ACSI 2015 Y3 Core Mathematics Paper 1

ACS(Independent)/Y3IPCoreMathsP1/2015/Final Year 1 Anglo - Chinese School (Independent) FINAL EXAMINATIONS 2015 YEAR 3 INTEGRATED PROGRAMME CORE MATHEMATICS PAPER 1 FRIDAY 2nd OCTOBER 2015 1 h 30 min Additional Material Graph Paper (1 sheet) INSTRUCTIONS TO CANDIDATES  Write your index number in the boxes above.  Do not open this examination paper until instructed to do so.  You are not permitted access to any calculator for this paper.  Answer all questions in the spaces provided.  Unless otherwise stated in the question, all numeri cal answers must be given exactly or correct to three significant figures.  The maximum mark for this paper is 80. For Examiner’s Use _______________________________________________________________ This paper consists of 14 printed pages. [Turn over Candidate Index Number

ACS(Independent)/Y3IPCoreMathsP1/2015/Final Year 2 Full marks are not necessarily awarded for a correct answer with no working. Answers must be supported by working and/or explanations. Where an answer is incorrect, some marks may be given for a correct method, provided this is shown by written working. You are therefore advised to show all working. Answer all the questions in the spaces provided. 1 [Maximum mark: 7] (a) Simplify 5 104532 ba . [2 marks] (b) Simplify 3 2 14 4 2             pq p p q , leaving your answer in positive indices. [3 marks] (c) Express abba 42 3 2 5  as a single fraction in its simplest form. [2 marks] ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… …………………………………………………………………………………………

ACS(Independent)/Y3IPCoreMathsP1/2015/Final Year 3 2 [Maximum mark: 4] The height, h metres, of the water sprayed from a fountain is given as 742  xxh , where x metre is the horizontal distance of the water from the fountain. Find the greatest height of the water sprayed and the horizontal distance from the fountain when this occurs. ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… …………………………………………………………………………………………

ACS(Independent)/Y3IPCoreMathsP1/2015/Final Year 4 3 [Maximum mark:6] In the diagram below, ABD is a straight line. oCAB 90 , 20CD cm, 7BD cm and the area of 42BCD cm2. (a) Express CDBsin as a fraction in its lowest terms. [2 marks] (b) Find the length of AB. [2 marks] (c) Express CBDcos as a fraction in its lowest terms. [2 marks] ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… A B D C 20 cm 7 cm

ACS(Independent)/Y3IPCoreMathsP1/2015/Final Year 5 4 [Maximum mark: 10] (a) Find the value of x when x9273 1 2 12     . [3 marks] (b) Find the value of x given that x27 833 1012  . [3 marks] (c) Solve the equation 01222 222  xx , leaving your answers in surds. [4 marks] ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… …………………………………………………………………………………………

ACS(Independent)/Y3IPCoreMathsP1/2015/Final Year 6 5 [Maximum mark: 5] (a) Factorize completely srsrp  )(3 . [2 marks] (b) Solve xx 382  and express your answers in the form 10ba , where a and b are constants. [3 marks] ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… …………………………………………………………………………………………

ACS(Independent)/Y3IPCoreMathsP1/2015/Final Year 7 6 [Maximum mark: 7] (a) Evaluate 9ln 2ln2108ln4log3log 32  . [3 marks] (b) Solve the equation x x 327 log13log  . [4 marks] ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… …………………………………………………………………………………………

ACS(Independent)/Y3IPCoreMathsP1/2015/Final Year 8 7 [Maximum mark: 11] The coordinates of the points R and S are (−4, 1) and (2, −7) respectively. (i) Find the length of RS. [2 marks] (ii) Find the equation of the line, l, passing through R and perpendicular to RS. [4 marks] (iii) Given that 1y is the line of symmetry of QRS , state the coordinates of Q. [2 marks] (iv) Hence, find the perpendicular distance from Q to SR produced. [3 marks] ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… …………………………………………………………………