Practise

Question bank

Original exam-style questions, mapped to your syllabus. Answers are checked for mathematical equivalence and every attempt updates your mastery.

TopicSkillDifficulty

12 questions

SA-IAL-P1-AL-0093 marksL1 FoundationCalculatorEquations & inequalities

The solution of

x^2-5x-14>0

x<a

x>b

. Find

a

and

b

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL2-0012 marksL1 FoundationNon-calculatorDiscriminant

Write

x^2+6x+11

in the form

(x+p)^2+q

. Find

p

and

q

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL2-0022 marksL1 FoundationNon-calculatorDiscriminant

Find the value of the discriminant of

2x^2-3x+5

, and hence state the number of real roots of

2x^2-3x+5=0

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL2-0032 marksL1 FoundationNon-calculatorEquations & inequalities

The solution of

x^2<9

a<x<b

. Find

a

and

b

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL-Q021 markL1 FoundationCalculatorDiscriminant

b^2-4ac<0

, the graph of

y=ax^2+bx+c

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL-0063 marksL2 StandardCalculatorDiscriminant

The equation

x^2+kx+9=0

, where

k>0

, has equal roots. Find

k

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL-0073 marksL2 StandardCalculatorDiscriminant

The equation

2x^2+4x+k=0

has two distinct real roots. This is true exactly when

k<c

. Find

c

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL-0085 marksL2 StandardCalculatorEquations & inequalities

Solve the simultaneous equations

y=x+1

and

x^2+y^2=25

. Give the two values of

x

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL-0114 marksL2 StandardCalculatorEquations & inequalities

Find the set of values of

x

for which

x^2+2x-3\le3x+3

. The answer is

a\le x\le b

; give

a

and

b

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL2-0044 marksL2 StandardNon-calculatorEquations & inequalities

Solve the simultaneous equations

y=2x

and

y=x^2-3

. Give the two values of

x

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL-0104 marksL3 ExamCalculatorEquations & inequalities

The solution of

\dfrac6x<2

x\neq0

, is

x<a

x>b

. Find

a

and

b

Salam Academy Original Practice · Proposed mark scheme

SA-IAL-P1-AL-0175 marksL4 ChallengingCalculatorDiscriminant

The line

y=kx-1

is a tangent to the curve

y=x^2+3

. Find the possible values of

k

Salam Academy Original Practice · Proposed mark scheme