Tiêu đề A-Level Maths Paper 1 Prediction Paper 2024 SOLUTIONS.docx.pdf ✅

Cambridge International AS & A Level INSTRUCTIONS Answer all questions. Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs. Write your name, centre number and candidate number in the boxes at the top of the page. Write your answer to each question in the space provided. Do not use an erasable pen or correction fluid. Do not write on any bar codes. If additional space is needed, you should use the lined page at the end of this booklet; the question number or numbers must be clearly shown. You should use a calculator where appropriate. You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. INFORMATION The total mark for this paper is 75. The number of marks for each question or part question is shown in brackets [ ]. This document has 19 pages. [Turn over]
2 1 (a) Express x in the form where p and q are constants. [2] 2 − 6x + 11 (x + p) 2 + q ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ (b) Hence find the exact solutions of the equation x 7 [2] 2 − 6x + 11 = ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ 2 (a) Find the first three terms in the expansion, in ascending powers of x, of (3 + 2x) . [2] 4
3 ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ (b) Find the first three terms in the expansion, in ascending powers of x, of (2 − x) . [2] 5 ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ (c) Hence find the coefficient of x in the expansion of [2] 2 (3 + 2x) 4 (2 − x) 5 ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ 3 A circle has equation (x − 2) . A line with equation y = 2x − 3 intersects the circle at 2 + (y − 1) 2 = 25 points A and B. (Turn over)
4 (a) Find the exact coordinates of the two points of intersection. [4] ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ (b) Find an equation of a circle with diameter AB. [3] ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ 4 (a) Prove the identity (cos x − tan x) [3] 2 + (sin x + 1) 2 ≡ 2 + x