You're viewing 3 free preview questions for Maths AA HL — subscribe to unlock 262 more, plus the Full Question Bank, Mock Papers & Worksheets.Upgrade

Polynomials and Rational Functions · Paper 1 — Free Maths AA HL Practice Questions

1FoundationSAQ-SPolynomial expressions and their factorizationss5 marksPaper 1~8 min

A rectangular garden has length

(x+4)

metres and width

(x-1)

metres, where

x > 1

(a)

Show that the area of the garden, in square metres, is

x^2 + 3x - 4

. [1 mark]

(b)

Given that the area of the garden is

70\,\text{m}^2

, find the value of

x

. [3 marks]

(c)

Hence find the perimeter of the garden. [1 mark]

Solutions

2MasterySAQ-SPolynomial expressions and their factorizationss5 marksPaper 1~8 min

The graph of the polynomial

y = P(x)

passes through the points

(-1,\,0)

(2,\,0)

, and

(0,\,-12)

. The polynomial is of degree 3 with leading coefficient

2

(a)

Show that

P(x) = 2x^3 + 4x^2 - 10x - 12

. [3 marks]

(b)

Find the

x

-coordinates of the turning points of the graph of

y = P(x)

, giving your answers in exact form. [2 marks]

Solutions

3ChallengeSAQ-LPolynomial expressions and their factorizationss8 marksPaper 1~12 min

A rectangular box has dimensions

x\,\text{cm}

(x+3)\,\text{cm}

, and

(2x-1)\,\text{cm}

, where

x > \dfrac{1}{2}

. The volume of the box is

V(x)

cubic centimetres.

(a)

Show that

V(x) = 2x^3 + 5x^2 - 3x

. [2 marks]

(b)

Find the three values of

x

for which

V(x) = 0

. State, with a reason, which of these values lie outside the physical domain

x > \dfrac{1}{2}

. [3 marks]

(c)

Given that

V(x) = 60

, show that

2x^3 + 5x^2 - 3x - 60 = 0

, and verify that a root lies in the interval $2.5 < x < 2.6$. [2 marks]

(d)

Use linear interpolation once on the interval $2.5 < x < 2.6$ to find an estimate for

x

, giving your answer correct to three significant figures. [1 mark]

Solutions

Questions 4-265

Unlock these questions with Premium

That's every free question here — 3 of 265.

+262 more questions, plus Mock Papers & Worksheets, are waiting in Premium.

Upgrade