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1.1.10 Algebra and functions

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Question 34

A chemical engineer models the rate of heat loss $H (T)$ , in kilowatts per degree Celsius, from a specific pressurized vessel using the formula

\frac{2T^2 - 3T - 7}{T - 4}, \quad T > 4

where $T$ is the temperature of the vessel in degrees Celsius.

Write $H (T)$ in the form

\frac{C}{T - 4}

where $A$ , $B$ , and $C$ are integers to be found.

[3]

Hence use algebraic integration to show that the total heat loss between temperature $T = 5$ and $T = 7$ , given by $dT\int_{5}^{7} H(T) \, dT$ , is equal to

\alpha + \beta \ln 3

where $α\alpha$ and $β\beta$ are integers to be found.

[4]

Markscheme

1.1.10 Algebra and functions Questions

A Level
Maths
1.1.10 Algebra and functions

64 exam-style questions on CCEA A Level Maths 1.1.10 Algebra and functions. Each one has a worked solution and a mark scheme showing where the marks go.

1.1.10 Algebra and functions

Question bank

1.1.10 Algebra and functions

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58

Question 34

A chemical engineer models the rate of heat loss $H (T)$ , in kilowatts per degree Celsius, from a specific pressurized vessel using the formula

\frac{2T^2 - 3T - 7}{T - 4}, \quad T > 4

where $T$ is the temperature of the vessel in degrees Celsius.

Write $H (T)$ in the form

\frac{C}{T - 4}

where $A$ , $B$ , and $C$ are integers to be found.

[3]

Hence use algebraic integration to show that the total heat loss between temperature $T = 5$ and $T = 7$ , given by $dT\int_{5}^{7} H(T) \, dT$ , is equal to

\alpha + \beta \ln 3

where $α\alpha$ and $β\beta$ are integers to be found.

[4]

Markscheme

1.1.10 Algebra and functions Questions

A Level
Maths
1.1.10 Algebra and functions

64 exam-style questions on CCEA A Level Maths 1.1.10 Algebra and functions. Each one has a worked solution and a mark scheme showing where the marks go.