Class 6 Maths Worksheet: Algebra Word Problems

Let's solve each problem step by step using the given values:

Given:
p = -2, q = -1, r = 3

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1. $ p^2 + q^2 - r^2 $

- $ p^2 = (-2)^2 = 4 $
- $ q^2 = (-1)^2 = 1 $
- $ r^2 = (3)^2 = 9 $

So:
$$
p^2 + q^2 - r^2 = 4 + 1 - 9 = -4
$$

✔ Answer: -4

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2. $ 2p^2 - q^2 + 3r^2 $

- $ p^2 = 4 $ → $ 2p^2 = 2 \times 4 = 8 $
- $ q^2 = 1 $
- $ r^2 = 9 $ → $ 3r^2 = 3 \times 9 = 27 $

So:
$$
2p^2 - q^2 + 3r^2 = 8 - 1 + 27 = 34
$$

✔ Answer: 34

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3. $ p - q - r $

- $ p = -2 $
- $ q = -1 $
- $ r = 3 $

So:
$$
p - q - r = -2 - (-1) - 3 = -2 + 1 - 3 = -4
$$

✔ Answer: -4

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4. $ p^4 + q^4 - r^4 $

- $ p^4 = (-2)^4 = 16 $
- $ q^4 = (-1)^4 = 1 $
- $ r^4 = (3)^4 = 81 $

So:
$$
p^4 + q^4 - r^4 = 16 + 1 - 81 = -64
$$

✔ Answer: -64

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5. $ p^3 + q^3 + r^3 + 3pqr $

- $ p^3 = (-2)^3 = -8 $
- $ q^3 = (-1)^3 = -1 $
- $ r^3 = (3)^3 = 27 $
- $ 3pqr = 3 \times (-2) \times (-1) \times 3 = 3 \times 6 = 18 $

Now add:
$$
p^3 + q^3 + r^3 + 3pqr = -8 + (-1) + 27 + 18 = -9 + 45 = 36
$$

✔ Answer: 36

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6. Perimeter of an equilateral triangle with side $ l $

An equilateral triangle has 3 equal sides.

So, perimeter = $ 3 \times l = 3l $

✔ Answer: $ 3l $

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7. Perimeter of a regular hexagon with side $ l $

A regular hexagon has 6 equal sides.

So, perimeter = $ 6 \times l = 6l $

✔ Answer: $ 6l $

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8. Total length of edges of a cube with edge length $ l $

A cube has 12 edges (each face has 4 edges, but shared), and all are equal.

So, total edge length = $ 12 \times l = 12l $

✔ Answer: $ 12l $

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9. Constant term of $ 3x^2 + 5x + 8 $

The constant term is the one without any variable — it's just a number.

Here, that’s 8

✔ Answer: 8

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10. Constant term of $ 2x^2 - 9 $

Again, the constant term is the number without variables.

Here, that’s -9

✔ Answer: -9

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✔ Final Answers:

1. -4
2. 34
3. -4
4. -64
5. 36
6. $ 3l $
7. $ 6l $
8. $ 12l $
9. 8
10. -9

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