Advanced Level Mathematics Revision: Pure Mathematics

Mastering Advanced Level Pure Mathematics requires precision in algebraic manipulation, calculus application, and logical analysis. Test your mathematical problem-solving skills with these multiple-choice questions from image_354461.jpg.

1. Algebra, Functions & Logic

Question 1: Partial Fractions

If M / (x – 1) + N / (x + 2) is identically equal to (2x – 1) / ((x – 1)(x + 2)), then:

• A) M = 1/3, N = -5/3

• B) M = 1/3, N = 5/3

• C) M = -3, N = 3

• D) M = 3, N = -3

Question 2: Modular Arithmetic & Equivalence Classes

In the set A = {0, 1, 2, 3, 4, 5, 6, 7}, a relation R is defined by x R y <=> x and y have the same remainder when divided by 3. The equivalence class of 3, i.e. [3], is:

• A) {3, 6}

• B) {1, 4, 7}

• C) {2, 5}

• D) {0, 3, 6}

Question 3: Mathematical Logic

If p and q are two statements, then the contrapositive of p => q is:

• A) q => p

• B) ~q => p

• C) ~p => ~q

• D) ~q => ~p

2. Calculus & Coordinate Geometry

Question 4: Differential Equations

The solution of the differential equation y * (dy/dx) = 3x, given that y = 1 when x = 1, is:

• A) y^2 = 3x^2 – 2

• B) y^2 = 3x^2 + 1

• C) y^2 = 3x^2 – 1

• D) y^2 = 3x^2 + 2

Question 5: Circle Equations

The line segment PQ, where P is the point (2, 4) and Q is the point (8, 10), is the diameter of a circle. The equation of the circle is:

• A) (x – 2)(x – 8) + (y – 4)(y – 10) = 0

• B) (x + 2)(x + 8) – (y + 4)(y + 10) = 0

• C) (x – 2)(x – 4) + (y – 8)(y – 10) = 0

• D) (x + 2)(x + 4) – (y + 8)(y + 10) = 0

Question 6: Integral Calculus (Volume of Revolution)

The volume generated when the area of the finite region enclosed by the x-axis and the curve y = 1 – x^2 is rotated completely about the x-axis is:

• A) pi * integral from 0 to 1 of (1 – x^2)^2 dx

• B) 2 * pi * integral from -1 to 1 of (1 – x^2)^2 dx

• C) pi * integral from -1 to 1 of (1 – x^2)^2 dx

• D) 2 * pi * integral from -1 to 1 of (1 – x^2) dx

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