Practise questions · Salam Academy

SA-9709-P1-FN1-0081 markL1 FoundationCalculatorNotation

Which of these rules, each with domain

x\ge0

, is not a function?

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN1-G012 marksL1 FoundationCalculatorRange on an interval

f(x)=3x+1

for

-2\le x\le3

. The range of

f

is

p\le f(x)\le q

. Find

p

and

q

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN1-Q011 markL1 FoundationCalculatorNotation

The domain of a function is

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SA-9709-P1-FN1-Q021 markL1 FoundationCalculatorNotation

A graph is the graph of a function if

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SA-9709-P1-FN1-Q031 markL1 FoundationCalculatorRange of quadratics

f(x)=(x+1)^2-4

,

x\in\mathbb{R}

. The range of

f

is

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN1-0013 marksL2 StandardCalculatorRange of quadratics

f(x)=x^2+4x+9

,

x\in\mathbb{R}

. By completing the square, find the least value of

f(x)

, and hence state the range of

f

as

f(x)\ge k

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN1-0021 markL2 StandardCalculatorRange on an interval

f(x)=5-2x

for

x>1

. The range of

f

is

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN1-0052 marksL2 StandardCalculatorRange of quadratics

f(x)=2(x-1)^2-7

for

x\ge3

. State the range of

f

in the form

f(x)\ge k

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN1-0062 marksL2 StandardCalculatorDomain

The largest possible domain of

f(x)=\sqrt{5-2x}

is

x\le k

. Find

k

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN1-0072 marksL2 StandardCalculatorDomain

g(x)=\dfrac{4}{x-3}+1

,

x\ne3

. One value is not in the range of

g

. State this value.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN1-0093 marksL2 StandardCalculatorRange of quadratics

f(x)=-x^2+4x+1

,

x\in\mathbb{R}

. The range of

f

is

f(x)\le k

. Find

k

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN1-0142 marksL2 StandardCalculatorRange of quadratics

f:x\mapsto7-(x-2)^2

,

x\ge1

. State the range of

f

in the form

f(x)\le k

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN1-0034 marksL3 ExamCalculatorRange of quadratics

f(x)=x^2-6x+11

for

0\le x\le4

. The range of

f

is

p\le f(x)\le q

. Find

p

and

q

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN1-0043 marksL3 ExamCalculatorRange of quadratics

f(x)=x^2-6x+11

for

4\le x\le7

. The range of

f

is

p\le f(x)\le q

. Find

p

and

q

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN1-0103 marksL3 ExamCalculatorRange of quadratics

f(x)=x^2-4x+k

,

x\in\mathbb{R}

, where

k

is a constant. The range of

f

is

f(x)\ge3

. Find

k

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN1-0114 marksL3 ExamCalculatorRange of quadratics

f(x)=2x^2-12x+7

for

1\le x\le5

. Express

f(x)

in the form

a(x+b)^2+c

, and hence find the range

p\le f(x)\le q

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN1-0122 marksL3 ExamCalculatorRange on an interval

f(x)=\dfrac{1}{x+2}

for

x\ge0

. (i) Find the greatest value of

f(x)

. (ii) Is

0

in the range of

f

?

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-FN1-0135 marksL5 ExtensionCalculatorRange of quadratics

f(x)=x^2-6x+11

for

p\le x\le6

. The range of

f

is

2\le f(x)\le11

. Find the set of possible values of

p

, in the form

m\le p\le M

.

Salam Academy Original Practice · Proposed mark scheme

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