Series RTEQ.P. Code 64/0/0
Roll No.
RTE LEARN · CBSE PATTERN 2026–27
MATHEMATICS
Annual 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
Figures with exactly the same shape and size are called
(A) congruent(B) parallel(C) symmetric(D) similar only
2.1
Which of these is NOT a condition for congruence of triangles?
(A) RHS(B) SSS(C) SAS(D) AAA
3.1
In an isosceles triangle, the angles opposite the equal sides are
(A) equal(B) always 90°(C) supplementary(D) unequal
4.1
(−8) × (−5) is equal to
(A) 40(B) 13(C) −13(D) −40
5.1
(−36) ÷ 4 is equal to
(A) 32(B) −9(C) 9(D) −32
6.1
The product of three negative integers is
(A) positive(B) zero(C) either positive or negative(D) negative
7.1
The HCF of 18 and 24 is
(A) 6(B) 3(C) 72(D) 12
8.1
The LCM of 4 and 6 is
(A) 2(B) 12(C) 10(D) 24
9.1
Two numbers are co-prime if their HCF is
(A) the smaller number(B) 0(C) 1(D) 2
10.1
0.4 × 0.3 is equal to
(A) 0.12(B) 12(C) 1.2(D) 0.012
11.1
7.5 ÷ 100 is equal to
(A) 7.500(B) 0.75(C) 0.075(D) 750
12.1
2.5 × 1000 is equal to
(A) 2500(B) 250(C) 25000(D) 25
13.1
The mean of 2, 4, 6 and 8 is
(A) 6(B) 20(C) 4(D) 5
14.1
The mode of 3, 5, 5, 7, 5, 2 is
(A) 5(B) 3(C) 7(D) 2
15.1
Which shape can tile a flat floor on its own without gaps?
(A) Circle(B) Regular octagon(C) Regular pentagon(D) Regular hexagon
16.1
The solution of x + 7 = 15 is
(A) 7(B) 22(C) −8(D) 8
17.1
The solution of 3x = 27 is
(A) 30(B) 81(C) 9(D) 24
18.1
If 2x − 5 = 11, then x is
(A) 3(B) 8(C) 6(D) 16
19.1
Assertion (A): The HCF of two consecutive numbers is 1.Reason (R): Two consecutive numbers have no common factor other than 1.
(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): (−5) × 0 = −5.Reason (R): Any integer multiplied by 0 gives 0.
(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
Triangle ABC has AB=5,BC=7,CA=6. Triangle DEF has DE=5,EF=7,FD=6. Are they congruent? By which rule?
22.2
Evaluate: (-3)×4+(-2)×(-5)
23.2
Two bells ring every 6 and 8 minutes. After how many minutes will they ring together?
24.2
What is 5.6 ÷ 0.7?
ORSolve: 6y + 7 = 4y + 21
25.2
Find the mean of 3, 8, 10, 5, 4.
ORDescribe the steps to construct the perpendicular bisector of segment XY.
SECTION C
This section comprises 6 short answer (SA) type questions of 3 marks each.
26.3
Triangle PQR has angle P=angle Q=50°, PQ=8cm. Triangle XYZ has angle X=angle Y=50°, XY=8cm. (a) Are they congruent? (b) By which rule? (c) Find angle R and Z.
ORAn equilateral triangle has side 6cm. (a) Find all angles. (b) Explain why it is also isosceles. (c) Is SSS a valid way to prove two such triangles congruent?
27.3
A shopkeeper has a profit of Rs 450 and a loss of Rs 680. (a) Represent as integers. (b) Find net result. (c) State overall profit or loss.
28.3
Two numbers have HCF 6 and LCM 72. (a) Find their product. (b) If one number is 24, find the other. (c) Verify using prime factorisation.
29.3
A rope of 8.4m is cut into 4 equal pieces, then one piece is cut in half. Find final length of smallest pieces.
30.3
A family's heights are 118,165,170,173,175cm. (a) Find the mean. (b) Find the median. (c) If 118 is removed, does mean increase or decrease?
31.3
Describe how to construct a 60-degree angle using compass and ruler, explaining why it works.
ORMadhubanti has Rs 500. Delivery costs Rs 50, each snack plate costs Rs 25. (a) Frame the equation. (b) Solve. (c) If she has 5 family members, how many friends can she invite?
SECTION D
This section comprises 4 long answer (LA) type questions of 5 marks each.
32.5
A right-angled triangle has legs 6 cm and 8 cm and hypotenuse 10 cm. (a) Find its area. (b) Find its perimeter. (c) State the RHS congruence condition. (d) What can we conclude about two triangles that are congruent by RHS? (e) Another right-angled triangle has hypotenuse 10 cm and one leg 8 cm. Is it congruent to the first triangle? Why?
33.5
Prove that if triangle ABC≅triangle DEF by SAS with AB=DE, angle A=angle D, and AC=DF, find the conclusions using CPCT. (a) Which sides/angles become equal? (b) State the full congruence conclusion. (c) Explain why SAS is sufficient (not requiring all 6 parts to be given).
34.5
A lift moves: down 3 floors, up 7, down 5, up 2 from ground floor(0). (a) Represent each as integers. (b) Find final position. (c) Find highest floor reached. (d) Find lowest floor reached. (e) Find total distance travelled.
ORA shop sells rice at ₹45.50 per kg. (a) Find the cost of 6.5 kg. (b) If a customer pays ₹500, find the change. (c) How many kg can be bought for ₹364? (d) Arrange 6.5 kg, 6.05 kg and 6.55 kg in increasing order. (e) Write 6.5 kg in grams.
35.5
A dot plot shows onion prices over 10 days: 20,22,20,25,20,22,24,20,22,25. (a) Find the mode. (b) Find the mean. (c) Find the median. (d) What does a dot plot show that a table doesn't? (e) Which measure best represents typical price?
ORA gardener has 90 roses and 60 marigolds. (a) Find the maximum number of identical bouquets with no flowers left over. (b) Find flowers per bouquet of each type. (c) If he also has 45 lilies, does adding lilies change the maximum bouquets? Find the new maximum.
SECTION E
This section comprises 3 source based / case based units of assessment of 4 marks each with sub-parts.
36.
In Leh, the temperature at 6 am was −8 °C. It rose by 3 °C every hour until noon.(i) What was the temperature at 9 am?1(ii) What was the temperature at noon?1(iii) By night it fell to −6 °C from the noon temperature. Find the total fall. If it fell evenly over 4 hours, find the fall per hour.2OR(iii) Find the difference between the highest and lowest temperatures of the day and write it as an integer expression.2
37.
Three school bells ring at intervals of 6, 8 and 12 minutes. They rang together at 8:00 am.(i) Find the LCM of 6, 8 and 12.1(ii) When will they next ring together?1(iii) How many more times will they ring together up to 10:00 am, and at what times?2OR(iii) A room is 420 cm by 360 cm. Find the side of the largest square tile that fits exactly, and the number of tiles needed.2
38.
Ravi’s age is three times his son’s age. The sum of their ages is 48 years.(i) If the son’s age is x years, write Ravi’s age.1(ii) Write an equation for the sum of their ages.1(iii) Solve the equation to find both ages, and check your answer.2OR(iii) "I think of a number, multiply it by 4 and add 6. The answer is 34." Form an equation and find the number.2
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