Class 7 Full Year 7th Grade Review worksheet with math problems and multiple-choice answers.

Let's solve each problem step by step.

---

Problem (1): Convert the following decimals into percent

#### Solution:
To convert a decimal to a percentage, multiply the decimal by 100 and add the `%` symbol.

- A) 0.00068
\[
0.00068 \times 100 = 0.068\%
\]

- B) 0.0286
\[
0.0286 \times 100 = 2.86\%
\]

- C) 2.56
\[
2.56 \times 100 = 256\%
\]

- D) 2.41
\[
2.41 \times 100 = 241\%
\]

- E) 0.00232
\[
0.00232 \times 100 = 0.232\%
\]

- F) 0.097
\[
0.097 \times 100 = 9.7\%
\]

#### Final Answers:
\[
\boxed{0.068\%, 2.86\%, 256\%, 241\%, 0.232\%, 9.7\%}
\]

---

Problem (2): Neha wants to print some brochures for her business. If she goes for one style, it will cost her Rs. 113.5 plus Rs. 0.2 per brochure. If she goes for the other style, it will cost her Rs. 5 plus Rs. 0.55 per brochure. For how many brochures will the price for both styles be the same?

#### Solution:
Let \( x \) be the number of brochures.

- Cost for the first style:
\[
\text{Cost} = 113.5 + 0.2x
\]

- Cost for the second style:
\[
\text{Cost} = 5 + 0.55x
\]

Set the costs equal to each other:
\[
113.5 + 0.2x = 5 + 0.55x
\]

Rearrange the equation to isolate \( x \):
\[
113.5 - 5 = 0.55x - 0.2x
\]
\[
108.5 = 0.35x
\]

Solve for \( x \):
\[
x = \frac{108.5}{0.35}
\]
\[
x = 310
\]

#### Final Answer:
\[
\boxed{310}
\]

---

Problem (3): One wall of the theater is 58 m long and 23 m high. If the cost of paint a sq. m. of the wall is Rs. 63.80, then what is the cost to paint the entire wall?

#### Solution:
First, calculate the area of the wall:
\[
\text{Area} = \text{Length} \times \text{Height} = 58 \, \text{m} \times 23 \, \text{m} = 1334 \, \text{sq. m}
\]

Next, calculate the total cost of painting the wall:
\[
\text{Cost} = \text{Area} \times \text{Cost per sq. m} = 1334 \, \text{sq. m} \times 63.80 \, \text{Rs/sq. m}
\]
\[
\text{Cost} = 85205.20 \, \text{Rs}
\]

#### Final Answer:
\[
\boxed{85205.20}
\]

---

Problem (4): Solve the equations to find the value of the variable in each equation

#### Solution:

- A) \(-3(4y - 2) + 4(-3y) = 3(y + 2)\)

Expand both sides:
\[
-3(4y - 2) = -12y + 6
\]
\[
4(-3y) = -12y
\]
\[
3(y + 2) = 3y + 6
\]

Combine terms:
\[
-12y + 6 - 12y = 3y + 6
\]
\[
-24y + 6 = 3y + 6
\]

Subtract 6 from both sides:
\[
-24y = 3y
\]

Add \(24y\) to both sides:
\[
0 = 27y
\]

Solve for \( y \):
\[
y = 0
\]

- B) \(-5(2y) + 5(-5y + 1) = 3y - 71\)

Expand both sides:
\[
-5(2y) = -10y
\]
\[
5(-5y + 1) = -25y + 5
\]
\[
-10y - 25y + 5 = 3y - 71
\]
\[
-35y + 5 = 3y - 71
\]

Subtract 5 from both sides:
\[
-35y = 3y - 76
\]

Subtract \(3y\) from both sides:
\[
-38y = -76
\]

Solve for \( y \):
\[
y = 2
\]

- C) \(-3(5z - 5) - 3(-4z - 3) = -4(z - 5)\)

Expand both sides:
\[
-3(5z - 5) = -15z + 15
\]
\[
-3(-4z - 3) = 12z + 9
\]
\[
-4(z - 5) = -4z + 20
\]

Combine terms:
\[
-15z + 15 + 12z + 9 = -4z + 20
\]
\[
-3z + 24 = -4z + 20
\]

Add \(4z\) to both sides:
\[
z + 24 = 20
\]

Subtract 24 from both sides:
\[
z = -4
\]

- D) \(-3(-2x - 3) - 3(-5x + 1) = -3(x + 38)\)

Expand both sides:
\[
-3(-2x - 3) = 6x + 9
\]
\[
-3(-5x + 1) = 15x - 3
\]
\[
-3(x + 38) = -3x - 114
\]

Combine terms:
\[
6x + 9 + 15x - 3 = -3x - 114
\]
\[
21x + 6 = -3x - 114
\]

Add \(3x\) to both sides:
\[
24x + 6 = -114
\]

Subtract 6 from both sides:
\[
24x = -120
\]

Solve for \( x \):
\[
x = -5
\]

#### Final Answers:
\[
\boxed{0, 2, -4, -5}
\]

---

Problem (5): A swimming pool is 33 meter long and covers an area of 891 sq. meter. What is the breadth of the swimming pool?

#### Solution:
The area of a rectangle is given by:
\[
\text{Area} = \text{Length} \times \text{Breadth}
\]

Given:
\[
\text{Length} = 33 \, \text{m}, \quad \text{Area} = 891 \, \text{sq. m}
\]

Let the breadth be \( b \). Then:
\[
33 \times b = 891
\]

Solve for \( b \):
\[
b = \frac{891}{33}
\]
\[
b = 27
\]

#### Final Answer:
\[
\boxed{27}
\]

---

Problem (6): Write the polynomial after subtracting \(-5p^2 - 7p - 8\) from the sum of \( p^2 + p + 7 \) and \( 2p^2 - 5p - 3 \)

#### Solution:
First, find the sum of \( p^2 + p + 7 \) and \( 2p^2 - 5p - 3 \):
\[
(p^2 + p + 7) + (2p^2 - 5p - 3) = p^2 + 2p^2 + p - 5p + 7 - 3
\]
\[
= 3p^2 - 4p + 4
\]

Next, subtract \(-5p^2 - 7p - 8\) from this sum:
\[
(3p^2 - 4p + 4) - (-5p^2 - 7p - 8)
\]

Distribute the negative sign:
\[
3p^2 - 4p + 4 + 5p^2 + 7p + 8
\]

Combine like terms:
\[
(3p^2 + 5p^2) + (-4p + 7p) + (4 + 8)
\]
\[
= 8p^2 + 3p + 12
\]

#### Final Answer:
\[
\boxed{8p^2 + 3p + 12}
\]

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Final Summary of All Answers:

1. \(\boxed{0.068\%, 2.86\%, 256\%, 241\%, 0.232\%, 9.7\%}\)
2. \(\boxed{310}\)
3. \(\boxed{85205.20}\)
4. \(\boxed{0, 2, -4, -5}\)
5. \(\boxed{27}\)
6. \(\boxed{8p^2 + 3p + 12}\)