Practise questions · Salam Academy

SA-9709-P1-QD-0012 marksL1 FoundationCalculatora = 1

Express

x^2+6x+11

in the form

(x+a)^2+b

, where

a

and

b

are constants.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD-0022 marksL1 FoundationCalculatora = 1

Express

x^2-10x+4

in the form

(x+a)^2+b

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD-0081 markL1 FoundationCalculatorVertex

What is the minimum value of

(x-3)^2+7

?

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD-0101 markL1 FoundationCalculatora = 1

Expand and simplify

(x-3)^2-4

. (Algebraic answers are checked for equivalence, so any correct form is accepted.)

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD-G013 marksL1 FoundationCalculatora = 1

x^2-4x+9=(x+p)^2+q

. Work through it in three steps.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD-Q011 markL1 FoundationCalculatora = 1

x^2+10x

is equal to

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD-Q021 markL1 FoundationCalculatorVertex

The vertex of

y=(x+2)^2-7

is

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD-0033 marksL2 StandardCalculatora = 1

Express

x^2+5x-3

in the form

(x+a)^2+b

, giving

a

and

b

as exact fractions.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD-0043 marksL2 StandardCalculatora ≠ 1

Express

2x^2-12x+5

in the form

a(x+b)^2+c

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD-0052 marksL2 StandardCalculatorVertex

Find the coordinates of the minimum point of the curve

y=x^2-8x+19

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD-0152 marksL2 StandardCalculatorVertex

The function

g

is defined by

g(x)=2(x+1)^2-8

for

x\in\mathbb{R}

. State the equation of the line of symmetry of

y=g(x)

and the least value of

g(x)

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD1-0014 marksL2 StandardCalculatorSketching & models

For the curve

y=x^2-2x-8

, find (a) the

x

-coordinates where it crosses the

x

-axis (b) where it crosses the

y

-axis (c) the coordinates of its vertex. (These are what a sketch must show.)

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD1-0023 marksL2 StandardCalculatorVertex

Express

-2x^2+8x-3

in the form

a(x+b)^2+c

, and hence find the greatest value of

-2x^2+8x-3

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD1-0042 marksL2 StandardCalculatora = 1

x^2+bx+20\equiv(x-5)^2+c

. Find

b

and

c

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD1-0063 marksL2 StandardCalculatorSketching & models

A ball's height after

t

seconds is

h=20t-5t^2

metres. Find (a) its greatest height (b) the time at which this happens.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD-Q031 markL2 StandardCalculatorUnknown constants

Which form shows directly that

x^2-6x+11>0

for all

x

?

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD-0074 marksL3 ExamCalculatora ≠ 1

The function

f

is defined by

f(x)=3x^2+12x+7

for

x\in\mathbb{R}

.
(a) Express

f(x)

in the form

a(x+b)^2+c

.
(b) Hence state the least value of

f(x)

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD1-0033 marksL3 ExamCalculatorUnknown constants

A parabola has its vertex at

(2,\,-3)

and passes through

(0,\,5)

. Its equation is

y=a(x-2)^2-3

. Find

a

.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD1-0054 marksL3 ExamCalculatorSketching & models

A farmer has

40

m of fencing to make three sides of a rectangular pen against a long straight wall. The two sides perpendicular to the wall are each

x

m long. (a) Show that the area is

A=x(40-2x)

. (b) By completing the square, find the greatest possible area.

Salam Academy Original Practice · Proposed mark scheme

SA-9709-P1-QD-0093 marksL4 ChallengingCalculatorUnknown constants

Find the set of values of

k

for which

x^2+6x+k>0

for all real values of

x

.

Salam Academy Original Practice · Proposed mark scheme

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