Sub-topic 1
2024 · National Preliminary
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Finding $k$ when $\int_0^1(3x^2-4kx+5)\,dx=0$
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Sub-topic 2
2024 · National Preliminary
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Evaluating $\int_1^2(6x^2+4x-8)\,dx$
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Sub-topic 3
2025 · National Preliminary
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Evaluating $\int_0^2(6x^2-10x)\,dx$
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Sub-topic 4
2026 · National Preliminary
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Evaluating $\int_1^2(3x^2-4x+5)\,dx$
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Sub-topic 5
2026 · National Preliminary
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Curve with gradient $3x^2-\dfrac{1}{x^2}$ through the point $(1,5)$
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Sub-topic 6
2025 · National Preliminary
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Curve with gradient $3x^2+4x+3$ through the point $(0,7)$
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Sub-topic 7
2025 · National Semifinal
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Integrating $(2x-3)(x^2-3x+2)^5$ by substitution
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Sub-topic 8
2021 · National One-Eighth
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Evaluating $\int_{-1}^{1}(4x^3-3x^2+2x)\,dx$
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Sub-topic 9
2021 · National Preliminary
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Curve $y=x(8-x)$: intersections with $y=12$, area under the curve and a tangent
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Sub-topic 10
2025 · National One-Eighth
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Area under $y=2x+1$ and volume of revolution about the $x$-axis
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Sub-topic 11
2025 · National Preliminary
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Power-rule antiderivatives such as $\int x^{1/2}\,dx$ (true/false)
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Sub-topic 12
2014 · National Final
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Integrating $x^2+4x+2$
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Sub-topic 13
2014 · National Final
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Integrating $3x^2-5x+3$
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Sub-topic 14
2014 · National Final
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Integrating $4x^3-3x^2+2x$
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Sub-topic 15
2020 · National One-Eighth
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Curve with gradient $3x^2-2x+1$ through a given point
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Sub-topic 16
2021 · National Preliminary
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Area enclosed by $y=3x(x-2)$ and the $x$-axis
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Sub-topic 17
2022 · National Preliminary
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Riddle: a definite integral, a number used for area and volume
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Sub-topic 18
2022 · National Preliminary
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Area bounded by $y=10-x^2$ and the line $y=1$
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Sub-topic 19
2022 · National Preliminary
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Curve with gradient $4x^3-3x^2+2x+5$ and $y$-intercept $6$
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Sub-topic 20
2022 · National Preliminary
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Area under $y=3x^2-2x$ from $x=1$ to $x=3$
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Sub-topic 21
2022 · National Preliminary
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Area under $y=5+2x$ from $x=0$ to $x=2$
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Sub-topic 22
2022 · National Preliminary
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Area under $y=4x^3+2x$ from $x=1$ to $x=2$
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Sub-topic 23
2023 · National Preliminary
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Curve with gradient $2x-k$ through $a(2,7)$ and $b(-1,-2)$
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Sub-topic 24
2023 · National Preliminary
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Curve with gradient $2kx+3$ through $a(1,5)$ and $b(-2,8)$
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Sub-topic 25
2023 · National Preliminary
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Curve with gradient $2x+3k$ through $a(1,13)$ and $b(-1,-11)$
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Sub-topic 26
2023 · National Quarterfinal
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Curve with gradient $2kx+2$ through $a(1,5)$ and $b(-2,11)$
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