Series RTEQ.P. Code 59/-1/-1
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
The perimeter of a rectangle 8 cm long and 5 cm wide is
(A) 40 cm(B) 80 cm(C) 13 cm(D) 26 cm
2.1
The area of a square of side 6 cm is
(A) 6 cm²(B) 24 cm²(C) 12 cm²(D) 36 cm²
3.1
The perimeter of a regular hexagon of side 4 cm is
(A) 28 cm(B) 24 cm(C) 16 cm(D) 20 cm
4.1
A rectangle 10 cm by 6 cm is cut along a diagonal. The area of each triangle is
(A) 30 cm²(B) 16 cm²(C) 32 cm²(D) 60 cm²
5.1
A fraction equivalent to 2/3 is
(A) 2/6(B) 4/9(C) 4/6(D) 3/2
6.1
7/4 written as a mixed fraction is
(A) 1 3/4(B) 1 4/7(C) 3 1/4(D) 2 1/4
7.1
1/2 + 1/4 is equal to
(A) 2/6(B) 3/4(C) 1/6(D) 2/4
8.1
18/24 in its lowest terms is
(A) 2/3(B) 9/12(C) 6/8(D) 3/4
9.1
Each angle of a square measures
(A) 45°(B) 60°(C) 90°(D) 120°
10.1
The diagonals of a rectangle are
(A) parallel(B) unequal(C) equal(D) always perpendicular
11.1
The instrument used to draw a circle is a
(A) compass(B) set square(C) ruler(D) protractor
12.1
The number of lines of symmetry of a square is
(A) 2(B) 4(C) 1(D) 8
13.1
The number of lines of symmetry of a circle is
(A) 4(B) infinitely many(C) 1(D) 2
14.1
The smallest angle of rotational symmetry of an equilateral triangle is
(A) 120°(B) 180°(C) 60°(D) 90°
15.1
(−5) + 8 is equal to
(A) −13(B) 3(C) 13(D) −3
16.1
Which of these is the greatest?
(A) −1(B) 0(C) −10(D) −2
17.1
4 − 9 is equal to
(A) −13(B) 5(C) 13(D) −5
18.1
The opposite (additive inverse) of −7 is
(A) −7(B) 7(C) 0(D) 1/7
19.1
Assertion (A): Two rectangles with the same area always have the same perimeter.Reason (R): Area of a rectangle = length × breadth.
(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): The letter A has a vertical line of symmetry.Reason (R): A line of symmetry divides a figure into two halves that are mirror images.
(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
Find the area of a triangle with base 12 cm and height 7 cm.
ORA rectangular garden is 15 m long and 9 m wide. Find its perimeter.
22.2
Simplify 24/36 to its lowest terms.
ORAdd: 2/3 + 1/6. Show your work.
23.2
Describe the steps to construct the perpendicular bisector of a line segment AB.
24.2
Which capital letters of the English alphabet have both line symmetry and rotational symmetry? Give two examples.
25.2
Calculate: (-15) + 8 - (-6)
SECTION C
This section comprises 6 short answer (SA) type questions of 3 marks each.
26.3
A square garden has area 225 m². (a) Find the side length. (b) Find the perimeter. (c) If a path 2m wide is built inside all around, find the area of the remaining garden.
ORA composite figure consists of a rectangle of 8 cm x 5 cm with a square of side 3 cm cut from one corner. (a) Find the perimeter of the composite figure. (b) Find the area of the composite figure. (c) If the figure is to be painted at Rs 15 per sq cm find the cost.
27.3
A triangular field has sides 13 m, 14 m, and 15 m. Its height corresponding to the 14 m base is 12 m. (a) Find its area. (b) Find its perimeter. (c) Compare which is greater — area (in m²) or perimeter (in m).
28.3
Ramesh ate 2/5 of a cake and Suresh ate 1/4 of the same cake. (a) What fraction of the cake did they eat together? (b) What fraction remains? (c) Who ate more?
29.3
Explain the construction of a 60-degree angle using compass and ruler. (a) What is the first step? (b) What is the second step? (c) Why does this method work?
30.3
A figure has rotational symmetry of order 5. (a) What is the angle of rotation? (b) If it also has 5 lines of symmetry, what shape could it be? (c) Does a regular pentagon fit this description?
31.3
The temperature in a city changed as follows: started at -8°C, rose by 15°C, then dropped by 6°C. (a) Find the temperature after the rise. (b) Find the final temperature after the drop. (c) What was the net change from the starting temperature?
ORA shopkeeper had a profit of Rs 450 on Monday and a loss of Rs 680 on Tuesday. (a) Represent both as integers. (b) Find the net profit or loss over the two days. (c) State whether it is an overall profit or loss.
SECTION D
This section comprises 4 long answer (LA) type questions of 5 marks each.
32.5
A rectangular hall is 20 m long and 15 m wide. (a) Find its area. (b) Find its perimeter. (c) If the cost of flooring is Rs 250 per m², find the total flooring cost. (d) If a border 1m wide is left all around the hall (unfinished), find the area to be floored. (e) Find the new flooring cost.
33.5
A tank is 3/4 full of water. (a) If the tank's total capacity is 200 litres, how much water is in it? (b) If 1/5 of the water is used, how much water is used? (c) How much water remains? (d) What fraction of the total capacity does the remaining water represent? (e) Verify your answer.
34.5
Describe fully how to construct a square with side 5 cm using ruler and compass. (a) What is the first step? (b) How do you ensure right angles? (c) How do you complete all four sides? (d) How can you verify your construction is accurate? (e) What geometric properties must a correctly constructed square satisfy?
ORA lift starts at the ground floor (0). It goes down 3 floors, then up 7 floors, then down 5 floors, then up 2 floors. (a) Represent each movement as an integer. (b) Find the final floor position. (c) What was the highest floor reached during the journey? (d) What was the lowest floor reached? (e) Find the total distance travelled (sum of absolute movements).
35.5
Compare the symmetry properties of a square, rectangle (non-square), and rhombus (non-square). (a) Lines of symmetry for each. (b) Order of rotational symmetry for each. (c) Which has the most symmetry overall? (d) Explain why a square has more symmetry than a rectangle. (e) Explain why a rhombus has different symmetry than a rectangle.
ORA company recorded profits and losses (in thousands of rupees) over 5 months: +25, -10, +18, -32, +15. (a) Find the net profit or loss over 5 months. (b) Find the average monthly result. (c) Which month had the worst performance? (d) Which month had the best performance? (e) If the company needs an average of at least +5000 per month to survive, does it meet this target?
SECTION E
This section comprises 3 source based / case based units of assessment of 4 marks each with sub-parts.
36.
A rectangular garden is 20 m long and 15 m wide.(i) Find its perimeter.1(ii) Find its area.1(iii) Find the cost of fencing it at ₹25 per metre and of laying grass at ₹40 per square metre.2OR(iii) A square garden has the same perimeter. Find its side and its area.2
37.
A pizza is cut into 8 equal slices. Anu eats 3 slices and Bala eats 2 slices.(i) What fraction of the pizza did Anu eat?1(ii) What fraction did they eat together?1(iii) What fraction is left? Who ate more, and by how much?2OR(iii) Which is greater, 3/8 or 2/5? Compare using equivalent fractions.2
38.
In a building, the ground floor is 0, floors above are 1, 2, 3, … and the basements are −1, −2, −3.(i) A lift at floor 3 goes down 5 floors. Where does it stop?1(ii) How many floors does the lift go up from −3 to 4?1(iii) Using the token model, find (+5) + (−8) and explain your steps.2OR(iii) Shimla is at −4 °C and Delhi is at 6 °C. Which is colder, and by how many degrees?2
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