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1.2.8 Algebra and Functions

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Question 34

A specialized drone's vertical displacement from a reference altitude, $h$ (in meters), is modeled by the function

h(t) = at^3 + 3t^2 + bt - 10

where $t\,$ is the time in seconds since the drone began its descent and $a\,$ and $b\,$ are constants.

When $h (t)$ is divided by $(t - 3)$ , the remainder is 44.

Use the remainder theorem to show that

9 a + b = 9

[3]

Given also that $(t + 1)$ is a factor of $h (t)$ ,

find the value of $a\,$ and the value of $b$ .

[3]

Find $h^{'} (t)$ .

[2]

Hence find the exact coordinates of the stationary points of the curve with equation $y = h (t)$ .

[4]

Markscheme

1.2.8 Algebra and Functions Questions

A Level
Maths
1.2.8 Algebra and Functions

72 exam-style questions on WJEC A Level Maths 1.2.8 Algebra and Functions. Each one has a worked solution and a mark scheme showing where the marks go.

1.2.8 Algebra and Functions

Question bank

1.2.8 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 59 60 61

Question 34

A specialized drone's vertical displacement from a reference altitude, $h$ (in meters), is modeled by the function

h(t) = at^3 + 3t^2 + bt - 10

where $t\,$ is the time in seconds since the drone began its descent and $a\,$ and $b\,$ are constants.

When $h (t)$ is divided by $(t - 3)$ , the remainder is 44.

Use the remainder theorem to show that

9 a + b = 9

[3]

Given also that $(t + 1)$ is a factor of $h (t)$ ,

find the value of $a\,$ and the value of $b$ .

[3]

Find $h^{'} (t)$ .

[2]

Hence find the exact coordinates of the stationary points of the curve with equation $y = h (t)$ .

[4]

Markscheme

1.2.8 Algebra and Functions Questions

A Level
Maths
1.2.8 Algebra and Functions

72 exam-style questions on WJEC A Level Maths 1.2.8 Algebra and Functions. Each one has a worked solution and a mark scheme showing where the marks go.