CBSE Class 6 Mathematics Question Paper Set 28 with Solutions

Answer: (b) 8. The sum of an integer and its additive inverse is zero, and (−8) + 8 = 0.

Teacher's Note:
1. Every integer has an additive inverse that is the same number with the opposite sign.
2. Do not confuse it with the number itself, which would give −16.

Answer: (a) Data. Facts and numbers collected to give information are called data.

Teacher's Note:
1. Data is the raw material; pictographs, bar graphs and tally marks are only ways of recording or showing it.
2. Learn the difference between the data and the method of presenting it.

Answer: (b) pentagon. A pentagon has 5 sides, a hexagon has 6 and a square has 4.

Teacher's Note:
1. The prefix tells the number of sides: penta means five, hexa means six.
2. A regular polygon has all sides equal and all angles equal.

Answer: (a) True. 7 + (−7) = 0.

Teacher's Note:
1. Additive inverse means the number that adds to give zero.
2. Notice that 7 and −7 are the same distance from 0 on the number line.

Answer: (a) True. A pictograph uses pictures or symbols, each standing for a fixed number of items.

Teacher's Note:
1. Always read the key of a pictograph to know what one picture stands for.
2. The word picto means picture.

Answer: (b) False. The distance around the boundary of a closed figure is its perimeter; area is the measure of the surface it covers.

Teacher's Note:
1. Perimeter is a length measured in cm or m, while area is measured in square units.
2. Imagine walking around a park for perimeter and covering its ground with grass for area.

Answer: (a) True. A line of symmetry acts like a mirror: one half of the figure is the mirror image of the other half.

Teacher's Note:
1. A figure has line symmetry if folding along a line makes both halves match exactly.
2. Placing a mirror along the line of symmetry shows the complete figure again.

Answer: (a) negative. For example, (−3) + (−5) = −8; moving left from a negative number keeps us on the negative side.

Teacher's Note:
1. Add the numbers without signs and put a negative sign on the result.
2. Check with an example such as −2 and −4 before choosing.

Answer: (b) A scale and a compass. An angle is bisected by drawing arcs with a compass and joining the vertex to the point where the arcs meet, using the scale (ruler).

Teacher's Note:
1. Construction means drawing with only a ruler and a compass, without measuring angles.
2. A protractor is for measuring angles, not for the construction method.

Answer: (a) l × b. A wall is a rectangle, and the area of a rectangle is length × breadth.

Teacher's Note:
1. Area uses multiplication, while perimeter uses addition of the sides.
2. Half of l × b is the area of a triangle, not a rectangle.

Answer: (a) 2r. The diameter is twice the radius.

Teacher's Note:
1. The diameter passes through the centre, so it is made of two radii.
2. Radius is half of the diameter.

Answer: (b) C. If C is folded along a horizontal line through its middle, the upper and lower halves coincide. A, J and L do not.

Teacher's Note:
1. Imagine a mirror lying flat across the middle of the letter.
2. A has a vertical line of symmetry, not a horizontal one.

Answer: (b) 3. Each line joins a vertex to the midpoint of the opposite side, and there are 3 vertices.

Teacher's Note:
1. All three sides and angles are equal, so folding from every vertex works.
2. An isosceles triangle which is not equilateral has only one line of symmetry.

Answer: (b) 1. Exactly one straight line passes through two distinct points.

Teacher's Note:
1. Through one point infinitely many lines can pass, but two points fix the line.
2. This is why we say two points determine a line.

Answer: 1. Add the positive numbers: 390 + 262 = 652.
2. Add the negative number: 652 + (−312) = 652 − 312 = 340.
Sum = 340.

Teacher's Note:
1. Group the positive numbers together first to make the working easier.
2. Write the subtraction carefully so that the sign of 312 is not lost.

Answer: The integers lying between −9 and 0 on the number line are −8, −7, −6, −5, −4, −3, −2, −1.

Teacher's Note:
1. Between means the two end numbers 0 and −9 are not included.
2. Check the count: there are 8 integers.

Answer: 1. Perimeter of the square park = 4 × side = 4 × 250 = 1000 m.
2. Cost of fencing = 1000 × ₹20 = ₹20,000.
OR
1. A regular pentagon has 5 equal sides.
2. Each side = 100 ÷ 5 = 20 cm.

Teacher's Note:
1. Fencing goes round the boundary, so find the perimeter and not the area.
2. Write the unit with each step, metre for length and rupees for cost.

Answer: The letters with no line of symmetry are F, G, J, L, N, P, Q, R, S, Z.

Teacher's Note:
1. Test each letter by imagining a vertical, then a horizontal fold line.
2. Letters such as N, S and Z look balanced, but their two halves do not match as mirror images.

Answer: 1. Open the compass so that the distance between the needle point and the pencil point is 3.5 cm, measured on the ruler.
2. Mark a point O on the paper as the centre and place the needle on it.
3. Without changing the opening, turn the compass fully round to draw the circle.
The result is a circle with centre O and radius 3.5 cm (diameter 7 cm).

Teacher's Note:
1. Do not change the compass opening while turning it.
2. Check your drawing by measuring a few radii; all must be 3.5 cm.

Answer: (a) A rectangle (or a square). Draw a rectangle of length 6 cm and breadth 4 cm. The vertical line through the midpoints of the two longer sides and the horizontal line through the midpoints of the two shorter sides are its lines of symmetry. A square also works, and it has two more diagonal lines.
(b) A regular hexagon with all six sides equal and all angles equal. Its six lines of symmetry are 3 lines joining opposite vertices and 3 lines joining midpoints of opposite sides.

Teacher's Note:
1. A figure has as many lines of symmetry as its regular shape allows; a regular polygon has as many as its number of sides.
2. Draw the lines of symmetry as dotted lines to show them clearly.

Answer: 1. Draw a line segment PQ and mark a point M on it.
2. With centre M and a convenient radius, draw arcs cutting PQ at A on one side of M and at B on the other side.
3. With centre A and a radius greater than AM, draw an arc above PQ. With centre B and the same radius, draw another arc cutting the first at C.
4. Join MC and extend it. MC is the perpendicular to PQ at M, so ∠CMQ = 90°.
OR
1. Draw a right angle ∠ABC = 90° (for example with the construction above).
2. With centre B draw an arc cutting BA at P and BC at Q.
3. With centres P and Q and the same radius (more than half of PQ), draw two arcs cutting at R.
4. Join BR. BR bisects the angle, so ∠ABR = ∠RBC = 45°.

Teacher's Note:
1. Use the same compass opening for both arcs in the last step.
2. Keep all construction arcs visible in the answer.

Answer: Draw a horizontal line with equally spaced marks from −13 to 5 and 0 in the middle; the right side is positive and the left side negative.
(a) −2 + 4 = 2.
(b) 1 − 5 = −4.
(c) −13 is smaller than −8, so move to the left (5 steps).
(d) −1 is greater than −6, so move to the right (5 steps).
OR
(a) 5 + 3 = 8.
(b) −5 + 5 = 0.
(c) 2 − 6 = −4.
(d) −2 − 3 = −5.

Teacher's Note:
1. Moving right increases a number and moving left decreases it.
2. Count the steps on the number line instead of guessing the answer, especially across zero.

Answer: Frequency table (using tally marks, with 5 as a bundle):

Teacher's Note:
1. Cross out each number in the list as you tally it so that none is missed or counted twice.
2. The total frequency must equal the number of items, here 25.

Answer: The length of the string is the perimeter of the shape formed.
(a) A square has 4 equal sides. Each side = 84 ÷ 4 = 21 cm.
(b) A regular hexagon has 6 equal sides. Each side = 84 ÷ 6 = 14 cm.

Teacher's Note:
1. Forming a shape with the string means the whole string becomes the boundary, so its length equals the perimeter.
2. More sides mean shorter sides for the same string.

Answer: 1. With centre C and radius 3.4 cm, draw a circle.
2. Mark two points A and B on the circle and join them to get the chord AB.
3. With centre A and a radius more than half of AB, draw arcs above and below AB.
4. With centre B and the same radius, draw arcs cutting the first arcs at P and Q.
5. Join PQ. It meets AB at its midpoint M and ∠PMA = 90°, so PQ is the perpendicular bisector of AB.
6. Observation: the line PQ passes through the centre C. So the perpendicular bisector of a chord passes through the centre of the circle.

Teacher's Note:
1. Use the same radius for the arcs from A and from B, and make it more than half of AB.
2. Extend the line PQ beyond the circle so that you can see it clearly pass through C.