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91579 – Worked Solutions - 2025

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QUESTION THREE

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3.7 (AS 91579) – 2025 Answers

Quite often, there are different ways to solve a Mathematics problem.

These solutions/strategies show one possible way to solve them.

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Question 3(a)

The diagram below shows the cross-section of a hole dug in the ground.

The depth of the hole is measured every 5 metres across the top of the hole.

Using the trapezium rule, find an estimate for the area of the cross-section of the hole.

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Question 3(a)

The diagram below shows the cross-section of a hole dug in the ground.

The depth of the hole is measured every 5 metres across the top of the hole.

Using the trapezium rule, find an estimate for the area of the cross-section of the hole.

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Question 3(a)

The diagram below shows the cross-section of a hole dug in the ground.

The depth of the hole is measured every 5 metres across the top of the hole.

Using the trapezium rule, find an estimate for the area of the cross-section of the hole.

0

5

10

15

20

1

2

3

4

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Question 3(a)

The diagram below shows the cross-section of a hole dug in the ground.

The depth of the hole is measured every 5 metres across the top of the hole.

Using the trapezium rule, find an estimate for the area of the cross-section of the hole.

0

5

10

15

20

1

2

3

4

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Question 3(a)

The diagram below shows the cross-section of a hole dug in the ground.

The depth of the hole is measured every 5 metres across the top of the hole.

Using the trapezium rule, find an estimate for the area of the cross-section of the hole.

0

5

10

15

20

1

2

3

4

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Question 3(a)

The diagram below shows the cross-section of a hole dug in the ground.

The depth of the hole is measured every 5 metres across the top of the hole.

Using the trapezium rule, find an estimate for the area of the cross-section of the hole.

0

5

10

15

20

1

2

3

4

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Question 3(a)

The diagram below shows the cross-section of a hole dug in the ground.

The depth of the hole is measured every 5 metres across the top of the hole.

Using the trapezium rule, find an estimate for the area of the cross-section of the hole.

0

5

10

15

20

1

2

3

4

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Question 3(a)

The diagram below shows the cross-section of a hole dug in the ground.

The depth of the hole is measured every 5 metres across the top of the hole.

Using the trapezium rule, find an estimate for the area of the cross-section of the hole.

0

5

10

15

20

1

2

3

4

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Question 3(a)

The diagram below shows the cross-section of a hole dug in the ground.

The depth of the hole is measured every 5 metres across the top of the hole.

Using the trapezium rule, find an estimate for the area of the cross-section of the hole.

0

5

10

15

20

1

2

3

4

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Question 3(a)

The diagram below shows the cross-section of a hole dug in the ground.

The depth of the hole is measured every 5 metres across the top of the hole.

Using the trapezium rule, find an estimate for the area of the cross-section of the hole.

0

5

10

15

20

1

2

3

4

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Question 3(a)

The diagram below shows the cross-section of a hole dug in the ground.

The depth of the hole is measured every 5 metres across the top of the hole.

Using the trapezium rule, find an estimate for the area of the cross-section of the hole.

0

5

10

15

20

1

2

3

4

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Question 3(a)

The diagram below shows the cross-section of a hole dug in the ground.

The depth of the hole is measured every 5 metres across the top of the hole.

Using the trapezium rule, find an estimate for the area of the cross-section of the hole.

0

5

10

15

20

1

2

3

4

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Question 3(a)

The diagram below shows the cross-section of a hole dug in the ground.

The depth of the hole is measured every 5 metres across the top of the hole.

Using the trapezium rule, find an estimate for the area of the cross-section of the hole.

0

5

10

15

20

1

2

3

4

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Question 3(a)

The diagram below shows the cross-section of a hole dug in the ground.

The depth of the hole is measured every 5 metres across the top of the hole.

Using the trapezium rule, find an estimate for the area of the cross-section of the hole.

0

5

10

15

20

1

2

3

4

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Question 3(b)

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Question 3(b)

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Question 3(b)

We can take the multiplier of 10 out the front

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Question 3(b)

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Question 3(c)

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Question 3(c)

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Question 3(c)

Take the integral of both sides

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Question 3(c)

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Question 3(c)

Simplify

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Question 3(c)

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Question 3(c)

Subtract 1.25 from both sides

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Question 3(c)

Multiply both sides by 2

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Question 3(c)

Square both sides

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Question 3(c)

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Question 3(d)

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Question 3(d)

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Question 3(d)

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Question 3(d)

Integrate the function;

Remember for polynomials, add one to the power and divide by the new power.

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Question 3(d)

Simplify

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Question 3(d)

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Question 3(d)

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Question 3(d)

Simplify

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Question 3(d)

Get common denominators

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Question 3(d)

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Question 3(d)

Get common denominator for the RHS

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Question 3(d)

Simplify into one fraction

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Question 3(d)

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Question 3(d)

Rearrange to get equal to zero

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Question 3(d)

Divide everything by 8

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Question 3(d)

Divide everything by 8

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Question 3(e)

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Question 3(e)

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Question 3(e)

Integrate the functions;

Remember for polynomials, add one to the power and divide by the new power.

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Question 3(e)

Simplify

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Question 3(e)

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Question 3(e)

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Question 3(e)

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Question 3(e)