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Practise

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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2730 questions · page 29 of 137 · choose a topic above to narrow them down

SA-9709-P1-IN4-0013 marksL1 FoundationCalculatorArea under
The line y=6−2xy=6-2x meets the xx-axis at x=3x=3. Use integration to find the area between the line, the xx-axis and the yy-axis.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN4-G013 marksL1 FoundationCalculatorArea under
Find the area of the region under y=x2+1y=x^2+1 between x=0x=0 and x=3x=3.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN5-G013 marksL1 FoundationCalculatorAbout the x-axis
The region under y=xy=x from x=0x=0 to x=3x=3 is rotated through 360∘360^\circ about the xx-axis. Find the exact volume.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-IN-G014 marksL1 FoundationCalculatorFinding the curve
A curve has gradient dydx=6x2−4x\dfrac{dy}{dx}=6x^2-4x and passes through the point (1,5)(1,5). Find the equation of the curve.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-QD-0012 marksL1 FoundationCalculatora = 1
Express x2+6x+11x^2+6x+11 in the form (x+a)2+b(x+a)^2+b, where aa and bb are constants.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-QD-0172 marksL1 FoundationCalculatorNature of roots
For the equation 2x2−3x+5=02x^2-3x+5=0, find the value of the discriminant and state the number of real roots.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-QD2-0072 marksL1 FoundationCalculatorFactorising
Solve x2=5xx^2=5x.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-QD2-G012 marksL1 FoundationCalculatorFactorising
Solve x2−7x+10=0x^2-7x+10=0.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-QD3-0022 marksL1 FoundationCalculatorUnknown constants
x2+4x+k=0x^2+4x+k=0 has equal roots. Find kk.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-QD3-G012 marksL1 FoundationCalculatorNature of roots
Find the discriminant of x2−6x+9x^2-6x+9, and state how many real roots x2−6x+9=0x^2-6x+9=0 has.
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-QD4-0012 marksL1 FoundationCalculatorQuadratic
The solution of x2>9x^2>9 is
Choose one option

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-QD4-G012 marksL1 FoundationCalculatorQuadratic
Solve x2−5x+4≤0x^2-5x+4\le0. Give your answer as a≤x≤ba\le x\le b.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-QD5-0013 marksL1 FoundationCalculatorSimultaneous
Solve the simultaneous equations x+y=5x+y=5 and xy=6xy=6. Give the possible values of xx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-QD5-G013 marksL1 FoundationCalculatorIntersections
The line y=x+1y=x+1 meets the curve y=x2−1y=x^2-1 at two points. Find (a) their xx-coordinates (b) the yy-coordinate of the point with positive xx.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-QD-G013 marksL1 FoundationCalculatora = 1
x2−4x+9=(x+p)2+qx^2-4x+9=(x+p)^2+q. Work through it in three steps.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-SR-0054 marksL1 FoundationCalculatorAP formulae
An arithmetic progression has first term 77 and common difference 33. Find the 20th term and the sum of the first 20 terms.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-SR-0084 marksL1 FoundationCalculatorGP formulae
A geometric progression has first term 33 and common ratio 22. Find the 10th term and the sum of the first 10 terms.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-SR-0102 marksL1 FoundationCalculatorSum to infinity
Find the sum to infinity of the geometric progression 81, 54, 36, …81,\ 54,\ 36,\ \dots

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-SR1-0011 markL1 FoundationCalculatorExpanding
Find the value of (73)\binom73.

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Salam Academy Original Practice · Proposed mark scheme
SA-9709-P1-SR2-0012 marksL1 FoundationCalculatorAP formulae
An arithmetic progression has first term 5050 and common difference −3-3. Find the 20th term.

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Salam Academy Original Practice · Proposed mark scheme