Mathematics Concepts for Class 7 Annual Exam

1. What is the sum of 3/4 and 2/5?

1/5

23/20

1/2

1

To find the sum of 3/4 and 2/5, first, convert both fractions to a common denominator. The least common multiple of 4 and 5 is 20. Convert 3/4 to 15/20 and 2/5 to 8/20. Adding these gives 15/20 + 8/20 = 23/20. Thus, the sum of 3/4 and 2/5 is 23/20.

Explanation

To find the sum of 3/4 and 2/5, first, convert both fractions to a common denominator. The least common multiple of 4 and 5 is 20. Convert 3/4 to 15/20 and 2/5 to 8/20. Adding these gives 15/20 + 8/20 = 23/20. Thus, the sum of 3/4 and 2/5 is 23/20.

2. Solve for x: 2x + 5 = 15.

5

10

7.5

2.5

To solve the equation 2x + 5 = 15, start by isolating the term with x. Subtract 5 from both sides, resulting in 2x = 10. Next, divide both sides by 2 to solve for x, yielding x = 5. This value satisfies the original equation when substituted back, confirming that it is the correct solution.

Explanation

To solve the equation 2x + 5 = 15, start by isolating the term with x. Subtract 5 from both sides, resulting in 2x = 10. Next, divide both sides by 2 to solve for x, yielding x = 5. This value satisfies the original equation when substituted back, confirming that it is the correct solution.

3. What is the area of a triangle with a base of 10 cm and a height of 5 cm?

25 cm²

50 cm²

15 cm²

30 cm²

To find the area of a triangle, the formula used is \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \). In this case, with a base of 10 cm and a height of 5 cm, the calculation is \( \frac{1}{2} \times 10 \times 5 = 25 \) cm². This formula accounts for the triangular shape, which is half of a rectangle with the same base and height, leading to an area of 25 cm².

Explanation

To find the area of a triangle, the formula used is \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \). In this case, with a base of 10 cm and a height of 5 cm, the calculation is \( \frac{1}{2} \times 10 \times 5 = 25 \) cm². This formula accounts for the triangular shape, which is half of a rectangle with the same base and height, leading to an area of 25 cm².

4. Which of the following is a rational number?

√2

3/4

π

E

A rational number is defined as any number that can be expressed as the quotient of two integers, where the denominator is not zero. The number 3/4 meets this criterion, as it can be represented as the fraction of two integers (3 and 4). In contrast, √2, π, and e are all irrational numbers because they cannot be expressed as simple fractions; their decimal expansions are non-repeating and non-terminating. Thus, among the given options, 3/4 is the only rational number.

Explanation

A rational number is defined as any number that can be expressed as the quotient of two integers, where the denominator is not zero. The number 3/4 meets this criterion, as it can be represented as the fraction of two integers (3 and 4). In contrast, √2, π, and e are all irrational numbers because they cannot be expressed as simple fractions; their decimal expansions are non-repeating and non-terminating. Thus, among the given options, 3/4 is the only rational number.

5. What is the perimeter of a rectangle with length 8 cm and width 3 cm?

22 cm

24 cm

30 cm

20 cm

To find the perimeter of a rectangle, you can use the formula: Perimeter = 2 × (length + width). In this case, the length is 8 cm and the width is 3 cm. Adding these together gives 8 + 3 = 11 cm. Multiplying by 2 results in 2 × 11 = 22 cm. Therefore, the perimeter of the rectangle is 22 cm.

Explanation

To find the perimeter of a rectangle, you can use the formula: Perimeter = 2 × (length + width). In this case, the length is 8 cm and the width is 3 cm. Adding these together gives 8 + 3 = 11 cm. Multiplying by 2 results in 2 × 11 = 22 cm. Therefore, the perimeter of the rectangle is 22 cm.

6. What is 2 raised to the power of 3?

6

8

4

10

To find 2 raised to the power of 3, you multiply 2 by itself three times: 2 × 2 × 2. This calculation equals 4 (from the first two 2s) and then multiplying that result by the last 2 gives you 8. Therefore, 2^3 equals 8, which is the correct answer.

Explanation

To find 2 raised to the power of 3, you multiply 2 by itself three times: 2 × 2 × 2. This calculation equals 4 (from the first two 2s) and then multiplying that result by the last 2 gives you 8. Therefore, 2^3 equals 8, which is the correct answer.

7. If the angles of a triangle are 60°, 90°, and x°, what is the value of x?

30°

60°

90°

120°

In a triangle, the sum of all interior angles must equal 180°. Given two angles of 60° and 90°, we can find the third angle by subtracting the sum of these angles from 180°. Thus, 180° - (60° + 90°) = 180° - 150° = 30°. Therefore, the value of x, the third angle, is 30°.

Explanation

In a triangle, the sum of all interior angles must equal 180°. Given two angles of 60° and 90°, we can find the third angle by subtracting the sum of these angles from 180°. Thus, 180° - (60° + 90°) = 180° - 150° = 30°. Therefore, the value of x, the third angle, is 30°.

8. Which of the following expressions is an algebraic expression?

5 + 3

X + 2

7 - 4

10

An algebraic expression is a mathematical phrase that includes numbers, variables, and operations. In the given options, "x + 2" contains the variable 'x' along with a constant, making it an algebraic expression. The other options, such as "5 + 3," "7 - 4," and "10," are numerical expressions as they do not contain any variables. Therefore, "x + 2" is the only option that qualifies as an algebraic expression.

Explanation

An algebraic expression is a mathematical phrase that includes numbers, variables, and operations. In the given options, "x + 2" contains the variable 'x' along with a constant, making it an algebraic expression. The other options, such as "5 + 3," "7 - 4," and "10," are numerical expressions as they do not contain any variables. Therefore, "x + 2" is the only option that qualifies as an algebraic expression.