Series RTEQ.P. Code 24/0/1
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
The next number in the pattern 1, 4, 9, 16, … is
(A) 36(B) 20(C) 25(D) 24
2.1
The sum of the first 5 odd numbers (1 + 3 + 5 + 7 + 9) is
(A) 30(B) 15(C) 20(D) 25
3.1
The triangular numbers are 1, 3, 6, 10, … The next one is
(A) 14(B) 16(C) 15(D) 12
4.1
A line segment has
(A) three end points(B) no end points(C) one end point(D) two end points
5.1
An angle of 90° is called
(A) an acute angle(B) a right angle(C) an obtuse angle(D) a straight angle
6.1
An angle of 135° is
(A) reflex(B) acute(C) right(D) obtuse
7.1
A straight angle measures
(A) 360°(B) 180°(C) 90°(D) 270°
8.1
Which of these numbers is a palindrome?
(A) 4554(B) 1230(C) 1234(D) 4545
9.1
The Kaprekar constant for 4-digit numbers is
(A) 4321(B) 1089(C) 6174(D) 9999
10.1
The best estimate of 48 × 21 is
(A) 1000(B) 10000(C) 100(D) 500
11.1
Data shown using pictures or symbols is called a
(A) pictograph(B) tally table(C) line(D) bar graph
12.1
In a pictograph, one symbol stands for 5 students. Six symbols stand for
(A) 6 students(B) 35 students(C) 30 students(D) 11 students
13.1
In a bar graph, all the bars should have
(A) no labels(B) random gaps(C) different widths(D) the same width
14.1
The smallest prime number is
(A) 3(B) 0(C) 1(D) 2
15.1
The greatest common factor of 12 and 18 is
(A) 36(B) 2(C) 3(D) 6
16.1
Which pair of numbers is co-prime?
(A) 10 and 15(B) 4 and 6(C) 8 and 15(D) 9 and 12
17.1
The prime factorisation of 60 is
(A) 4 × 15(B) 6 × 10(C) 2 × 2 × 3 × 5(D) 2 × 30
18.1
A number divisible by both 2 and 5 always ends in
(A) 0(B) any even digit(C) 5(D) 2
19.1
Assertion (A): 1 is not a prime number.Reason (R): A prime number has exactly two factors.
(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): A ray has two end points.Reason (R): A ray goes on endlessly in one direction.
(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
The triangular numbers are 1, 3, 6, 10, 15... Find the 7th and 8th triangular numbers.
ORFind the sum of the first 8 odd numbers using the pattern rule.
22.2
∠AOB is a straight angle. A ray OC makes ∠AOC = 55°. Find ∠COB and name the type of each angle.
ORTwo angles are supplementary. If one angle is 65 degrees more than the other, find both angles.
23.2
Apply Kaprekar's routine to the number 3524 for one step.
24.2
A survey of 20 students' favourite fruits gave: Apple-8, Banana-5, Mango-7. Create a frequency table description and find the total.
25.2
List all the factors of 36 and identify which are prime.
SECTION C
This section comprises 6 short answer (SA) type questions of 3 marks each.
26.3
A staircase pattern has Step 1 with 1 block, Step 2 with 3 blocks, Step 3 with 6 blocks (triangular numbers). (a) Find blocks in Step 6. (b) Find the total blocks needed for a 6-step staircase. (c) Write the general formula for Step n.
ORPascal triangle starts: Row 1: 1, Row 2: 1 1, Row 3: 1 2 1, Row 4: 1 3 3 1. (a) Write Row 5 and Row 6. (b) What is the sum of numbers in Row 5? (c) What pattern do you see in the row sums?
27.3
Pascal's triangle Row 5 is 1,4,6,4,1 and Row 6 is 1,5,10,10,5,1. (a) Write Row 7. (b) Find the sum of Row 7. (c) What is the pattern in row sums?
28.3
(a) Classify the angles 35°, 90°, 140° and 180°. (b) Find the angle that makes a straight angle together with 65°. (c) Through how many degrees does the minute hand of a clock turn in 20 minutes?
29.3
The number 142857 has an interesting property. (a) Calculate 142857 × 2. (b) Calculate 142857 × 3. (c) What do you notice about the digits in each product?
30.3
The following data shows marks scored by 5 students: 45, 60, 55, 70, 50. (a) Organise this data in ascending order. (b) Find the range of the data. (c) If drawn as a bar graph, what scale would be appropriate?
31.3
Find the HCF and LCM of 24 and 36 using prime factorisation. (a) Write prime factorisation of both. (b) Find HCF. (c) Find LCM.
ORUsing the Sieve of Eratosthenes method, list all prime numbers between 30 and 50.
SECTION D
This section comprises 4 long answer (LA) type questions of 5 marks each.
32.5
A pattern of dots forms hexagonal numbers: 1, 7, 19, 37... (a) Find the difference between consecutive terms. (b) Predict the 5th hexagonal number. (c) Verify using the formula 3n²-3n+1. (d) Find the 6th hexagonal number. (e) What type of sequence is formed by the differences?
33.5
Look at the hands of a clock. (a) Through what angle does the minute hand turn in 15 minutes? (b) In 40 minutes? (c) What is the angle between the hands at 4 o'clock? (d) Classify each of the angles in (a), (b) and (c). (e) At which o'clock time between 12 and 6 do the hands make a right angle?
ORRays OP and OQ point in opposite directions, so ∠POQ is a straight angle. A ray OR makes ∠POR = 3x and ∠ROQ = 2x. (a) Write an equation for x. (b) Solve for x. (c) Find ∠POR. (d) Find ∠ROQ. (e) Classify both angles.
34.5
Explore Kaprekar's routine fully with the number 5432. (a) Perform step 1 (descending minus ascending). (b) Perform step 2 using the result. (c) Continue until you reach 6174 or explain why it stops early. (d) How many steps did it take? (e) What is significant about 6174?
35.5
A class of 30 students was surveyed on their favourite subject: Maths-10, Science-8, English-6, Hindi-6. (a) Create a frequency table. (b) Draw conclusions about the most and least popular subjects. (c) What fraction of students prefer Maths? (d) If represented as a bar graph, suggest a suitable scale. (e) Verify the total matches 30 students.
ORTwo numbers have HCF 6 and LCM 72. (a) Use the relationship between HCF, LCM and the product of numbers to find their product. (b) If one number is 24, find the other number. (c) Verify your answer using prime factorisation. (d) Are 24 and your answer co-prime? (e) Explain why or why not.
SECTION E
This section comprises 3 source based / case based units of assessment of 4 marks each with sub-parts.
36.
40 students voted for their favourite fruit: Apple 12, Mango 15, Banana 8, Grapes 5.(i) Which fruit is liked the most?1(ii) How many more students like mango than banana?1(iii) In a pictograph where one symbol = 2 students, how many symbols are needed for each fruit?2OR(iii) In a bar graph with the scale 1 unit = 3 students, how tall should the bars for apple and mango be?2
37.
A shopkeeper wants to pack 24 chocolates and 36 toffees into identical gift packets, with nothing left over.(i) List all the factors of 24.1(ii) List the common factors of 24 and 36.1(iii) What is the greatest number of packets she can make, and what will each packet contain?2OR(iii) Two lights blink every 4 seconds and every 6 seconds. If they blink together now, after how many seconds will they blink together again, and how many times will this happen in one minute?2
38.
Look at an ordinary clock with hour and minute hands.(i) What is the angle between the hands at 3 o’clock?1(ii) What kind of angle do the hands make at 4 o’clock?1(iii) How many degrees does the minute hand turn from 12 to 6, and from 12 to 9? Name each kind of angle.2OR(iii) Write the steps to draw an angle of 65° using a protractor.2
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