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Question bank

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

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2401 questions · page 48 of 121 · choose a topic above to narrow them down

SA-IAL-P1-IN1-0032 marksL1 FoundationNon-calculatorPower rule
Find ∫(4−3x2) dx\displaystyle\int(4-3x^2)\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-IN2-0013 marksL1 FoundationNon-calculatorFinding the curve
dydx=2x\dfrac{dy}{dx}=2x, and the curve passes through (1,4)(1,4). Find yy in terms of xx.

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-IN2-0033 marksL1 FoundationNon-calculatorFinding the curve
dydx=4x−1\dfrac{dy}{dx}=4x-1, and the curve passes through (2,5)(2,5). Find the constant of integration cc in y=2x2−x+cy=2x^2-x+c.

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-IN-G012 marksL1 FoundationCalculatorPower rule
Find ∫(6x2+4x) dx\displaystyle\int(6x^2+4x)\,dx.

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-TR-0013 marksL1 FoundationCalculatorSine & cosine rules
In triangle ABCABC, angle A=40∘A=40^\circ, angle B=65∘B=65^\circ and a=8a=8 cm. Find bb, to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-TR-0062 marksL1 FoundationCalculatorArcs & sectors
A sector has radius 66 cm and angle 1.21.2 radians. Find the arc length.

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-TR-0072 marksL1 FoundationCalculatorArcs & sectors
A sector has radius 55 cm and angle 0.80.8 radians. Find its area.

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-TR-0101 markL1 FoundationCalculatorTrig graphs
Write down the period of y=sin⁡2xy=\sin2x, in degrees.

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-TR1-0012 marksL1 FoundationNon-calculatorSine & cosine rules
In triangle ABCABC, b=3b=3 cm, c=5c=5 cm and angle A=60∘A=60^\circ. Find the exact length of aa.

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-TR2-0011 markL1 FoundationNon-calculatorRadians
Convert 150∘150^\circ to radians, giving an exact answer.

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-TR2-0021 markL1 FoundationCalculatorRadians
Convert 2.52.5 radians to degrees, to 1 decimal place.

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-TR2-0031 markL1 FoundationNon-calculatorArcs & sectors
A sector has radius 88 cm and angle π4\tfrac\pi4. Find the exact arc length.

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-TR3-0011 markL1 FoundationNon-calculatorTrig graphs
Write down the period of y=cos⁡3xy=\cos3x, in degrees.

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-TR3-0021 markL1 FoundationNon-calculatorTrig graphs
Write down the period of y=tan⁡xy=\tan x, in degrees.

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-TR3-0031 markL1 FoundationNon-calculatorTrig graphs
Write down the minimum value of y=2sin⁡x+1y=2\sin x+1.

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-TR3-0061 markL1 FoundationNon-calculatorTrig graphs
Write down the exact value of sin⁡π3\sin\tfrac\pi3.

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-P1-TR-G013 marksL1 FoundationCalculatorSine & cosine rules
In triangle ABCABC, a=7a=7 cm, b=5b=5 cm and angle C=60∘C=60^\circ. Find the length cc, to 3 significant figures.

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-S1-CR-0012 marksL1 FoundationCalculatorS values
For the same 88 pairs, ∑y=120\sum y=120 and ∑xy=760\sum xy=760. Find SxyS_{xy}.

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-S1-CR1-0012 marksL1 FoundationNon-calculatorS values
For 1010 values, ∑y=50\sum y=50 and ∑y2=290\sum y^2=290. Find SyyS_{yy}.

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Salam Academy Original Practice · Proposed mark scheme
SA-IAL-S1-CR1-0022 marksL1 FoundationNon-calculatorPMCC
For a set of bivariate data, Sxx=16S_{xx}=16, Syy=25S_{yy}=25 and Sxy=12S_{xy}=12. Find the PMCC.

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Salam Academy Original Practice · Proposed mark scheme