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Paper 1
How many integers nnn satisfy n2<2n+8n^2 < 2n + 8n2<2n+8?
Logic & Proof
Paper 1
Find the remainder when x4−3x2+2x^4 - 3x^2 + 2x4−3x2+2 is divided by x−1x - 1x−1.
Algebra
Paper 2
Find ddx(x2e−x)\frac{d}{dx}(x^2 e^{-x})dxd​(x2e−x) and the coordinates of any turning points.
Differentiation
Paper 1
The function fff is defined by f(x)=x+4f(x) = \sqrt{x+4}f(x)=x+4​. State the domain and range of fff.
Functions
Paper 1
How many integers nnn satisfy n2<2n+8n^2 < 2n + 8n2<2n+8?
Logic & Proof
Paper 1
Find the remainder when x4−3x2+2x^4 - 3x^2 + 2x4−3x2+2 is divided by x−1x - 1x−1.
Algebra
Paper 2
Find ddx(x2e−x)\frac{d}{dx}(x^2 e^{-x})dxd​(x2e−x) and the coordinates of any turning points.
Differentiation
Paper 1
The function fff is defined by f(x)=x+4f(x) = \sqrt{x+4}f(x)=x+4​. State the domain and range of fff.
Functions
Paper 1
How many integers nnn satisfy n2<2n+8n^2 < 2n + 8n2<2n+8?
Logic & Proof
Paper 1
Find the remainder when x4−3x2+2x^4 - 3x^2 + 2x4−3x2+2 is divided by x−1x - 1x−1.
Algebra
Paper 2
Find ddx(x2e−x)\frac{d}{dx}(x^2 e^{-x})dxd​(x2e−x) and the coordinates of any turning points.
Differentiation
Paper 1
The function fff is defined by f(x)=x+4f(x) = \sqrt{x+4}f(x)=x+4​. State the domain and range of fff.
Functions
Paper 1
Solve 2cos⁡2θ−5cos⁡θ+3=02\cos^2\theta - 5\cos\theta + 3 = 02cos2θ−5cosθ+3=0 for 0≤θ<2π0 \le \theta < 2\pi0≤θ<2π.
Trigonometry
Paper 2
Evaluate ∫01(3x2+1) dx\int_0^1 (3x^2 + 1)\,dx∫01​(3x2+1)dx.
Integration
Paper 1
Sketch y=∣2x−3∣y = |2x - 3|y=∣2x−3∣, stating intercepts and the vertex.
Graphs
Paper 2
The points A(1,2)A(1, 2)A(1,2) and B(4,6)B(4, 6)B(4,6) lie in the plane. Find ∣AB⃗∣|\vec{AB}|∣AB∣.
Vectors
Paper 1
Solve 2cos⁡2θ−5cos⁡θ+3=02\cos^2\theta - 5\cos\theta + 3 = 02cos2θ−5cosθ+3=0 for 0≤θ<2π0 \le \theta < 2\pi0≤θ<2π.
Trigonometry
Paper 2
Evaluate ∫01(3x2+1) dx\int_0^1 (3x^2 + 1)\,dx∫01​(3x2+1)dx.
Integration
Paper 1
Sketch y=∣2x−3∣y = |2x - 3|y=∣2x−3∣, stating intercepts and the vertex.
Graphs
Paper 2
The points A(1,2)A(1, 2)A(1,2) and B(4,6)B(4, 6)B(4,6) lie in the plane. Find ∣AB⃗∣|\vec{AB}|∣AB∣.
Vectors
Paper 1
Solve 2cos⁡2θ−5cos⁡θ+3=02\cos^2\theta - 5\cos\theta + 3 = 02cos2θ−5cosθ+3=0 for 0≤θ<2π0 \le \theta < 2\pi0≤θ<2π.
Trigonometry
Paper 2
Evaluate ∫01(3x2+1) dx\int_0^1 (3x^2 + 1)\,dx∫01​(3x2+1)dx.
Integration
Paper 1
Sketch y=∣2x−3∣y = |2x - 3|y=∣2x−3∣, stating intercepts and the vertex.
Graphs
Paper 2
The points A(1,2)A(1, 2)A(1,2) and B(4,6)B(4, 6)B(4,6) lie in the plane. Find ∣AB⃗∣|\vec{AB}|∣AB∣.
Vectors
Paper 2
The sequence (un)(u_n)(un​) satisfies un+1=3un−2u_{n+1} = 3u_n - 2un+1​=3un​−2 with u1=4u_1 = 4u1​=4. Find u5u_5u5​.
Sequences
Paper 1
Find the equation of the circle with centre (2,−1)(2,-1)(2,−1) passing through (5,3)(5,3)(5,3).
Coordinate Geometry
Paper 2
A fair die is rolled twice. Find the probability the product of the scores is even.
Probability
Paper 1
Solve 22x−1=5x2^{2x-1} = 5^x22x−1=5x, giving your answer in exact form.
Exponentials
Paper 2
The sequence (un)(u_n)(un​) satisfies un+1=3un−2u_{n+1} = 3u_n - 2un+1​=3un​−2 with u1=4u_1 = 4u1​=4. Find u5u_5u5​.
Sequences
Paper 1
Find the equation of the circle with centre (2,−1)(2,-1)(2,−1) passing through (5,3)(5,3)(5,3).
Coordinate Geometry
Paper 2
A fair die is rolled twice. Find the probability the product of the scores is even.
Probability
Paper 1
Solve 22x−1=5x2^{2x-1} = 5^x22x−1=5x, giving your answer in exact form.
Exponentials
Paper 2
The sequence (un)(u_n)(un​) satisfies un+1=3un−2u_{n+1} = 3u_n - 2un+1​=3un​−2 with u1=4u_1 = 4u1​=4. Find u5u_5u5​.
Sequences
Paper 1
Find the equation of the circle with centre (2,−1)(2,-1)(2,−1) passing through (5,3)(5,3)(5,3).
Coordinate Geometry
Paper 2
A fair die is rolled twice. Find the probability the product of the scores is even.
Probability
Paper 1
Solve 22x−1=5x2^{2x-1} = 5^x22x−1=5x, giving your answer in exact form.
Exponentials

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