ukg - sample(august)

 

Answer key- class 7 annual practice paper

 Answer key

SECTION A

1. 3x − 5 = 2x + 7 ⇒ 3x − 2x = 7 + 5 ⇒ x = 12 → a

2. 2³ × 4² = 8 × 16 = 128 → b

3. 25% of 400 = 100, so new value = 500 → b

4. 650 is not a perfect square → d

5. Third angle = 180 − (45 + 65) = 70° → a

6. Rhombus has 2 lines of symmetry → b

7. SP = 1000, discount 20% ⇒ SP = 800, gain 20% ⇒ CP = 800 ÷ 1.2 = 666.67 ≈ 700 → b

8. (3²)³ = 3⁶ = 729 → c

9. Area = ½ × base × height, if base doubles → area doubles → a

10. Cuboid has 12 edges → b

11. Congruent triangles: equal sides and angles → b

12. Mean = (2+4+6+8)/4 = 20/4 = 5 → b

13. Smallest 3-digit perfect square = 100 → a

14. 10² ÷ 10⁰ = 100 ÷ 1 = 100 → a

15. Parallelogram rotational symmetry order = 2 → b

SECTION B

16. 8 − {3 + 2[5 − (3 − 1)]}
    = 8 − {3 + 2[5 − 2]}
    = 8 − {3 + 2×3}
    = 8 − {3 + 6}
    = 8 − 9 = −1

17. 7x/8 + 1/4 = 3/4
    Convert 1/4 = 2/8 ⇒ 7x/8 + 2/8 = 6/8
    ⇒ (7x + 2)/8 = 6/8 ⇒ 7x + 2 = 6 ⇒ 7x = 4 ⇒ x = 4/7

18. Successive discounts:
    1000 × 0.9 × 0.8 = 1000 × 0.72 = ₹720

19. (3⁵ × 10⁵ × 25)/(5⁷ × 6⁵)
    10⁵ = (2×5)⁵ = 2⁵×5⁵
    25 = 5²
    6⁵ = (2×3)⁵ = 2⁵×3⁵
    Cancel: 3⁵ cancels, 2⁵ cancels
    Remaining: (5⁵×5²)/5⁷ = 1 → 1

20. Let equal sides = x, base = x/2
    Perimeter = x + x + x/2 = 30
    ⇒ (5x /2) = 30 ⇒ x = 12
    Base = 6
    Sides: 12 cm, 12 cm, 6 cm

21. Total outcomes = 25
    (i) Multiples of 3 or 5: {3,5,6,9,10,12,15,18,20,21,24,25} = 12
    Probability = 12/25
    (ii) Perfect squares: {1,4,9,16,25} = 5
    Probability = 5/25 = 1/5

22. Regular pentagon: 5 lines, order 5
    Parallelogram: 0 lines, order 2
    Equilateral triangle: 3 lines, order 3

23. QRS ≅ QPS
    QS common
    ∠RQS = ∠SQP (angle bisector)
    ∠RSQ = ∠QSP (angle bisector)
    Hence congruent (ASA)

24. Construction steps:
    Draw AB = 5 cm
    At B construct 60°
    Cut BC = 6 cm on that ray
    Join AC

25. Circumference = πd = (22/7)×49 = 154 cm
    Distance in 100 rotations = 154 × 100 = 15400 cm = 154 m

SECTION C

26. 2^x × 4^{x+1} = 128
    4 = 2² ⇒ 4^{x+1} = 2^{2x+2}
    So 2^x × 2^{2x+2} = 2^{3x+2}
    128 = 2⁷ ⇒ 3x + 2 = 7 ⇒ 3x = 5 ⇒ x = 5/3

27. In Δ ABC, AB = AC, D midpoint of BC ⇒ BD = DC
    AD common
    AB = AC
    So Δ ABD ≅ Δ ACD ⇒ ∠ADB = ∠ADC = 90°
    Hence AD ⟂ BC

28. In triangle ABC:
    Angle A = 30° + 60° = 90°
    Angle C = 70°
    Angle B = 180 − (90 + 70) = 20° ⇒ a = 20°
    In triangle ADC: angles 60° and 70°, so c = 50°
    Then b = 180 −  50 = 130°
    Final: a = 20°, b = 130°, c = 50°

29. SI = 1768 − 1600 = 168
    SI = (P×R×T) /100 ⇒ 168 = (1600×6×T) /100
    ⇒ 168 = 96 T ⇒ T = 168/96 = 1.75 years (1 year 9 months)

30. Area of big circle = (22/7)×14² = 616
    Area of 2 small circles = 2×[(22/7)×3.5²] = 77
    Rectangle area = 3×1 = 3
    Remaining area = 616 − (77 + 3) = 536 cm²

SECTION D

31. Initial: 25² = 7² + x² ⇒ x² = 625 − 49 = 576 ⇒ x = 24
    New base = 24 + 8 = 32
    New height = √(625 − 1024) = √(−399) → not possible (ladder too short)
    So ladder cannot reach wall after moving → No height (invalid situation)

32. Bar graph: Plot students on x-axis and marks on y-axis with values
    Ajay 450, Bali 500, Dipti 300, Geetika 360, Hari 400, Faiyaz 540

33. (i) Rectangle area = 18×10 = 180
    Subtract triangles (calculate from diagram) → shaded area = 110 cm²
    (ii) Square = 20×20 = 400
    Subtract triangles → shaded area = 150 cm²

Annual practice question paper- class 7

CLASS VII – MATHEMATICS ANNUAL EXAMINATION 

Time: 2 hours 15 minutes
Maximum Marks: 80

SECTION A – OBJECTIVE (1 × 15 = 15)

(

1. If ( 3x - 5 = 2x + 7 ), then x =
   a) 12 b) -12 c) 2 d) 7

2. ( 2^3 × 4^2 = )
   a) 64 b) 128 c) 32 d) 256

3. Increase ₹400 by 25%:
   a) 425 b) 500 c) 480 d) 450

4. Which is NOT a perfect square?
   a) 441 b) 529 c) 625 d) 650

5. If two angles of a triangle are 45° and 65°, third angle is:
   a) 70° b) 80° c) 90° d) 100°

6. Number of lines of symmetry in a rhombus:
   a) 1 b) 2 c) 4 d) 0

7. A shopkeeper gives 20% discount on ₹1000 and still gains 20%. CP =
   a) 600 b) 700 c) 800 d) 900

8. ( (3^2)^3 = )
   a) 9 b) 27 c) 729 d) 81

9. Area of a triangle = 1/2 × base × height. If base doubles, area:
   a) doubles b) halves c) same d) quadruples

10. Number of edges in a cuboid:
    a) 8 b) 12 c) 6 d) 10

11. Congruent triangles must have:
    a) equal area only
    b) equal sides and angles
    c) equal perimeter only
    d) same shape only

12. Mean of 2, 4, 6, 8 is:
    a) 4 b) 5 c) 6 d) 8

13. The smallest 3-digit perfect square is:
    a) 100 b) 121 c) 144 d) 169

14. ( 10² ÷ 10⁰ = )
    a) 100 b) 0.01 c) 10 d) -100

15. A parallelogram has rotational symmetry of order:
    a) 1 b) 2 c) 3 d) 4

SECTION B – (10 × 3 = 30)

16. Simplify:
    ( 8 - { 3 + 2[5 - (3 - 1)] } )

17. Solve and check:     

    
    
    

18. After two successive discounts of 10% and 20%, find the final price of ₹1000.

19. Evaluate:
    
    

    
    
    

20. The base of an isosceles triangle is half the other two equal sides. The perimeter of the triangle is 30cm. What is the length of each side of the triangle.

21. A bag contains 25 cards numbered from 1 to 25. A card is drawn at random 

    from the bag. Find the probability that the number on the drawn card is:

    (i) divisible by 3 or 5.                 (ii) A perfect square number.

22. Complete the table:

Polygon	Lines of symmetry	Order of rotation
Regular pentagon	?	?
Parallelogram Equilateral triangle	?                     ?	?                         ?

23. In Fig., QX bisects ∠PQR as well as ∠PSR. State the three facts needed to ensure that △QRS = △QPS.Give reasons for each statement.

    
    
    

24. Construct a triangle ABC  with sides AB= 5 cm, BC = 6 cm and angle B = 60 ⁰ with a pair of compasses amd a ruler.

25. Find the distance covered by the wheel of a truck in 100 rotations if the diameter of the wheel is 49 cm.

SECTION C – (5 × 4 = 20)

26. If ( 2^x × 4^{x+1} = 128 ), find x.

27. In ΔABC, AB = AC. D is midpoint of BC. Prove that AD ⟂ BC.

28. Find the value of a, b, and c 

    
    
    

29. In what time will Rs. 1600 amount to Rs. 1768 at 6% per annum simple interest?

30. From a circular card sheet of radius 14 cm, two circles of radius 3.5 cm and a rectangle of length 3 cm and breadth 1 cm are removed (as shown in the following figure.) Find the area of the remaining sheet. (take π = 22/7)                                                                       

SECTION D – (3 × 5 = 15)

31. A ladder of length 25 m reaches a wall at 7 m height.
    If the base is moved 8 m away, find the new height reached.

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32. Following data gives total marks (out of 600) obtained by six children of a particular class. 

    Represent the data on a bar graph.

    
    
    

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33. In the following figures, find the area of the shaded portions: (i)

Class 2- English model question paper

CLASS 2 – ENGLISH QUESTION PAPER

A. Reading Comprehension

Read the passage carefully.

Riya has a small puppy named Bruno. Bruno is soft and brown. He likes to run in the garden and play with a red ball. Every morning Riya gives him milk and biscuits. Bruno follows Riya everywhere in the house. When Riya comes back from school, Bruno wags his tail and jumps happily. Sometimes Riya takes Bruno to the park. They run and play together. Bruno is a very loyal and loving pet.

Answer the questions

What is the name of the puppy?

___________________________________________________________________________________.

What colour is Bruno?

___________________________________________________________________________________

What does Bruno like to play with?

___________________________________________________________________________________

What does Riya give Bruno in the morning?

___________________________________________________________________________________

What does Bruno do when Riya comes back from school?

___________________________________________________________________________________

Choose the correct answer

The rabbit moves by

a) flying

b) hopping

c) swimming

B. Advertisement Comprehension

Read the advertisement.

Answer the questions.

6. What is the name of the event?

         ___________________________________________________________________________________

     7. Write two things children can enjoy there.

        ___________________________________________________________________________________

      8. What is the ticket price if you and your mother and father attend the fun fair?

        ___________________________________________________________________________________

      9. On which day is the fair and when it starts?

         ___________________________________________________________________________________

C. Androcles and the Lion

Match the word with the meaning

10. Cruel          a. Big open place

11. Arena         b. Thankful

12. Grateful     c. Run away

13. Escape        d. Hurting others

Fill the missing letters

14. L _ O N

15. A _ D R O C L _ S

16. F _ R _ S T

17. T _ O R _

Answer the questions

18. Why did Androcles run away?

          __________________________________________________________________________________

          __________________________________________________________________________________

          __________________________________________________________________________________

18. Why was the lion in pain?

          __________________________________________________________________________________

          __________________________________________________________________________________

          _________________________________________________________________________________

18. What did Androcles remove from the lion’s paw?

          __________________________________________________________________________________

          __________________________________________________________________________________

          _________________________________________________________________________________

D. Poem – Who Has Seen the Wind

Fill in the blanks

21. Who has seen the ______?

22. The leaves hang ______.

23. The trees bow down their ______.

True or False

24. The wind can be seen clearly. ______

25. The leaves tremble when the wind blows. ______

Missing letters

26. W _ N D

27. T _ E M B L _ N G

28. L _ A V _ S

---

Answer the questions

29. How do we know the wind is passing?

          __________________________________________________________________________________

          __________________________________________________________________________________

          _________________________________________________________________________________

29. What happens to the trees when the wind blows?

          __________________________________________________________________________________

          __________________________________________________________________________________

          _________________________________________________________________________________

E. Poem – My Ship

Fill in the blanks

I had the prettiest little __________

__________________________________________

__________________________________________

__________________________________________

Analogy

35. Ship : Sail :: Bird : ______

36. River : Water :: Tree : ______

37. Wind : Blow :: Bird : ______

Rhyming words

38. snow – ______

39. me – ______

40. by – ______

F. Vocabulary (Lessons)

Match the words with meanings

41. Pity               a. Shaking slightly

42. Trembling   b. Person who sells goods

43. Kind              c. Feeling sorry for someone

44. Merchant     d. Good and helpful

Missing letters

45. M _ R C _ A N _

46. G _ A T _ F U _

47. P _ W

48. A _ E N _

G. Do As Directed (Grammar)

49. Write the plural:
    The child is playing in the park.
    (child → ______)

50. Choose the correct word:
    Riya ______ two pencils.
    (has / have)

51. Change into feminine:
    The lion is sleeping.
    (lion → ______)

52. Fill the correct pronoun:
    Rahul and Raja are my brother. ______ are kind.

53. Fill the correct  word:
    ______ flowers are very pretty.
    (this / these)

54. Add the correct article:
    She saw ______ elephant in the zoo.

55. Choose the correct conjunction:
    Which fruit do u like? apples ______ oranges?
    (and / or)

56. Choose the correct adverb:
    The rabbit runs ______.(quick)
    

57. Fill the preposition:
    The cat is ______ the table. ( across / under)

58. Change into past tense:
    She __________ (go) to school yesterday.

59. Make it a question:
    Tomorrow is my Birthday .  (Rewrite as question)

         ____________________________________________________________.

49. Punctuate:
    riya rahul aman and sita are friends

          ____________________________________________________________.

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Math Modal question paper - ct 4 (class 4)

 Class IV – CT 4 Model Question Paper

 SECTION A – OBJECTIVE QUESTIONS

(10 × 1 = 10)

I. Fill in the blanks (4 × 1 = 4)

1. 0.6 is equal to ______ tenths.

2. 1 m = ______ cm.

3. 7:45 pm in 24-hour clock is written as ______.

4. A rectangle is 15 m long and 4 m wide.Its area is ______ sq m.

II. Choose the correct answer (3 × 1 = 3)

5. 3/5 of 25 is:
   a) 10
   b) 12
   c) 15
   d) 20

6. Which of the following is the smallest?
   a) 0.9
   b) 0.09
   c) 0.19
   d) 0.5

7. 2.5 kg is equal to:
   a) 2050 g
   b) 250 g
   c) 2500 g
   d) 25 g

III. True or False (3 × 1 = 3)

8. 1 litre = 100 ml. ______

9. 0.25 means 25 hundredths. _______

10. If a movie starts at 3:00 PM and ends at 5:00 PM, it lasted 3 hours. ______

SECTION B- Answer the following. Show the working:

(9 × 2 = 18)

1. Convert:
   4 ½ kg to g.

2. A square field has area 64 sq m. What is the length of one side?

1. The duration of a movie is 2 hrs 45 mins.
   If the movie starts at 5:35 pm, at what time will it end?

2. A farmer planted 150 trees. 2/3  are neem trees. How many are not neem trees?

1. The circle chart shows different games liked by students.
   The circle represents 80 students.

   
   
   
   
   

   (a) How many students like tennis?
   (b) How many more students like cricket than football?
   (c) Write one benefit of playing games.

2. Convert:
   a) 3 kg 250 g to grams
   b) 4750 ml to litres

3. If 1 kg apples cost ₹120, find the cost of:
   a) 500 g
   b) 3 kg

4. What will be the time 5 hrs 30 mins after 9:45 am?
   Write the answer in both 12- hour and 24- hour clock.

5. The following pictograph shows number of students attending hobby classes:

   Dance – 😀 😀 😀 😀 😀 😀
   Music – 😀 😀 😀 😀 😀 😀 😀
   Drawing – 😀 😀 😀 😀 😀 😀 😀 😀
   Craft – 😀 😀 😀 😀
   Yoga – 😀 😀 😀 😀 😀

   (Each 😀 represents 3 students)

   a) Which class has the most students?
   b) How many students attend dance class?
   c) How many more students attend drawing than craft?
   d) Which class has half the strength of drawing?

Answer the following:

(4 × 3 = 12)

10. A rectangle has length 18 cm and breadth 12 cm.A square has side 12 cm.Which shape has more area? How much more?

10. ½ kg onion costs ₹24 and 2 kg tomato costs ₹80.
    How much should you pay in all if you buy 1½ kg onion and 1 kg tomato?

11. Neha studied from 4:35 PM to 5:20 PM.She again studied from 6:00 PM to 6:45 PM. For how long did she study in total?

12. The bar graph shows the number of ice cream bars sold in a week:

a) Which flavour was sold the most?
b) How many more mango bars were sold than vanilla?
c) How many bars were sold in total?

                                                         *************************

Class 7