RGS 2021 Y4 MATH2 EYA

This Question Paper consists of 23 printed pages including the cover page. [Turn Over ` Raffles Girls’ School (SECONDARY) Name: Class: 4 / Register No: MATHEMATICS 2 YEAR FOUR End-of-Year Assessment Monday 4 October 2021 2 hours 30 minutes For examiners’ use Question Marks Obtained 1 / 5 2 / 4 3 / 6 4 / 10 5 / 4 6 / 7 7 / 7 8 / 7 9 / 7 10 / 8 11 / 12 12 / 11 13 / 12 P, A, U Total Marks 100 Parent’s / guardian’s Name: Signature: Date: Established in 1879 INSTRUCTIONS TO CANDIDATES Write your name, class and register number on all the work you hand in. Write in dark blue or black pen. You may use a 2B pencil for any diagram or graph. Do not use paper clips, glue or correction tape. Answer all the questions in the space provided. 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 scientific calculator is expected, where appropriate. Omission of essential working will result in a loss of marks. You are reminded of the need for clear presentation in your answers. INFORMATION FOR CANDIDATES 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 100 and the weighting is 40%.

Raffles Girls’ School (Secondary) 2021 Y4 Math 2 End-of-Year Assessment 2 MATHEMATICAL FORMULAE 1. ALGEBRA Quadratic Equation For the equation 2 0ax bx c+ += , Binomial Expansion where n is a positive integer and 2. TRIGONOMETRY Identities ( ) ( ) ( ) 22 22 22 22 2 2 2 sin cos 1 sec 1 tan cosec 1 cot sin sin cos cos sin cos cos cos sin sin tan tantan 1 tan tan sin 2 2sin cos cos 2 cos sin 2cos 1 1 2sin 2 tantan 2 1 tan AA AA AA AB A B A B AB A B A B ABAB AB A AA A AA A A AA A += = + = + ±= ± ±= ±±= = = − = −=− = −   Formulae for ∆ABC 2 22 2 cosa b c bc A=+− 1 sin2 bc A∆ =

Raffles Girls’ School (Secondary) 2021 Y4 Math 2 End-of-Year Assessment 3 [Turn Over 1 Differentiate each of the following with respect to x, leaving your answers in the simplest form. (a) [2] (b) [3]

Raffles Girls’ School (Secondary) 2021 Y4 Math 2 End-of-Year Assessment 4 2 The variables x and y are related by an equation of the form , where a and b are constants. The diagram shows part of a straight line graph obtained by plotting against . It is given that the line passes through the points and . Find the value of a and of b. [4]

Raffles Girls’ School (Secondary) 2021 Y4 Math 2 End-of-Year Assessment 5 [Turn Over 3 (i) By finding the general term in the binomial expansion , where p is a constant, explain if every term is dependent on x. [3] (ii) Given that the coefficient of in the expansion of is 1701, find the value(s) of the constant p. [3]

Raffles Girls’ School (Secondary) 2021 Y4 Math 2 End-of-Year Assessment 6 4 (i) Express 2 2 3 45 (2 )( 3) xx xx ++ −+ in partial fractions. [5] (ii) Hence find the equation of the curve with gradient function 2 2 d 3 45 d (2 )( 3) y xx x xx ++= −+ , given that the curve passes through the point (1, −2). [5]

Raffles Girls’ School (Secondary) 2021 Y4 Math 2 End-of-Year Assessment 7 [Turn Over THIS PAGE IS INTENTIONALLY LEFT BLANK FOR QUESTION 4.

Raffles Girls’ School (Secondary) 2021 Y4 Math 2 End-of-Year Assessment 8 5 Given that , find (i) the range of f, and [2] (ii) the value of x for which f is minimum. [2]

Raffles Girls’ School (Secondary) 2021 Y4 Math 2 End-of-Year Assessment 9 [Turn Over 6 (i) Prove that . [3] (ii) Hence solve the equation for . [4]

Raffles Girls’ School (Secondary) 2021 Y4 Math 2 End-of-Year Assessment 10 7 Given that A and B are acute angles such that and . Without finding the angles A and B, (i) explain why the angle lies in the fourth quadrant [1] (ii) find the exact value of (a) . [1] (b) . [3] (c) . [2]