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1.10.7 Upper and lower bounds using rectangles (A-level only)

Question 1

The interval $0\leq x\leq4\,$ is divided into $n\,$ equal strips to bound the area under $y=xy=\sqrt{x}$ using left- and right-endpoint rectangles.

For $n = 4$ , find exact lower and upper bounds for the area.

[4]

Show that, for general $n$ , the difference between the upper and lower bounds is $8n\displaystyle \frac{8}{n}$ .

[2]

Determine the least value of $n\,$ for which the difference is less than 0.1.

[1]

Markscheme

1.10.7 Upper and lower bounds using rectangles (A-level only) Questions

A Level
Maths
1.10.7 Upper and lower bounds using rectangles (A-level only)

8 exam-style questions on OCR (MEI) A Level Maths 1.10.7 Upper and lower bounds using rectangles (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

1.10.7 Upper and lower bounds using rectangles (A-level only)

Question bank

1.10.7 Upper and lower bounds using rectangles (A-level only)

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Question 1

The interval $0\leq x\leq4\,$ is divided into $n\,$ equal strips to bound the area under $y=xy=\sqrt{x}$ using left- and right-endpoint rectangles.

For $n = 4$ , find exact lower and upper bounds for the area.

[4]

Show that, for general $n$ , the difference between the upper and lower bounds is $8n\displaystyle \frac{8}{n}$ .

[2]

Determine the least value of $n\,$ for which the difference is less than 0.1.

[1]

Markscheme

1.10.7 Upper and lower bounds using rectangles (A-level only) Questions

A Level
Maths
1.10.7 Upper and lower bounds using rectangles (A-level only)

8 exam-style questions on OCR (MEI) A Level Maths 1.10.7 Upper and lower bounds using rectangles (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.