Series RTEQ.P. Code 27/0/1
Roll No.
RTE LEARN · CBSE PATTERN 2026–27
MATHEMATICS
Half-Yearly Exam
Time allowed : 3 HoursMaximum Marks : 80
General Instructions :
Read the following instructions carefully and follow them :
(i)This question paper contains 38 questions. All questions are compulsory.
(ii)This question paper is divided into five sections – A, B, C, D and E.
(iii)In Section A, Question numbers 1 to 18 are multiple choice questions (MCQs) and Question numbers 19 to 20 are Assertion–Reason based questions of 1 mark each.
(iv)In Section B, Question numbers 21 to 25 are very short answer (VSA) type questions carrying 02 marks each.
(v)In Section C, Question numbers 26 to 31 are short answer (SA) type questions carrying 03 marks each.
(vi)In Section D, Question numbers 32 to 35 are long answer (LA) type questions carrying 05 marks each.
(vii)In Section E, Question numbers 36 to 38 are case-based integrated units of assessment carrying 04 marks each, with sub-parts.
(viii)There is no overall choice. However, an internal choice has been provided in some questions. Attempt only one of the alternatives in such questions.
(ix)Draw neat figures wherever required. Take π = 22/7 wherever required, if not stated.
(x)Use of calculators is not allowed.
SECTION A
This section comprises 20 multiple choice questions (MCQs) of 1 mark each.
1.1
One lakh is equal to
(A) 10,00,000(B) 1,000(C) 10,000(D) 1,00,000
2.1
One crore is equal to how many lakhs?
(A) 1,000(B) 10,000(C) 10(D) 100
3.1
4,56,78,912 rounded off to the nearest crore is
(A) 4.5 crore(B) 6 crore(C) 5 crore(D) 4 crore
4.1
The value of 25 − 5 × 3 is
(A) 10(B) 15(C) −10(D) 60
5.1
The value of 48 − (12 + 8) is
(A) 68(B) 44(C) 52(D) 28
6.1
0.7 written as a fraction is
(A) 7/10(B) 70/10(C) 1/7(D) 7/100
7.1
3.25 + 1.8 is equal to
(A) 5.05(B) 4.33(C) 3.43(D) 5.5
8.1
Which of these is the greatest?
(A) 0.405(B) 0.054(C) 0.5(D) 0.45
9.1
The perimeter of a square of side s is
(A) 4s(B) s + 4(C) s²(D) 2s
10.1
If a = 3, the value of 5a − 4 is
(A) 1(B) 15(C) 11(D) 19
11.1
3x + 5x − 2x simplifies to
(A) 3x(B) 10x(C) 6x(D) 8x
12.1
Vertically opposite angles are always
(A) supplementary(B) equal(C) complementary(D) unequal
13.1
Two angles that form a linear pair add up to
(A) 360°(B) 90°(C) 180°(D) 270°
14.1
When a transversal cuts two parallel lines, the corresponding angles are
(A) supplementary(B) complementary(C) always 90°(D) equal
15.1
The sum of two odd numbers is
(A) always odd(B) sometimes odd(C) always even(D) always prime
16.1
The Virahāṅka–Fibonacci number that comes after 1, 2, 3, 5, 8 is
(A) 16(B) 11(C) 12(D) 13
17.1
Which set of lengths can form a triangle?
(A) 1 cm, 2 cm, 3 cm(B) 4 cm, 4 cm, 9 cm(C) 2 cm, 3 cm, 6 cm(D) 3 cm, 4 cm, 5 cm
18.1
2/3 × 9/4 is equal to
(A) 6(B) 3/2(C) 18/7(D) 11/7
19.1
Assertion (A): A triangle can have two right angles.Reason (R): The sum of the angles of a triangle is 180°.
(A) Both A and R are true, and R is the correct explanation of A.(B) Both A and R are true, but R is not the correct explanation of A.(C) A is true, but R is false.(D) A is false, but R is true.
20.1
Assertion (A): 1/2 ÷ 1/4 = 2.Reason (R): Dividing by a fraction is the same as multiplying by its reciprocal.
(A) Both A and R are true, and R is the correct explanation of A.(B) Both A and R are true, but R is not the correct explanation of A.(C) A is true, but R is false.(D) A is false, but R is true.
SECTION B
This section comprises 5 very short answer (VSA) type questions of 2 marks each.
21.2
Compare: 45 lakh and 4.5 million. Which is greater?
22.2
Use distributive property to calculate 9×101.
23.2
A ribbon is 4.5m long. If 1.75m is cut, how much remains?
24.2
If a=4, b=2, find 3a+2b.
ORSimplify: 5x + 3y − 2x + 4y.
25.2
One angle of a linear pair is 65°. Find the other angle.
ORFind the Collatz sequence starting from 6 until it reaches 1.
SECTION C
This section comprises 6 short answer (SA) type questions of 3 marks each.
26.3
A city has population 34,56,789. (a) Round to nearest lakh. (b) Round to nearest ten-thousand. (c) Write in words.
27.3
Simplify step-by-step: 8×(5+3)-4×(7-2), showing BODMAS applied.
28.3
A bag weighs 2.35kg and another 1.65kg. (a) Find total weight. (b) Find the difference.
29.3
A pattern has n squares at step n given by 2n+1. (a) Find squares at step 6. (b) Find squares at step 12. (c) State the rule.
30.3
Two angles are supplementary. If one is 30° more than twice the other, find both angles.
ORA tank is 3/4 full. If 1/5 of the water is used, (a) what fraction is used from total? (b) what fraction remains?
31.3
Apply Kaprekar's routine fully to 3524 until it reaches 6174. Show all steps.
ORIn ΔPQR, ∠P = 70° and ∠Q = 45°. (a) Find ∠R. (b) Classify the triangle by its angles. (c) Can a triangle have angles 90°, 60° and 40°? Explain.
SECTION D
This section comprises 4 long answer (LA) type questions of 5 marks each.
32.5
India's population is approximately 140 crore. (a) Express in international system. (b) Write in digits. (c) Explain why exact figures are impossible. (d) If China's population is 142 crore, find the difference. (e) Express the difference in lakhs.
33.5
The cost of x pens at Rs 8 each and y notebooks at Rs 12 each is given by an expression. (a) Write the expression. (b) Find cost for x=5,y=3. (c) If total cost is Rs 100 and y=3, find x. (d) Verify your answer. (e) If y increases to 4, find the new total cost with x=8.
34.5
(a) Can a triangle have sides 4 cm, 5 cm and 10 cm? Give a reason. (b) In ΔABC, ∠A = 55° and ∠B = 65°. Find ∠C. (c) Can a triangle have two obtuse angles? Why? (d) Write the steps to construct a triangle with sides 5 cm, 6 cm and 7 cm. (e) Classify a triangle with angles 40°, 60° and 80° by its angles.
35.5
A recipe needs 2/3 cup flour per batch. (a) Find flour needed for 5 batches. (b) If only 3 cups available, how many full batches can be made? (c) How much flour is left over? (d) If the recipe is doubled, find new flour requirement per batch. (e) Find flour needed for 5 batches with the doubled recipe.
ORRavi reads 2/5 of a book on Monday and 1/3 of the remaining part on Tuesday. (a) What fraction of the book is left after Monday? (b) What fraction of the whole book does he read on Tuesday? (c) What fraction is still left? (d) If the book has 150 pages, how many pages are still left? (e) How many pages did he read on Monday?
SECTION E
This section comprises 3 source based / case based units of assessment of 4 marks each with sub-parts.
36.
The population of Town A is 12,45,670 and that of Town B is 9,87,345.(i) Write the population of Town A in words (Indian system).1(ii) Find the total population of the two towns.1(iii) Find how many more people live in Town A than in Town B, and round off the total to the nearest lakh.2OR(iii) Write the total population using the international system of commas and in words.2
37.
Riya buys 2.5 kg of apples, 1.75 kg of grapes and 0.8 kg of cherries.(i) Find the total weight of the fruit.1(ii) How much more apples than grapes did she buy?1(iii) Her bag holds 6 kg. How much more can she put in it? Write the total weight of the fruit in grams.2OR(iii) Arrange the three weights in increasing order and write the weight of cherries in grams.2
38.
Two railway tracks are parallel. A straight road crosses both tracks, making an angle of 65° with the first track.(i) What angle does the road make with the second track at the corresponding position?1(ii) What angle forms a linear pair with the 65° angle?1(iii) Name a pair of alternate interior angles and give their measures, with a reason.2OR(iii) If the road were perpendicular to the first track, what angle would it make with the second track? Give a reason.2
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