PractiseQuestion bank
Original exam-style questions, mapped to your syllabus. Answers are checked for mathematical equivalence and every attempt updates your mastery.
Sign in to check answers. Your attempts build your mastery and error book.
12 questions
SA-FP-ROOT-0021 markL1 FoundationNon-calculatorRoot relations
2x3−3x2+4x−5=0 has roots α,β,γ. Find αβγ. Salam Academy Original Practice · Proposed mark scheme
SA-FP-ROOT-Q011 markL1 FoundationNon-calculatorRoot relations
The product of the roots of ax2+bx+c=0 is Salam Academy Original Practice · Proposed mark scheme
SA-FP-ROOT-X011 markL1 FoundationNon-calculatorRoot relations
The roots of x3−6x2+11x−6=0 are α,β,γ. Find α+β+γ. Salam Academy Original Practice · Proposed mark scheme
SA-FP-ROOT-X021 markL1 FoundationNon-calculatorRoot relations
For the same cubic, find αβ+βγ+γα. Salam Academy Original Practice · Proposed mark scheme
SA-FP-ROOT-0012 marksL2 StandardNon-calculatorSymmetric functions
For the same equation x2−5x+3=0, find α1+β1. Salam Academy Original Practice · Proposed mark scheme
SA-FP-ROOT-0033 marksL2 StandardNon-calculatorSymmetric functions
x3+2x2−x+3=0 has roots α,β,γ. Find α2+β2+γ2. Salam Academy Original Practice · Proposed mark scheme
SA-FP-ROOT-0043 marksL2 StandardNon-calculatorTransformed roots
x2−5x+3=0 has roots α,β. The equation y2+py+q=0 has roots 2α and 2β. Find q. Salam Academy Original Practice · Proposed mark scheme
SA-FP-ROOT-G012 marksL2 StandardNon-calculatorSymmetric functions
x2−5x+3=0 has roots α and β. Find α2+β2. Salam Academy Original Practice · Proposed mark scheme
SA-FP-ROOT-X032 marksL2 StandardNon-calculatorSymmetric functions
For the same cubic, find α2+β2+γ2. Salam Academy Original Practice · Proposed mark scheme
SA-FP-ROOT-X042 marksL2 StandardNon-calculatorSymmetric functions
For the same cubic, find α1+β1+γ1. Salam Academy Original Practice · Proposed mark scheme
SA-FP-ROOT-X053 marksL3 ExamNon-calculatorTransformed roots
The equation with roots 2α,2β,2γ is x3+px2+qx+r=0. Find r. Salam Academy Original Practice · Proposed mark scheme
SA-FP-ROOT-0054 marksL4 ChallengingNon-calculatorSymmetric functions
x3−3x+1=0 has roots α,β,γ. Find α3+β3+γ3. Salam Academy Original Practice · Proposed mark scheme