June 2006 MS – FP2 OCR.pdf

Mark Scheme 4726, June 2006, contains solutions and grading criteria for various math problems.

1. The first problem involves finding the expansion of sin(x) and using it to derive an expression. Grading criteria include correct expansion (B1), ignoring extra terms (M1), and using the product rule (M1).

2. The second problem requires solving a differential equation involving sec(y) and dy/dx. Grading criteria include getting sec(y) dy = 1 (M1), using the chain or quotient rule (M1), and arriving at the correct answer (A1).

3. The third problem involves finding the solution to a quadratic inequality. Grading criteria include stating y = 0 (B1), writing the inequality as a quadratic in x (M1), and justifying the answer (A1).

4. The fourth problem requires solving a trigonometric equation involving cosh(x). Grading criteria include correct definition of cosh(x) (B1), substituting and simplifying (M1), and solving the quadratic equation (A1).

5. The fifth problem involves deriving expressions for dx and sin(x) in terms of t. Grading criteria include getting (t + ½)² + ¾ (B1), deriving dx = 2 dt / (1 + t²) (B1), and replacing x and dx with expressions involving t (M1).

6. The sixth problem requires summing areas of rectangles using a geometric progression. Grading criteria include attempting to sum areas (M1), using a geometric progression (M1), and simplifying to the correct answer (A1).

7. The seventh problem involves solving a trigonometric equation and finding the value of r. Grading criteria include attempting to solve r = 0 (M1), getting θ = -1/3 π (A1), and finding the correct value of r (B1).

8. The eighth problem requires differentiating a function using the product or quotient rule and solving for dy/dx = 0. Grading criteria include attempting to differentiate (M1), solving dy/dx = 0 (M1), and rewriting the answer in the correct form (A1).