CBSE Class 5 Mathematics Revision Worksheet Set 07

Question 1. Use the given motifs to make a pattern with given rule :-
a) \((\diamond, \frac{1}{4} \text{ turn clockwise})\)
b) \((\Box, \frac{1}{2} \text{ turn})\)
c) \(A (\frac{1}{8} \text{ turn anti-clockwise})\)
d) \((\updownarrow, \frac{1}{6} \text{ turn})\)
Answer:
a) Rotating the diamond shape by \(\frac{1}{4}\) turn clockwise (90 degrees each time):
\(\diamond \rightarrow \diamond \rightarrow \diamond \rightarrow \diamond\)
b) Rotating the square box by \(\frac{1}{2}\) turn (180 degrees each time):
\(\Box \rightarrow \Box \rightarrow \Box\)
c) Rotating letter A by \(\frac{1}{8}\) turn (45 degrees) anti-clockwise successively:
\(A \rightarrow \text{rotated } A \rightarrow \text{rotated } A\)
d) Rotating the vertical arrow by \(\frac{1}{6}\) turn (60 degrees) successively:
\(\updownarrow \rightarrow \text{slanted arrow} \rightarrow \text{slanted arrow}\)
In simple words: Apply the specified fractional turns to rotate the given shape step by step to form a repetitive pattern.

Exam Tip: Remember that a full turn is 1. A fraction like \(\frac{1}{4}\) means a quarter turn (90 degrees), and \(\frac{1}{2}\) means a half turn (180 degrees).

Question 2. Write 6 English alphabets which look the same after being rotated by half a turn .
Answer:
The 6 English capital alphabets that look the same after a half turn (180-degree rotation) are:
H, I, N, O, S, Z
In simple words: These letters look identical even if you turn the page upside down.

Exam Tip: Capital letters with rotational symmetry of order 2 are H, I, N, O, S, X, Z.

Question 3. Write 5 four digit numbers which look the same after being rotated by half a turn .
Answer:
The digits that look the same after a half turn (180-degree rotation) are 0, 1, and 8 (using digital display style or standard symmetrical digits).
Five 4-digit numbers formed using these digits that look the same upside down are:
1. 1001
2. 8008
3. 8118
4. 1881
5. 8088
In simple words: Choose numbers made of digits like 0, 1, and 8 which do not change their shape when turned upside down.

Exam Tip: Ensure every digit in the 4-digit number is individually rotationally symmetric (0, 1, 8).

Question 4. Draw the lines of symmetry for the following shapes :-
a) Star
b) Arrow
c) Circle
d) Smiley face
Answer:
a) A standard 5-pointed star has 5 lines of symmetry passing from each vertex to the opposite side.
b) A standard symmetrical arrow has 1 vertical line of symmetry down its middle.
c) A circle has an infinite number of lines of symmetry passing through its center.
d) A symmetrical smiley face has 1 vertical line of symmetry down its center.
In simple words: Lines of symmetry divide a shape into two identical mirror-image halves.

Exam Tip: A circle always has infinite lines of symmetry, whereas regular polygons have as many lines of symmetry as they have sides.

Question 5. Convert the following numbers into palindromes :-
a) 783
b) 519
c) 748
Answer:
To convert a number into a palindrome, reverse its digits and add it to the original number. Repeat if necessary.
a) For 783:
Original = 783, Reversed = 387
\(783 + 387 = 1170\)
Now take 1170, Reversed = 0711 (or 711)
\(1170 + 0711 = 1881\)
Palindrome = 1881

b) For 519:
Original = 519, Reversed = 915
\(519 + 915 = 1434\)
Now take 1434, Reversed = 4341
\(1434 + 4341 = 5775\)
Palindrome = 5775

c) For 748:
Original = 748, Reversed = 847
\(748 + 847 = 1595\)
Now take 1595, Reversed = 5951
\(1595 + 5951 = 7546\)
Now take 7546, Reversed = 6457
\(7546 + 6457 = 14003\)
Now take 14003, Reversed = 30041
\(14003 + 30041 = 44044\)
Palindrome = 44044
In simple words: A palindrome number reads the same forwards and backwards. Keep adding the reverse of the number until you get a palindromic number.

Exam Tip: Always double-check your addition at each step when reversing and adding numbers.

Question 6. Draw mirror halves of the following shapes :-
a) Shape with circles inside
b) Arrowhead shape
Answer:
a) Complete the asymmetrical blob and circle patterns symmetrically across the dotted mirror line.
b) Complete the chevron/arrowhead polygon across the vertical mirror line so that corresponding points are equidistant from the mirror line.
In simple words: Draw the exact reflection of the given half on the other side of the mirror line.

Exam Tip: Measure the perpendicular distance from key vertices to the mirror line and plot points at the same distance on the opposite side.

Question 7. Fill this magic square using all the numbers from 41 to 49 .
Rule :- The total of each line is 135 .
Answer:
Using numbers from 41 to 49, the magic square with a line sum of 135 is arranged as follows:

Verification: Each row, column, and diagonal adds up to 135 (e.g., \(48 + 43 + 44 = 135\)).
In simple words: Place numbers 41 to 49 in the 3 by 3 grid such that every row, column, and diagonal adds up to 135.

Exam Tip: In a 3 by 3 magic square, the middle number is always the average of the sequence (\(45\)).

Question 8. Guess the secret number using the clues given below :-
a) It is larger than \(\frac{3}{4}\) of 100.
b) It is more than 8 tens and less than 9 tens.
c) The tens digit is one less than the ones digit.
d) Together the digits have a sum of 17.
Answer:
a) \(\frac{3}{4}\) of 100 = \(3 \times 25 = 75\). The number is larger than 75.
b) More than 8 tens (80) and less than 9 tens (90), so the number lies between 80 and 90.
c) Tens digit is one less than the ones digit. Since it is in the eighties, tens digit is 8, so ones digit is \(8 + 1 = 9\). The number is 89.
d) Sum of digits of 89 = \(8 + 9 = 17\).
Answer: 89
In simple words: Following all clues step by step leads us directly to the number 89.

Exam Tip: Break down multi-clue word problems one condition at a time to narrow down the possibilities.

Question 9. Draw any two shapes which look the same after \(\frac{1}{3}\) turn .
Answer:
Two shapes that look the same after a \(\frac{1}{3}\) turn (120-degree rotation) are:
1. An equilateral triangle.
2. A three-bladed fan (or Mercedes-Benz logo style propeller shape).
In simple words: Shapes with 3-fold rotational symmetry look identical when rotated by one-third of a full circle.

Question 10. Draw any two shapes which look the same after \(\frac{1}{6}\) turn .
Answer:
Two shapes that look the same after a \(\frac{1}{6}\) turn (60-degree rotation) are:
1. A regular hexagon.
2. A six-pointed star (Star of David).
In simple words: Shapes with 6-fold rotational symmetry fit onto themselves when rotated by one-sixth of a full circle (60 degrees).

Exam Tip: Regular hexagons and six-pointed stars have 6 lines of symmetry and rotational symmetry of order 6.

Question 11. Complete the pattern :-
4x 4 = 16
34x 34 = 11 56
334x 334 = 11156
[... continuing the pattern]
Answer:
Analyzing the pattern:
\(4 \times 4 = 16\)
\(34 \times 34 = 1156\)
\(334 \times 334 = 11156\)
Continuing the pattern for four and five digits:
\(3334 \times 3334 = 111156\)
\(33334 \times 33334 = 1111156\)
In simple words: For each additional 3 added to the number, another 1 is inserted before 56 in the product.

Exam Tip: Look for repeating structural patterns in multiplication sequences.

Question 12. Make them equal:-
a) _____ + _____ + _____ = _____ + _____ + _____
b) _____ + _____ + _____ = _____ + _____ + _____
Answer:
This is an open-ended number sentence balancing problem. Any set of addends that sum to the same total on both sides is correct.
Example a) \(10 + 20 + 30 = 15 + 25 + 20\)
Example b) \(5 + 15 + 25 = 10 + 15 + 20\)
In simple words: Fill in numbers such that the total sum on the left side equals the total sum on the right side.

Exam Tip: Always verify that both sides of the equals sign add up to the exact same sum.

Question 13. Draw two more sides in the given figure to complete the shape such that it is area is 10 sq cm .
Answer:
Given the grid where each square is 1 sq cm, the existing partial shape has a certain area. To make the total area 10 sq cm, draw two straight line segments connecting the endpoints such that the enclosed region covers exactly 10 unit squares.
In simple words: Add two lines to enclose a total region equal to 10 grid squares.

Exam Tip: Count the full squares and half squares carefully on the grid to ensure the total area equals 10 sq cm.

Question 14. Draw 5 different shapes using 6 squares of side 1 sq cm. Find the perimeter of each shape .
Answer:
Using 6 unit squares (tetrominoes/pentominoes/hexominoes concept), we can draw different arrangements:
1. A straight line of 6 squares (1 by 6):
Perimeter = \(6 + 1 + 6 + 1 = 14 \text{ cm}\)
2. A rectangle of 2 by 3 squares:
Perimeter = \(3 + 2 + 3 + 2 = 10 \text{ cm}\)
3. An L-shape arrangement of 6 squares:
Perimeter = \(12 \text{ cm}\)
4. A T-shape arrangement of 6 squares:
Perimeter = \(14 \text{ cm}\)
5. A stepped staircase arrangement of 6 squares:
Perimeter = \(14 \text{ cm}\)
In simple words: Arrange 6 small squares in 5 different ways and count the total outer boundary length for each.

Exam Tip: Perimeter is the distance around the outer boundary. Shapes made of the same number of squares can have different perimeters depending on how they are arranged.

Question 15. Draw different possible rectangles using 24 squares . Side of each square is 1 cm .
Answer:
To find all possible rectangles with an area of 24 sq cm (using 24 unit squares), find the factor pairs of 24:
1. \(1 \text{ cm} \times 24 \text{ cm}\) rectangle
2. \(2 \text{ cm} \times 12 \text{ cm}\) rectangle
3. \(3 \text{ cm} \times 8 \text{ cm}\) rectangle
4. \(4 \text{ cm} \times 6 \text{ cm}\) rectangle
In simple words: Draw rectangles whose length and breadth multiply to give 24. There are 4 possible rectangles.

Exam Tip: List all factor pairs of the given area to ensure you do not miss any possible rectangle dimensions.

Question 16. Draw a grid of 17 x 10 cm . How many shapes each of 5 squares can be drawn into the grid .
Answer:
Total area of the grid = \(17 \text{ cm} \times 10 \text{ cm} = 170 \text{ sq cm}\).
Area of each small shape = 5 squares (each of 1 sq cm) = 5 sq cm.
Number of shapes that can fit = \(\frac{170}{5} = 34\).
In simple words: Divide the total grid area by the area of one shape to find how many such shapes can fit inside.

Exam Tip: Total shapes = Total area \(\div\) Area of one shape, assuming they tile perfectly without overlapping.

Question 17. Calculate the perimeter of a rectangle whose l = 5 cm and b = 3 cm .
Answer:
Length (\(l\)) = 5 cm
Breadth (\(b\)) = 3 cm
Perimeter of a rectangle = \(2 \times (l + b)\)
\(= 2 \times (5 + 3)\)
\(= 2 \times 8 = 16 \text{ cm}\)
In simple words: Add length and breadth together, then multiply the sum by 2 to get the perimeter.

Exam Tip: Always include proper units (cm) in your final answer.

Question 18. Calculate the area of a square of side 8 cm .
Answer:
Side of the square (\(s\)) = 8 cm
Area of a square = \(s \times s\)
\(= 8 \times 8 = 64 \text{ sq cm}\)
In simple words: Multiply the side length by itself to find the area of a square.

Exam Tip: Area is always expressed in square units (sq cm or cm\(^2\)).

Question 19. Draw the following shapes on the square grid :-
a) A square with perimeter 12 cm .
b) A rectangle of area 14 sq cm .
Answer:
a) Perimeter of square = 12 cm
Side of square = \(\frac{12}{4} = 3 \text{ cm}\). Draw a square with each side equal to 3 cm on the grid.
b) Area of rectangle = 14 sq cm
Choose factor pair \(2 \text{ cm} \times 7 \text{ cm}\). Draw a rectangle with length 7 cm and breadth 2 cm on the grid.
In simple words: Calculate the side or dimensions first, then draw the square (3 cm by 3 cm) and rectangle (7 cm by 2 cm) on the grid.

Exam Tip: For a square, divide perimeter by 4 to get the side length. For a rectangle, use factor pairs of the given area.

Question 20. Find the side of a square whose perimeter is 40 cm .
Answer:
Perimeter of square = 40 cm
Side of a square = \(\frac{\text{Perimeter}}{4}\)
\(= \frac{40}{4} = 10 \text{ cm}\)
In simple words: Divide the total perimeter by 4 to find the length of one side of the square.

Exam Tip: Since all four sides of a square are equal, dividing the perimeter by 4 always gives the side length.