Cambridge A Level Mathematics Exams Questions with Correct Answers

3, 4, 0, 0 Correct Answer State the degree of each of the following polynomials. (write your answer like "ans1, ans2, ans3") a) x³ - 3x² + 2x - 7 b) 8 + 5x - 3x² + 7x + 6x⁴ c) 3 d) x⁰ 3x + 1 Correct Answer One factor of 3x² -5x -2 is x - 2. Find the other factor. A = 4, B = 10, C = 20, R = 43 Correct Answer If 4x³ + 2x² + 3 ≡ (x - 2)(Ax² + Bx + C) + R, find A, B, C and R A = 3, B = 1, C = -1, D = 2, R = 0 Correct Answer Find the values of A, B, C, D and R. 6x⁴ + 5x³ - x² + 3x + 2 ≡ (2x + 1)(Ax³ + Bx² + Cx + D) + R x³ - x² + x, R = 2 Correct Answer Find the quotient and remainder when x⁴ + x +2 is divided by x + 1 using equating coefficients x³ - x² + x, R = 2 Correct Answer Find the quotient and remainder when x⁴ + x +2 is divided by x + 1 using long division When a polynomial p(x) is divided by x - t, let the quotient be q(x) and the remainder be R. Then p(x) = (x - t)q(x) + R Correct Answer What is the remainder theorem? (x + 3 = 0) (x = -3, sub x into the equation) -14 Correct Answer Find the remainder when x³ - 3x + 4 is divided by (x + 3) using the remainder theorem. When a polynomial p(x) is divided by sx - t, the remainder is the constant p(t/s) Correct Answer What is the extended remainder theorem? (the useful one) (x³ + 2x² - px + 1 = 5) (x - 1 = 0, x = 1) p = -1 Correct Answer When x³ + 2x² - px + 1 is divided by x - 1 the remainder is 5. Find the value of p (Need help) Correct Answer Find the quotient and the remainder when x⁴ - 2x³ -7x² + 7x + 5 is divided by x² + 2x -1