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1.2.10 Manipulating polynomials

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Question 20

The displacement of a particle $s$ (in meters) from a reference point at time $t$ (in seconds) is modeled by the function:

s(t) = (t - 2)(3t^2 + 10t + k) + 48

where $k\,$ is a constant.

State the remainder when $s (t)$ is divided by $(t - 2)$ .

[2]

Given that the particle is at the reference point ( $s = 0$ ) when $t=23\displaystyle t = \frac{2}{3}$ , show that $k = 28$ .

[4]

ci.

Hence

fully factorise the expression for $s (t)$ ,

[3]

cii.

Hence

find the number of real solutions of the equation $s (t) = 0$ , giving a reason for your answer.

[3]

Markscheme

1.2.10 Manipulating polynomials Questions

A Level
Maths
1.2.10 Manipulating polynomials

72 exam-style questions on OCR A Level Maths 1.2.10 Manipulating polynomials. Each one has a worked solution and a mark scheme showing where the marks go.

1.2.10 Manipulating polynomials

Question bank

1.2.10 Manipulating polynomials

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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 20

The displacement of a particle $s$ (in meters) from a reference point at time $t$ (in seconds) is modeled by the function:

s(t) = (t - 2)(3t^2 + 10t + k) + 48

where $k\,$ is a constant.

State the remainder when $s (t)$ is divided by $(t - 2)$ .

[2]

Given that the particle is at the reference point ( $s = 0$ ) when $t=23\displaystyle t = \frac{2}{3}$ , show that $k = 28$ .

[4]

ci.

Hence

fully factorise the expression for $s (t)$ ,

[3]

cii.

Hence

find the number of real solutions of the equation $s (t) = 0$ , giving a reason for your answer.

[3]

Markscheme

1.2.10 Manipulating polynomials Questions

A Level
Maths
1.2.10 Manipulating polynomials

72 exam-style questions on OCR A Level Maths 1.2.10 Manipulating polynomials. Each one has a worked solution and a mark scheme showing where the marks go.