2024 ACJC H1 LCP MidYear QP

ANGLO-CHINESE JUNIOR COLLEGE JC2 MID-YEAR LEARNING CHECKPOINT Higher 1 CANDIDATE NAME TUTORIAL/ INDEX FORM CLASS NUMBER MATHEMATICS 8865/01 Paper 1 24 June 2024 2 hours Candidates answer on the Question Paper. Additional Materials: List of Formulae (MF26) READ THESE INSTRUCTIONS FIRST Write your index number, class and name on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all the questions. Write your answers in the spaces provided in the question paper. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. The use of an approved graphing calculator is expected, where appropriate. Unsupported answers from a graphing calculator are allowed unless a question specifically states otherwise. Where unsupported answers from a graphing calculator are not allowed in a question, you are required to present the mathematical steps using mathematical notations and not calculator commands. You are reminded of the need for clear presentation in your answers. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 65. _________________________________________________________________________________ This document consists of 16 printed pages. [Turn over Question Marks 1 /6 2 /6 3 /10 4 /4 5 /7 6 /9 7 /11 8 /12 /65

2 ANGLO-CHINESE JUNIOR COLLEGE 2024 H1 MATHEMATICS 8865/01 Section A: Pure Mathematics [22 marks] 1 (a) Differentiate ( ) 2ln 5 x+ with respect to x. [1] (b) Differentiate 27xx x − with respect to x. [2] (c) Find 2 1 d .4 xxx  + [3] 2 A curve C has equation 324e e xxy −−=+ . (a) Sketch C, stating the exact value of the y-coordinate of its point of intersection with the -axisy and the equation of the asymptote. [2] (b) Without using a calculator, find the equation of the tangent to C at the point where x = 3, giving your answer in the form y mx c=+ , where m and c are exact constants. [4] 3 A manufacturing company makes doors. The manufacturer makes x doors per order, where x is a positive integer, to prevent overstocking of inventory. He estimates that the total production cost for each order consists of the following components: • raw material, • wages for the workers, • fixed cost and maintenance cost. The manufacturing process per order requires 7 workers. The cost of raw material for every 5 doors manufactured is $1200, the wages for each worker is $1200 and the total fixed cost and maintenance cost is 2 1875000$ x . (a) Show that the estimated total cost for one order, $T, is given by 2 1875000240 8400Tx x= + + . [1] (