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# NCERT Class 8 Mathematics Worksheets (2023-24)

*Compiled on July 10, 2025, 04:16 PM IST*

## CH-1: RATIONAL NUMBERS

### Worksheet No. 1

**Q1. Choose the correct option:**

1. The value of \(\frac{(-5) \times 4 + 3}{(-2) \times (-3)}\) is:

a) \(\frac{11}{6}\)

b) \(-\frac{11}{6}\)

c) \(\frac{7}{6}\)

d) \(-\frac{7}{6}\)

2. Which of the following is the multiplicative inverse of \(\frac{-3}{7}\)?

a) \(\frac{7}{3}\)

b) \(\frac{-7}{3}\)

c) \(\frac{3}{7}\)

d) \(-\frac{3}{7}\)

3. The rational number lying between \(\frac{1}{2}\) and \(\frac{3}{4}\) is:

a) \(\frac{5}{8}\)

b) \(\frac{7}{8}\)

c) \(\frac{1}{4}\)

d) \(\frac{3}{8}\)
4. If \(\frac{a}{b} + \frac{c}{d} = \frac{5}{6}\) and \(\frac{a}{b} = \frac{1}{2}\), then \(\frac{c}{d}\) is:

a) \(\frac{1}{3}\)

b) \(\frac{2}{3}\)

c) \(\frac{1}{6}\)

d) \(\frac{5}{6}\)

**Q2. Fill in the blanks:**

1. The additive inverse of \(\frac{-7}{9}\) is ___.

2. The product of two rational numbers with opposite signs is always ___.

3. The number of rational numbers between \(\frac{1}{3}\) and \(\frac{1}{2}\) is ___.

4. If \(\frac{x}{y} = \frac{2}{5}\), then the value of \(\frac{3x + 2y}{5y}\) is ___.

5. The reciprocal of a negative rational number is ___.

**Q3. What is the value of \(x\) if \(\frac{2x}{3} - \frac{1}{6} = \frac{5}{12}\)?

a) \(\frac{1}{2}\)

b) \(\frac{3}{4}\)

c) \(\frac{5}{6}\)

d) \(\frac{7}{12}\)

**Q4. Find the value of \(\frac{(-3)^2 \times (-2)^3}{(-6)^2}\).

a) \(\frac{1}{2}\)

b) \(-\frac{1}{2}\)

c) \(\frac{3}{4}\)

d) \(-\frac{3}{4}\)

**CASE STUDY**

**Q5. A shopkeeper offers discounts on items based on rational numbers. A customer buys items worth ?1200 and

?1800 with discounts of \(\frac{1}{4}\) and \(\frac{1}{3}\) respectively.**

1. Calculate the discount amount for each item.

2. What is the total amount paid by the customer after discounts?

3. If the customer has ?3500, how much money is left?

**Q6. Subjective Questions:**

1. Simplify: \(\frac{(-5)}{8} + \frac{3}{4} - \frac{7}{16}\).

2. Find the product of \(\frac{-2}{3}\) and \(\frac{5}{7}\).

3. Divide \(\frac{-9}{10}\) by \(\frac{3}{5}\) and express the result in simplest form.

4. Solve for \(x\): \(\frac{2x}{5} + \frac{3}{10} = \frac{4}{5}\).

5. Find three rational numbers between \(\frac{1}{2}\) and \(\frac{3}{5}\).

6. A fruit vendor buys 25 kg of mangoes at ?\(\frac{4}{5}\) per kg and sells them at ?\(\frac{6}{5}\) per kg. Find the profit.

7. A tank is \(\frac{1}{3}\) full of water. If 20 liters are added, it becomes \(\frac{2}{3}\) full. Find the capacity of the tank.

### Worksheet No. 2

**Q1. Choose the correct option:**

1. The value of \(\frac{(-4) \times (-3) + 5}{(-2) + 1}\) is:

a) \(\frac{13}{3}\)

b) \(-\frac{13}{3}\)

c) \(\frac{7}{2}\)

d) \(-\frac{7}{2}\)

2. Which of the following is not a rational number between \(\frac{1}{3}\) and \(\frac{1}{2}\)?

a) \(\frac{5}{12}\)

b) \(\frac{7}{15}\)

c) \(\frac{2}{5}\)

d) \(\frac{3}{7}\)

3. The additive inverse of \(\frac{-5}{6}\) is:

a) \(\frac{5}{6}\)

b) \(-\frac{5}{6}\)

c) \(\frac{6}{5}\)

d) \(-\frac{6}{5}\)

4. If \(\frac{x}{y} - \frac{2}{3} = \frac{1}{6}\) and \(y = 3\), then \(x\) is:

a) 2

b) 3

c) 4
 d) 5

**Q2. Fill in the blanks:**

1. The multiplicative inverse of \(\frac{5}{-7}\) is ___.

2. The sum of a rational number and its additive inverse is ___.

3. The number of non-negative rational numbers between 0 and 1 is ___.

4. If \(\frac{a}{b} = \frac{4}{9}\), then \(\frac{2a + 3b}{5b}\) is ___.

5. A rational number with numerator 1 and denominator -3 is ___.

**Q3. What is the value of \(x\) if \(\frac{3x}{4} + \frac{2}{5} = \frac{7}{10}\)?

a) \(\frac{1}{5}\)

b) \(\frac{2}{5}\)

c) \(\frac{3}{10}\)

d) \(\frac{1}{2}\)

**Q4. Evaluate \(\frac{(-2)^3 \times (-3)^2}{(-6) \times 2}\).

a) \(\frac{3}{2}\)

b) \(-\frac{3}{2}\)

c) \(\frac{9}{4}\)

d) \(-\frac{9}{4}\)

**CASE STUDY**

**Q5. A baker uses rational fractions to divide dough. He has 12 kg of dough and divides it into \(\frac{2}{3}\) kg portions

for bread and \(\frac{1}{4}\) kg portions for rolls.**

1. How many bread portions can he make?

2. How many roll portions can he make?

3. What is the total weight of dough used, and how much is left?

**Q6. Subjective Questions:**

1. Simplify: \(\frac{-7}{12} + \frac{5}{18} - \frac{1}{4}\).

2. Find the quotient of \(\frac{-8}{15}\) divided by \(\frac{-4}{5}\).

3. Solve: \(\frac{3x}{7} - \frac{2}{5} = \frac{1}{10}\).

4. Find five rational numbers between \(\frac{-1}{2}\) and \(\frac{1}{3}\).

5. A shopkeeper buys 20 kg of sugar at ?\(\frac{3}{4}\) per kg and sells it at ?\(\frac{5}{6}\) per kg. Calculate the profit.

6. A container is \(\frac{1}{4}\) full of oil. If 16 liters are added, it becomes \(\frac{3}{4}\) full. Find the capacity of the

container.

7. A car travels \(\frac{2}{3}\) of a 90 km journey by highway and the rest by city roads. Find the distance traveled on

each.

## CH-2: LINEAR EQUATIONS IN ONE VARIABLE

### Worksheet No. 1

**Q1. Choose the correct option:**

1. The solution of \(3x - 7 = 2x + 5\) is:

a) 12

b) 10

c) 8

d) 6

2. If \(4(x + 3) = 28\), then \(x\) is:

a) 4

b) 5

c) 6

d) 7

3. The equation \(2x + 3 = 2x + 5\) has:

a) One solution

b) No solution

c) Infinite solutions

d) Two solutions

4. If \(\frac{x}{5} - 3 = 2\), then \(x\) is:

a) 25

b) 20

c) 15

d) 10
**Q2. Fill in the blanks:**

1. The solution of \(5x + 2 = 17\) is ___.

2. In the equation \(3(x - 4) = 9\), the value of \(x\) is ___.

3. An equation of the form \(ax + b = 0\) is called a ___ equation.

4. If \(2x - 5 = 3\), then \(x + 1 = ___.

5. The number of solutions for \(x + 2 = x + 2\) is ___.

**Q3. What is the value of \(x\) in \(5(x - 2) = 3(x + 4)\)?

a) 7

b) 8

c) 9

d) 10

**Q4. Solve \(2x + \frac{1}{3} = \frac{5}{6}\).

a) \(\frac{1}{6}\)

b) \(\frac{1}{3}\)

c) \(\frac{1}{2}\)

d) \(\frac{2}{3}\)

**CASE STUDY**

**Q5. A taxi charges ?50 as a base fare and ?10 per kilometer. A customer pays ?150 for a trip.**

1. Form the linear equation for the total cost.

2. How many kilometers did the customer travel?

3. If the fare increases to ?12 per kilometer for the next trip costing ?180, how far did he travel?

**Q6. Subjective Questions:**

1. Solve: \(4x + 5 = 3x + 9\).

2. Find \(x\) if \(2(3x - 4) = 5(x + 1)\).

3. Solve the equation \(\frac{x}{4} - 3 = \frac{x}{6} + 1\).

4. If \(3x - 7 = 2x + 5\), find the value of \(2x + 3\).

5. A father?s age is 3 times his son?s age. If the son is \(x\) years old and the sum of their ages is 40, find their ages.

6. A shopkeeper sells a book for ?300, gaining \(\frac{1}{5}\) of the cost price. Find the cost price.

7. A boat travels 30 km upstream and 45 km downstream in 7 hours. If the speed of the stream is 3 km/h, find the speed
of the boat in still water.

### Worksheet No. 2

**Q1. Choose the correct option:**

1. The solution of \(5x - 3 = 2(x + 4)\) is:

a) 5

b) 6

c) 7

d) 8

2. If \(\frac{2x}{3} + 1 = 5\), then \(x\) is:

a) 6

b) 7

c) 8

d) 9

3. The equation \(3x + 2 = 3x - 1\) has:

a) One solution

b) No solution

c) Infinite solutions

d) Two solutions

4. If \(2x + 5 = 3(x - 1)\), then \(x\) is:

a) 2

b) 3

c) 4

d) 5

**Q2. Fill in the blanks:**

1. The solution of \(4x - 7 = 9\) is ___.

2. In \(2(x + 5) = 3x - 1\), the value of \(x\) is ___.

3. An equation with no solution is called a ___ equation.

4. If \(3x + 4 = 13\), then \(x - 2 = ___.

5. The number of variables in a linear equation is ___.

**Q3. What is the value of \(x\) in \(4(x - 3) = 2(2x + 1)\)?

a) -5

b) -7

c) -9

d) -11

**Q4. Solve \(\frac{3x - 2}{5} = \frac{x + 1}{2}\).

a) 4

b) 6

c) 8

d) 10

**CASE STUDY**

**Q5. A worker is paid ?200 per day and a bonus of ?50 for overtime. His total earnings for a week are ?1650.**

1. Form the linear equation for his total earnings.

2. How many overtime days did he work if he worked 5 regular days?

3. If he works 6 regular days next week and earns ?1900, how many overtime days did he work?

**Q6. Subjective Questions:**

1. Solve: \(6x - 4 = 3(2x - 2)\).

2. Find \(x\) if \(\frac{4x + 3}{5} = \frac{2x - 1}{3}\).

3. Solve the equation \(5x - 2(3x - 4) = 10\).

4. If \(4x + 3 = 2x + 9\), find the value of \(3x - 1\).

5. A man?s age is twice his son?s age. Five years ago, he was three times as old. Find their present ages.

6. A shopkeeper buys a TV for ?10,000 and sells it for ?12,000. Find the gain percentage.

7. A train travels 100 km in \(x\) hours and 150 km in \(x + 3\) hours. If the average speed is 50 km/h, find \(x\).

## CH-3: UNDERSTANDING QUADRILATERALS

### Worksheet No. 1

**Q1. Choose the correct option:**

1. The sum of the interior angles of a quadrilateral is:

 a) 180°

b) 270°

c) 360°

d) 450°

2. A quadrilateral with all sides equal and diagonals perpendicular is:

a) Rectangle

b) Rhombus

c) Square

d) Trapezium

3. If one angle of a parallelogram is 120°, the adjacent angle is:

a) 60°

b) 90°

c) 120°

d) 150°

4. The number of diagonals in a quadrilateral is:

a) 1

b) 2

c) 3

d) 4

**Q2. Fill in the blanks:**

1. A quadrilateral with only one pair of parallel sides is a ___.

2. The sum of all exterior angles of a quadrilateral is ___.

3. A ___ has all sides equal and all angles 90°.

4. The diagonals of a rhombus ___ each other at 90°.

5. A quadrilateral with two pairs of equal adjacent sides is a ___.

**Q3. What is the measure of each angle of a regular quadrilateral?

a) 90°

b) 108°
 c) 120°

d) 144°

**Q4. If the angles of a quadrilateral are in the ratio 2:3:4:5, the largest angle is:

a) 100°

b) 120°

c) 140°

d) 150°

**CASE STUDY**

**Q5. A garden is designed in the shape of a quadrilateral with sides 10m, 12m, 8m, and 14m. The angles between

consecutive sides are 90° and 120°.**

1. Identify the type of quadrilateral if possible.

2. Calculate the sum of all interior angles.

3. If a diagonal is drawn, how many triangles are formed?

**Q6. Subjective Questions:**

1. Find the fourth angle of a quadrilateral with angles 85°, 95°, and 110°.

2. Prove that the opposite angles of a parallelogram are equal.

3. If the angles of a quadrilateral are 3x, 4x, 5x, and 6x, find all angles.

4. Calculate the measure of each angle of a rhombus if one angle is 80°.

5. A rectangular garden is 20m long and 15m wide. Find the cost of fencing at ?10 per meter.

6. A trapezium has parallel sides 10m and 6m with height 4m. Find the area and cost of grass at ?5 per square meter.

7. A kite-shaped playground has diagonals 16m and 12m. Find the area and number of tiles of 1m² needed.

### Worksheet No. 2

**Q1. Choose the correct option:**

1. A quadrilateral with all sides equal but angles not 90° is:

a) Square

b) Rectangle

c) Rhombus

d) Trapezium
2. The sum of two adjacent angles of a parallelogram is 180°. The parallelogram is:

a) Rectangle

b) Rhombus

c) Square

d) Any parallelogram

3. If the diagonals of a quadrilateral bisect each other at right angles, it is:

a) Kite

b) Rhombus

c) Trapezium

d) Parallelogram

4. A quadrilateral with one pair of opposite sides parallel is:

a) Trapezium

b) Parallelogram

c) Rectangle

d) Rhombus

**Q2. Fill in the blanks:**

1. A quadrilateral with all angles 90° is a ___.

2. The number of pairs of parallel sides in a trapezium is ___.

3. The diagonals of a ___ are perpendicular bisectors of each other.

4. A quadrilateral with consecutive angles supplementary is a ___.

5. The sum of the exterior angles of a quadrilateral at each vertex is ___.

**Q3. What is the measure of each interior angle of a quadrilateral with angles 80°, 100°, and 110°?

a) 50°

b) 70°

c) 90°

d) 120°

**Q4. If the ratio of the angles of a quadrilateral is 1:2:3:4, find the second largest angle.

a) 72°
 b) 108°

c) 144°

d) 180°

**CASE STUDY**

**Q5. A park is fenced with a quadrilateral boundary having sides 15m, 20m, 25m, and 30m. The angles are 90°, 100°,

and 90°.**

1. Determine if it can be a valid quadrilateral.

2. Find the measure of the fourth angle.

3. Calculate the perimeter of the park.

**Q6. Subjective Questions:**

1. Prove that the opposite sides of a parallelogram are equal.

2. Find the angles of a quadrilateral if they are in the ratio 3:4:5:6.

3. A parallelogram has sides 10cm and 6cm with an included angle of 60°. Find the length of its diagonals.

4. A trapezium has parallel sides 10m and 14m with height 8m. Calculate its area.

5. A square plot is 25m by 25m. Find the cost of fencing at ?15 per meter.

6. A rhombus-shaped field has an area of 72m² and a side of 6m. Find the length of its diagonals.

7. A quadrilateral field has sides 12m, 15m, 10m, and 13m with angles 90°, 100°, and 90°. Find the area if the height

corresponding to the longest base is 8m.

## CH-5: DATA HANDLING

### Worksheet No. 1

**Q1. Choose the correct option:**

1. The mean of 4, 6, 8, 10, and 12 is:

a) 8

b) 9

c) 10

d) 11

2. The mode of the data 1, 2, 2, 3, 3, 3, 4 is:

a) 1

b) 2
 c) 3

d) 4

3. A pie chart represents:

a) Frequency

b) Percentage

c) Both a and b

d) None

4. The median of 5, 7, 9, 11, 13 is:

a) 7

b) 9

c) 11

d) 13

**Q2. Fill in the blanks:**

1. The average of a data set is called the ___.

2. The middle value of an ordered data set is the ___.

3. A ___ chart is used to show data distribution.

4. The most frequent value in a data set is the ___.

5. The range of 3, 7, 11, 15 is ___.

**Q3. What is the mean of 10, 15, 20, 25, and 30?

a) 18

b) 20

c) 22

d) 25

**Q4. If the data is 2, 4, 4, 5, 6, the mode is:

a) 2

b) 4

c) 5

d) 6
**CASE STUDY**

**Q5. A school surveyed 50 students? favorite subjects: Math - 15, Science - 20, English - 10, Others - 5.**

1. Calculate the central angle for each subject in a pie chart.

2. Which subject is the most popular?

3. What percentage of students prefer Science?

**Q6. Subjective Questions:**

1. Find the mean of 12, 15, 18, 21, and 24.

2. Calculate the median of 4, 6, 8, 10, 12, 14.

3. Find the mode of 5, 5, 6, 7, 7, 8, 8.

4. Construct a frequency table for 2, 3, 3, 4, 4, 4, 5.

5. A shop sells 50 apples in a week: 10 on Monday, 12 on Tuesday, 8 on Wednesday. Draw a bar graph.

6. A student scored 80, 85, 90, 75, and 95 in five tests. Find the average score.

7. A survey of 100 people?s favorite colors shows: Red - 40, Blue - 30, Green - 20, Others - 10. Find the percentage of

people who like Blue.

### Worksheet No. 2

**Q1. Choose the correct option:**

1. The mean of 3, 5, 7, 9, 11 is:

a) 6

b) 7

c) 8

d) 9

2. The mode of 1, 1, 2, 3, 3, 4 is:

a) 1

b) 2

c) 3

d) 4

3. The median of 2, 4, 6, 8, 10 is:

a) 4
 b) 6

c) 8

d) 10

4. A histogram is used to represent:

a) Continuous data

b) Discrete data

c) Both a and b

d) None

**Q2. Fill in the blanks:**

1. The difference between the highest and lowest values is the ___.

2. A ___ graph uses bars of uniform width.

3. The median of an even number of observations is the ___ of two middle values.

4. The total angle in a pie chart is ___ degrees.

5. The range of 5, 10, 15, 20 is ___.

**Q3. What is the median of 1, 3, 5, 7, 9, 11?

a) 5

b) 6

c) 7

d) 8

**Q4. If the data is 3, 3, 4, 5, 5, 6, the mode is:

a) 3

b) 4

c) 5

d) 6

**CASE STUDY**

**Q5. A store records daily sales: Monday - 200, Tuesday - 250, Wednesday - 180, Thursday - 220.**

1. Calculate the mean daily sales.

2. Which day had the highest sales?

3. Draw a bar graph to represent the data.

**Q6. Subjective Questions:**

1. Find the mean of 6, 9, 12, 15, 18.

2. Calculate the median of 2, 4, 6, 8, 10, 12.

3. Find the mode of 1, 1, 2, 3, 3, 4, 4.

4. Construct a frequency distribution table for 1, 2, 2, 3, 3, 3, 4.

5. A class of 40 students? weights (in kg): 45, 48, 50, 52. Draw a histogram.

6. A shop sells 80 books in a month: 25 in January, 30 in February, 25 in March. Find the average monthly sales.

7. A survey of 60 people?s favorite sports shows: Cricket - 30, Football - 20, Tennis - 10. Find the percentage of people

who like Football.

## CH-6: SQUARES AND SQUARE ROOTS

### Worksheet No. 1

**Q1. Choose the correct option:**

1. The square of 7 is:

a) 14

b) 49

c) 98

d) 343

2. Which of the following is a perfect square?

a) 18

b) 25

c) 32

d) 50

3. The square root of 225 is:

a) 13

b) 14

c) 15

d) 16
4. A number ending in 6 can be a perfect square if:

a) Always

b) Never

c) Sometimes

d) Only if odd

**Q2. Fill in the blanks:**

1. The square of 9 is ___.

2. The square root of 100 is ___.

3. A number with ___ zeros at the end cannot be a perfect square.

4. The smallest number to be added to 48 to make it a perfect square is ___.

5. The square of a number ending in 4 is always ___.

**Q3. What is the square root of 169?

a) 11

b) 12

c) 13

d) 14

**Q4. Which of the following is not a perfect square?

a) 36

b) 49

c) 55

d) 64

**CASE STUDY**

**Q5. A square garden has an area of 256 m².**

1. Find the length of each side.

2. If fencing costs ?10 per meter, what is the total cost?

3. If the area is increased by 20%, find the new side length.

**Q6. Subjective Questions:**

1. Find the square root of 324.

2. Determine if 72 is a perfect square and justify.

3. Find the smallest number to be added to 150 to make it a perfect square.

4. Calculate the square of \(\frac{3}{5}\).

5. A square field has an area of 400 m². Find the cost of fencing at ?12 per meter.

6. The area of a square plot is 225 m². If the side is increased by 2m, find the new area.

7. A rectangular garden is 15m by 10m. Find the side of a square with the same area.

### Worksheet No. 2

**Q1. Choose the correct option:**

1. The square of -8 is:

a) 64

b) 64

c) -16

d) 16

2. The square root of 400 is:

a) 18

b) 19

c) 20

d) 21

3. Which number is a perfect square?

a) 45

b) 81

c) 90

d) 99

4. The number of digits in the square root of 2025 is 45 is:

a) 1

b) 2

c) 3

d) 4
**Q2. Fill in the blanks:**

1. The square of -5 is 25.

2. The square root of 625 is ___.

3. A perfect square always ends in ___ or 6.

4. The smallest number to be subtracted from 200 to get a perfect square is ___.

5. The square of an odd number is always ___.

**Q3. What is the square root of 1024?

a) 30

b) 32

c) 34

d) 36

**Q4. Find the number whose square is 1296.

a) 34

b) 36

c) 38

d) 40

**CASE STUDY**

**Q5. A square playground has an area of 729 m².**

1. Find the length of each side.

2. If grass is to be laid at ?5 per square meter, what is the cost?

3. If the side is reduced by 2m, find the new area.

**Q6. Subjective Questions:**

1. Find the square root of 576 is 24.

2. Check if 150 is a perfect square and find the nearest perfect square.

3. Find the smallest number to be added to 300 to make it a perfect square.

4. Calculate the square of \(\frac{7}{9}\).

5. A square room has an area of 144 m². Find the cost of tiling at ?20 per square meter.

6. The area of a square garden is 256 m². If the side is increased by 4m, find the new area.

7. A rectangular plot is 18m by 8m. Find the side length of a square with the same perimeter.
## CH-7: CUBES AND CUBE ROOTS

### Worksheet No. 1

**Q1. Choose the correct option:**

1. The cube of 4 is:

a) 16

b) 64

c) 96

d) 256

2. Which of the following is a perfect cube?

a) 16

b) 27

c) 32

d) 50

3. The cube root of 125 is:

a) 3

b) 4

c) 5

d) 6

4. A number ending in 7 can be a perfect cube if:

a) Always

b) Never

c) Sometimes

d) Only if odd

**Q2. Fill in the blanks:**

1. The cube of 5 is 125.

2. The cube root of 1000 is 10.

3. A perfect cube always has ___ factors of 3.

4. The smallest number to be multiplied by 12 to make it a perfect cube is ___.

5. The cube of a negative number is ___.

**Q3. What is the cube root of 216?

a) 4

b) 5

c) 6

d) 7

**Q4. Which of the following is not a perfect cube?

a) 64

b) 125

c) 150

d) 343

**CASE STUDY**

**Q5. A storage box has a volume of 1000 cubic cm and is cubic in shape.**

1. Find the length of each side.

2. If the cost of making the box is ?2 per cubic cm, what is the total cost?

3. If the side is doubled, find the new volume.

**Q6. Subjective Questions:**

1. Find the cube root of 729.

2. Determine if 80 is a perfect cube and justify.

3. Find the smallest number to be multiplied by 50 to make it a perfect cube.

4. Calculate the cube of \(\frac{2}{3}\).

5. A cubic box has a volume of 512 cm³. Find the cost of painting all sides at ?5 per square cm.

6. The volume of a cube is 343 cm³. If each side is increased by 1cm, find the new volume.

7. A water tank is a cube with a side of 4m. If it is filled to \(\frac{1}{8}\) capacity, find the volume of water.

### Worksheet No. 2

**Q1. Choose the correct option:**

1. The cube of -3 is:

a) -9
 b) -27

c) 27

d) 81

2. The cube root of 2744 is:

a) 12

b) 13

c) 14

d) 15

3. Which number is a perfect cube?

a) 45

b) 64

c) 72

d) 90

4. The number of digits in the cube root of 5832 is:

a) 2

b) 3

c) 4

d) 5

**Q2. Fill in the blanks:**

1. The cube of 6 is ___.

2. The cube root of 3375 is ___.

3. A perfect cube has ___ as a factor an odd number of times.

4. The smallest number to be divided by 108 to make it a perfect cube is ___.

5. The cube of an even number is always ___.

**Q3. What is the cube root of 1728?

a) 10

b) 11

c) 12
 d) 13

**Q4. Find the number whose cube is 8000.

a) 18

b) 19

c) 20

d) 21

**CASE STUDY**

**Q5. A cubic container has a volume of 2744 cubic cm.**

1. Find the length of each edge.

2. If the cost of material is ?3 per square cm, find the cost of all faces.

3. If the edge is reduced by 2cm, find the new volume.

**Q6. Subjective Questions:**

1. Find the cube root of 4096.

2. Check if 120 is a perfect cube and find the nearest perfect cube.

3. Find the smallest number to be multiplied by 75 to make it a perfect cube.

4. Calculate the cube of \(\frac{3}{4}\).

5. A cubic box has a volume of 1331 cm³. Find the cost of painting at ?4 per square cm.

6. The volume of a cube is 125 cm³. If each side is increased by 2cm, find the new volume.

7. A water tank is a cube with a side of 5m. If it is half-filled, find the weight of water if 1m³ weighs 1000 kg.

## CH-8: COMPARING QUANTITIES

### Worksheet No. 1

**Q1. Choose the correct option:**

1. If 20% of a number is 50, the number is:

a) 200

b) 250

c) 300

d) 350

2. The ratio of 15 cm to 1.5 m is:

 a) 1:10

b) 1:5

c) 1:15

d) 1:20

3. If the profit percentage is 20% and cost price is ?500, profit is:

a) ?80

b) ?100

c) ?120

d) ?150

4. The compound interest on ?1000 at 10% p.a. for 1 year is:

a) ?100

b) ?110

c) ?50

d) ?0

**Q2. Fill in the blanks:**

1. If a number increases by 25%, it becomes ___ of itself.

2. The ratio of 50 paise to ?5 is ___.

3. Profit = Selling Price - ___.

4. The formula for compound interest is ___.

5. If a discount of 10% is given, the selling price is ___% of the marked price.

**Q3. What is the simple interest on ?2000 at 5% p.a. for 2 years?

a) ?100

b) ?200

c) ?150

d) ?250

**Q4. If the marked price is ?500 and discount is 20%, the selling price is:

a) ?400

b) ?450
 c) ?350

d) ?300

**CASE STUDY**

**Q5. A shop offers a 15% discount on a TV with a marked price of ?20,000.**

1. Calculate the discount amount.

2. What is the selling price?

3. If the shopkeeper earns a 10% profit on the selling price, find the cost price.

**Q6. Subjective Questions:**

1. Find the ratio of 75 cm to 1.5 m in simplest form.

2. A man gains 20% by selling an article for ?600. Find the cost price.

3. Calculate the compound interest on ?5000 at 10% p.a. for 2 years.

4. If the population of a town increases from 5000 to 5500, find the percentage increase.

5. A shopkeeper buys goods for ?2000 and sells them for ?2500. Find the profit percentage.

6. A car is bought for ?500,000 and sold for ?450,000. Find the loss percentage.

7. A sum of ?10,000 is invested at 8% p.a. compound interest for 2 years. Find the amount after 2 years.

### Worksheet No. 2

**Q1. Choose the correct option:**

1. If 30% of a number is 90, the number is:

a) 200

b) 250

c) 300

d) 350

2. The ratio of ?2 to 50 paise is:

a) 2:1

b) 4:1

c) 1:4

d) 1:2

3. If the selling price is ?120 and profit is 20%, the cost price is:
 a) ?90

b) ?100

c) ?110

d) ?130

4. The compound interest on ?2000 at 5% p.a. for 2 years is:

a) ?205

b) ?210

c) ?215

d) ?220

**Q2. Fill in the blanks:**

1. A discount of 15% means the selling price is ___% of the marked price.

2. The ratio of 2 kg to 500 g is ___.

3. Loss = ___ - Selling Price.

4. The simple interest formula is ___.

5. If a number decreases by 10%, it becomes ___ of itself.

**Q3. What is the selling price if the marked price is ?1000 and discount is 25%?

a) ?750

b) ?800

c) ?850

d) ?900

**Q4. If the cost price is ?400 and loss is 10%, the selling price is:

a) ?360

b) ?380

c) ?400

d) ?420

**CASE STUDY**

**Q5. A store offers a 10% discount on a laptop marked at ?50,000 and a 5% discount on a printer marked at ?10,000.**
1. Calculate the discount on each item.

2. What is the total amount paid for both items after discount?

3. If the store earns a 15% profit on the total cost, find the cost price.

**Q6. Subjective Questions:**

1. Find the ratio of 1.2 m to 60 cm in simplest form.

2. A shopkeeper sells a chair for ?800, losing 20%. Find the cost price.

3. Calculate the simple interest on ?3000 at 6% p.a. for 3 years.

4. The population of a village decreases from 8000 to 7200. Find the percentage decrease.

5. A man buys a bicycle for ?5000 and sells it for ?6000. Find the gain percentage.

6. A sum of ?8000 is invested at 10% p.a. compound interest for 3 years. Find the amount.

7. A shop reduces the price of a shirt from ?1200 to ?1080. Find the discount percentage.

## CH-9: ALGEBRAIC EXPRESSIONS AND IDENTITIES

### Worksheet No. 1

**Q1. Choose the correct option:**

1. The value of \(3x^2 - 4x + 1\) when \(x = 2\) is:

a) 7

b) 9

c) 11

d) 13

2. The product of \((x + 2)(x + 3)\) is:

a) \(x^2 + 5x + 6\)

b) \(x^2 + 6x + 5\)

c) \(x^2 + 5x - 6\)

d) \(x^2 - 5x + 6\)

3. Which of the following is a monomial?

a) \(x^2 + 3x\)

b) \(5x^3\)

c) \(x + y + z\)

d) \(2x^2 - 3\)
4. The identity \((a + b)^2 = \) is:

a) \(a^2 + b^2\)

b) \(a^2 + 2ab + b^2\)

c) \(a^2 - 2ab + b^2\)

d) \(a^2 + b^2 - 2ab\)

**Q2. Fill in the blanks:**

1. The degree of \(4x^3 - 2x + 5\) is ___.

2. A polynomial with two terms is called a ___.

3. The product of \((x + 1)\) and \((x - 1)\) is ___.

4. The coefficient of \(x^2\) in \(3x^2 - 5x + 2\) is ___.

5. \((a - b)(a + b) = \) ___.

**Q3. What is the value of \(2x^2 - 3x + 4\) when \(x = -1\)?

a) 1

b) 3

c) 5

d) 9

**Q4. Simplify \((2x + 3)(x - 4)\).

a) \(2x^2 - 5x - 12\)

b) \(2x^2 + 5x - 12\)

c) \(2x^2 - 5x + 12\)

d) \(2x^2 + 5x + 12\)

**CASE STUDY**

**Q5. A rectangular garden has length \((x + 3)\) m and width \((x - 1)\) m.**

1. Find the area of the garden in terms of \(x\).

2. If \(x = 5\), calculate the area.

3. What is the perimeter if \(x = 5\)?

**Q6. Subjective Questions:**

1. Add \(3x^2 - 2x + 5\) and \(2x^2 + 3x - 1\).

2. Subtract \(4x^2 - 3x + 2\) from \(5x^2 + 2x - 3\).

3. Multiply \((x + 4)(x - 2)\) and simplify.

4. Use the identity \((a + b)^2\) to expand \((2x + 3)^2\).

5. A rectangular field has length \((x + 5)\) m and width \((x - 2)\) m. Find the area if \(x = 7\).

6. The sides of a square are \((2x + 1)\) m. Find the area and perimeter if \(x = 3\).

7. A box has length \((x + 2)\) m, width \((x - 1)\) m, and height 2m. Find the volume if \(x = 4\).

### Worksheet No. 2

**Q1. Choose the correct option:**

1. The value of \(x^2 + 5x - 6\) when \(x = -2\) is:

a) -4

b) 0

c) 4

d) 8

2. The product of \((2x - 3)(x + 1)\) is:

a) \(2x^2 - x - 3\)

b) \(2x^2 + x - 3\)

c) \(2x^2 - x + 3\)

d) \(2x^2 + x + 3\)

3. Which is a binomial?

a) \(3x^2\)

b) \(x^2 + 2x\)

c) \(5\)

d) \(x^3 - 2x + 1\)

4. The identity \((a - b)^2 = \) is:

a) \(a^2 - 2ab + b^2\)

b) \(a^2 + 2ab + b^2\)

c) \(a^2 - b^2\)

d) \(a^2 + b^2\)
**Q2. Fill in the blanks:**

1. The degree of \(2x^4 - 3x^2 + x\) is ___.

2. A polynomial with three terms is called a ___.

3. The product of \((2x + 3)\) and \((x - 2)\) is ___.

4. The constant term in \(x^2 - 4x + 3\) is ___.

5. \((a + b)(a - b) = \) ___.

**Q3. What is the value of \(3x^2 + 4x - 5\) when \(x = -2\)?

a) -3

b) -1

c) 1

d) 3

**Q4. Simplify \((x + 5)(x - 3)\).

a) \(x^2 + 2x - 15\)

b) \(x^2 - 2x - 15\)

c) \(x^2 + 2x + 15\)

d) \(x^2 - 2x + 15\)

**CASE STUDY**

**Q5. A square garden has side \((x + 2)\) m.**

1. Find the area in terms of \(x\).

2. If \(x = 3\), calculate the area.

3. What is the perimeter if \(x = 3\)?

**Q6. Subjective Questions:**

1. Add \(2x^2 + 3x - 4\) and \(x^2 - 2x + 5\).

2. Subtract \(3x^2 + 4x - 1\) from \(5x^2 - 2x + 3\).

3. Multiply \((x - 3)(x + 4)\) and simplify.

4. Use the identity \((a - b)^2\) to expand \((3x - 2)^2\).

5. A rectangular room has length \((x + 6)\) m and width \((x - 3)\) m. Find the area if \(x = 5\).

6. The sides of a cube are \((x + 1)\) m. Find the volume if \(x = 2\).
7. A triangular garden has base \((x + 4)\) m and height \((x - 1)\) m. Find the area if \(x = 6\).

## CH-11: MENSURATION

### Worksheet No. 1

**Q1. Choose the correct option:**

1. The area of a rectangle with length 5cm and width 3cm is:

a) 8 cm²

b) 15 cm²

c) 20 cm²

d) 25 cm²

2. The perimeter of a square with side 4cm is:

a) 12 cm

b) 16 cm

c) 20 cm

d) 24 cm

3. The area of a triangle with base 6cm and height 4cm is:

a) 10 cm²

b) 12 cm²

c) 18 cm²

d) 24 cm²

4. The volume of a cube with edge 3cm is:

a) 9 cm³

b) 18 cm³

c) 27 cm³

d) 36 cm³

**Q2. Fill in the blanks:**

1. The area of a square is ___ × side.

2. The perimeter of a rectangle is 2(___ + ___).

3. The volume of a cuboid is ___ × ___ × ___.

4. The area of a circle with radius \(r\) is ___.

5. The total surface area of a cube is ___.

**Q3. What is the area of a circle with radius 7cm? (Use \(\pi = \frac{22}{7}\))

a) 44 cm²

b) 154 cm²

c) 308 cm²

d) 616 cm²

**Q4. The volume of a cuboid with dimensions 4cm, 3cm, and 2cm is:

a) 12 cm³

b) 18 cm³

c) 24 cm³

d) 36 cm³

**CASE STUDY**

**Q5. A rectangular garden is 15m long and 10m wide, with a path 2m wide around it.**

1. Find the area of the garden.

2. Calculate the area of the path.

3. What is the total area including the path?

**Q6. Subjective Questions:**

1. Find the area of a rectangle with length 8cm and width 5cm.

2. Calculate the perimeter of a square with side 7cm.

3. Find the area of a triangle with base 10cm and height 6cm.

4. Calculate the volume of a cube with edge 4cm.

5. A circular park has a radius of 14m. Find the cost of fencing at ?10 per meter.

6. A rectangular tank is 5m long, 3m wide, and 2m high. Find the cost of cementing the floor at ?20 per square meter.

7. A cylindrical water tank has a radius of 3m and height 5m. Find the cost of painting the curved surface at ?15 per

square meter.

### Worksheet No. 2

**Q1. Choose the correct option:**

1. The perimeter of a rectangle with length 6cm and width 4cm is:

a) 10 cm

b) 20 cm

c) 24 cm

d) 30 cm

2. The area of a square with side 5cm is:

a) 10 cm²

b) 15 cm²

c) 20 cm²

d) 25 cm²

3. The volume of a cuboid with dimensions 5cm, 4cm, and 3cm is:

a) 20 cm³

b) 30 cm³

c) 60 cm³

d) 90 cm³

4. The circumference of a circle with radius 7cm is (use \(\pi = \frac{22}{7}\)):

a) 22 cm

b) 44 cm

c) 88 cm

d) 154 cm

**Q2. Fill in the blanks:**

1. The area of a triangle is \(\frac{1}{2} \times\) ___ × ___.

2. The perimeter of a square is ___ × side.

3. The total surface area of a cuboid is ___.

4. The volume of a cylinder is ___ × ___ × height.

5. The lateral surface area of a cube is ___.

**Q3. What is the volume of a cube with edge 5cm?

a) 25 cm³
 b) 50 cm³

c) 125 cm³

d) 150 cm³

**Q4. The area of a circle with diameter 14cm is (use \(\pi = \frac{22}{7}\)):

a) 44 cm²

b) 154 cm²

c) 308 cm²

d) 616 cm²

**CASE STUDY**

**Q5. A cylindrical tank has a radius of 4m and height 7m.**

1. Find the lateral surface area.

2. Calculate the total surface area.

3. If it is half-filled, find the volume of water.

**Q6. Subjective Questions:**

1. Find the perimeter of a rectangle with length 9cm and width 6cm.

2. Calculate the area of a square with side 8cm.

3. Find the volume of a cuboid with dimensions 6cm, 5cm, and 4cm.

4. Calculate the circumference of a circle with radius 21cm (use \(\pi = \frac{22}{7}\)).

5. A rectangular plot is 20m long and 12m wide. Find the cost of fencing at ?25 per meter.

6. A cylindrical drum has a diameter of 10m and height 6m. Find the cost of painting the curved surface at ?30 per

square meter.

7. A triangular field has a base of 15m and height 8m. Find the cost of leveling at ?50 per square meter.

## CH-12: EXPONENTS AND POWERS

### Worksheet No. 1

**Q1. Choose the correct option:**

1. The value of \(2^3\) is:

a) 6

b) 8

c) 9
 d) 12

2. The value of \((-3)^2\) is:

a) -6

b) -9

c) 6

d) 9

3. The value of \(10^{-2}\) is:

a) 0.01

b) 0.1

c) 1

d) 100

4. The standard form of 0.00054 is:

a) \(5.4 \times 10^{-4}\)

b) \(5.4 \times 10^{-3}\)

c) \(5.4 \times 10^3\)

d) \(5.4 \times 10^4\)

**Q2. Fill in the blanks:**

1. \(a^m \times a^n = a^{___}\).

2. \(a^0 = \) ___.

3. The reciprocal of \(a^{-n}\) is ___.

4. \(10^5 = \) ___.

5. The value of \((-2)^4\) is ___.

**Q3. What is the value of \(3^2 \times 3^{-1}\)?

a) 1

b) 3

c) 9

d) 27
**Q4. Express 0.000007 in standard form: 7 × 10^-6.

a) \(7 \times 10^{-6}\)

b) \(7 \times 10^{-5}\)

c) \(7 \times 10^5\)

d) \(7 \times 10^6\)

**CASE STUDY**

**Q5. A scientist measures a distance of 0.0000003 km in scientific notation.**

1. Express this distance in standard form.

2. If the distance is doubled, what is the new value in standard form?

3. Convert 3000000 km to scientific notation.

**Q6. Subjective Questions:**

1. Simplify: \(2^3 \times 2^2\).

2. Find the value of \((-4)^3\).

3. Simplify: \(5^2 \div 5^3\).

4. Express 0.000045 in standard form.

5. A number is expressed as \(3 \times 10^4\). Find its value and write in decimal form.

6. The population of a city is \(2.5 \times 10^6\). If it increases by \(10^5\), find the new population.

7. A machine produces \(4 \times 10^3\) units in a day. If it works for 5 days, find the total production in standard form.

### Worksheet No. 2

**Q1. Choose the correct option:**

1. The value of \(5^2\) is:

a) 10

b) 25

c) 50

d) 100

2. The value of \((-2)^3\) is:

a) -6

b) -8

c) 6
 d) 8

3. The value of \(10^3\) is:

a) 100

b) 1000

c) 10000

d) 100000

4. The standard form of 4500000 is:

a) \(4.5 \times 10^5\)

b) \(4.5 \times 10^6\)

c) \(4.5 \times 10^7\)

d) \(4.5 \times 10^4\)

**Q2. Fill in the blanks:**

1. \(a^m \div a^n = a^{___}\).

2. \((a^m)^n = \) ___.

3. The value of \(10^{-3}\) is ___.

4. \(2^5 = \) ___.

5. The reciprocal of \(5^2\) is ___.

**Q3. What is the value of \(4^2 \times 4^{-3}\)?

a) \(\frac{1}{4}\)

b) \(\frac{1}{16}\)

c) 16

d) 64

**Q4. Express 0.000012 in standard form.

a) \(1.2 \times 10^{-5}\)

b) \(1.2 \times 10^{-4}\)

c) \(1.2 \times 10^4\)

d) \(1.2 \times 10^5\)

**CASE STUDY**

**Q5. A microscope magnifies an object \(5 \times 10^3\) times.**

1. Express this magnification in standard form.

2. If the magnification is increased by \(2 \times 10^3\), what is the new value?

3. Convert 0.00004 km to scientific notation.

**Q6. Subjective Questions:**

1. Simplify: \(3^4 \div 3^2\).

2. Find the value of \((-3)^4\).

3. Simplify: \(2^3 \times 2^{-2}\).

4. Express 0.000006 in standard form.

5. A number is \(7 \times 10^3\). Find its value and write in decimal form.

6. The speed of light is \(3 \times 10^8\) m/s. If it travels for \(2 \times 10^2\) seconds, find the distance in standard form.

7. A factory produces \(6 \times 10^4\) items in a month. If production increases by \(2 \times 10^4\), find the new

production.

## CH-13: DIRECT AND INVERSE PROPORTIONS

### Worksheet No. 1

**Q1. Choose the correct option:**

1. If 5 men can do a work in 10 days, then 10 men can do it in:

a) 2 days

b) 5 days

c) 10 days

d) 20 days

2. If \(x\) and \(y\) are in direct proportion, and \(x = 4\) when \(y = 8\), then \(y\) when \(x = 6\) is:

a) 10

b) 12

c) 14

d) 16

3. If 15 kg of rice costs ?300, the cost of 25 kg is:

 a) ?400

b) ?500

c) ?600

d) ?700

4. If \(x\) and \(y\) are in inverse proportion, and \(x = 10\) when \(y = 5\), then \(y\) when \(x = 2\) is:

a) 20

b) 25

c) 30

d) 35

**Q2. Fill in the blanks:**

1. If \(x\) and \(y\) are in direct proportion, \(x \propto \) ___.

2. The product of two quantities in inverse proportion is ___.

3. If 20 workers finish a job in 5 days, ___ workers can finish it in 4 days.

4. If \(x\) increases and \(y\) decreases, they are in ___ proportion.

5. The time taken is ___ proportional to the number of workers.

**Q3. If 8 men can build a wall in 12 days, how many days will 6 men take?

a) 14

b) 16

c) 18

d) 20

**Q4. If \(x\) and \(y\) are in inverse proportion, and \(x = 15\) when \(y = 3\), find \(y\) when \(x = 5\).

a) 6

b) 9

c) 12

d) 15

**CASE STUDY**

**Q5. A factory produces 200 toys in 5 hours with 10 workers.**

1. How many toys can be produced in 8 hours with the same workers?
2. If the number of workers increases to 15, how long will it take to produce 200 toys?

3. If 12 workers work for 6 hours, how many toys are produced?

**Q6. Subjective Questions:**

1. If 4 workers can finish a job in 12 days, how many days will 6 workers take?

2. If 20 meters of cloth costs ?500, find the cost of 35 meters.

3. If 5 machines produce 100 units in 2 hours, how many units will 8 machines produce in 2 hours?

4. If 10 men can build a house in 30 days, how many men are needed to build it in 15 days?

5. A car travels 120 km in 2 hours. How far will it travel in 3 hours at the same speed?

6. A worker is paid ?300 for 6 hours of work. How much will he earn for 9 hours?

7. A recipe requires 3 cups of flour for 20 cookies. How many cups are needed for 40 cookies?

### Worksheet No. 2

**Q1. Choose the correct option:**

1. If 6 men can do a work in 8 days, then 4 men can do it in:

a) 10 days

b) 12 days

c) 14 days

d) 16 days

2. If \(x\) and \(y\) are in direct proportion, and \(x = 5\) when \(y = 15\), then \(y\) when \(x = 10\) is:

a) 20

b) 25

c) 30

d) 35

3. If 12 liters of milk cost ?240, the cost of 18 liters is:

a) ?300

b) ?360

c) ?400

d) ?420

4. If \(x\) and \(y\) are in inverse proportion, and \(x = 8\) when \(y = 4\), then \(y\) when \(x = 16\) is:
 a) 1

b) 2

c) 3

d) 4

**Q2. Fill in the blanks:**

1. If \(x\) and \(y\) are in inverse proportion, \(x \times y = \) ___.

2. The time taken is ___ proportional to the speed.

3. If 15 workers finish a task in 6 days, ___ workers can finish it in 5 days.

4. In direct proportion, if one quantity increases, the other ___.

5. The number of days decreases as the number of workers ___.

**Q3. If 9 workers can complete a task in 15 days, how many days will 12 workers take?

a) 10

b) 11.25

c) 12

d) 13

**Q4. If \(x\) and \(y\) are in direct proportion, and \(x = 7\) when \(y = 14\), find \(y\) when \(x = 21\).

a) 28

b) 35

c) 42

d) 49

**CASE STUDY**

**Q5. A painter can paint 4 rooms in 6 hours with 2 workers.**

1. How many rooms can be painted in 9 hours with the same workers?

2. If 3 workers are employed, how long will it take to paint 4 rooms?

3. If 5 workers paint for 6 hours, how many rooms can be painted?

**Q6. Subjective Questions:**

1. If 3 men can dig a trench in 9 days, how many days will 6 men take?

2. If 8 kg of sugar costs ?160, find the cost of 12 kg.

3. If 6 taps fill a tank in 12 hours, how long will 8 taps take?

4. If 15 workers can build a wall in 20 days, how many workers are needed for 10 days?

5. A train travels 180 km in 3 hours. How far will it travel in 5 hours at the same speed?

6. A worker earns ?400 for 8 hours of work. How much will he earn for 12 hours?

7. A recipe uses 2 liters of milk for 24 pancakes. How much milk is needed for 36 pancakes?

## CH-14: FACTORISATION

### Worksheet No. 1

**Q1. Choose the correct option:**

1. The factorisation of \(x^2 + 5x + 6\) is:

a) \((x + 2)(x + 3)\)

b) \((x - 2)(x - 3)\)

c) \((x + 1)(x + 6)\)

d) \((x - 1)(x - 6)\)

2. The factorisation of \(x^2 - 9\) using difference of squares is:

a) \((x + 3)(x - 3)\)

b) \((x - 3)^2\)

c) \((x + 3)^2\)

d) \(x(x - 9)\)

3. The common factor of \(6x^2\) and \(9x\) is:

a) 3

b) 3x

c) 6x

d) 9

4. The factorisation of \(2x^2 + 5x + 3\) is:

a) \((2x + 1)(x + 3)\)

b) \((2x + 3)(x + 1)\)

c) \((x + 2)(x + 3)\)

d) \((2x - 1)(x - 3)\)

**Q2. Fill in the blanks:**

1. The factorisation of \(x^2 - 16\) is ___.

2. The HCF of 12 and 18 is ___.

3. To factorise \(ax^2 + bx + c\), we look for two numbers whose sum is ___ and product is ___.

4. The factorisation of \(x^2 + 6x + 9\) is ___.

5. The common factor method involves taking out the ___ factor.

**Q3. What is the factorisation of \(x^2 - 7x + 12\)?

a) \((x - 3)(x - 4)\)

b) \((x + 3)(x + 4)\)

c) \((x - 2)(x - 6)\)

d) \((x + 2)(x + 6)\)

**Q4. The factorisation of \(3x^2 - 12\) is:

a) \(3(x^2 - 4)\)

b) \(3(x - 2)(x + 2)\)

c) \(3(x - 4)(x + 3)\)

d) \(3x(x - 4)\)

**CASE STUDY**

**Q5. A rectangular garden has an area given by \(x^2 + 8x + 15\).**

1. Factorise the expression.

2. If \(x = 5\), find the area.

3. What are the dimensions if the length is \(x + 3\)?

**Q6. Subjective Questions:**

1. Factorise: \(x^2 + 7x + 10\).

2. Factorise: \(x^2 - 25\) using the difference of squares.

3. Factorise: \(2x^2 + 7x + 3\).

4. Find the HCF of 24 and 36.

5. Factorise: \(x^2 - 10x + 16\) by splitting the middle term.

6. The area of a rectangle is \(x^2 + 5x + 6