 33 = 0
7:(a)
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?
(b)
Fahad runs 600m at a certain pace, and then doubling his pace,
does another 600m. If he took
5
2
to cover the distance 1200m, find the pace he started at,
in meters per seconds.
(Part-III) Note: Attempt any one (01) question.
(1 × 8 = 8)
8:(a) Simplify:
a2 − (b − c)2
(a + b)2 − c2
×
a2 − (b + c)2
(a − b)2 − c2
(b) Solve the equation:
4x4 − 16x2 + 15 = 0
9:(a)
Solve the equation:
(x + 9)(x − 3)(x − 7)(x + 5) = 385
(b)
Solve the equation:
(
x2 +
1
x2
)
+
(
x +
1
x
)
= 4
