2023 Springfield 3G3 Mathematics (4052) (P1-QP)

[Turn Over SPRINGFIELD SECONDARY SCHOOL End-Of-Year Examination 2023 Sec 3 Express STUDENT NAME CLASS REGISTER NUMBER MATHEMATICS 4052/01 Paper 1 5 October 2023 2 hours 15 minutes Candidates answer on the question paper Additional Materials: NIL READ THESE INSTRUCTIONS FIRST Write your class, index number 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, graphs or rough working. Do not use staples, paper clips, glue or correction fluid. Answer all the questions. If working is needed for any question it must be shown with the answer. Omission of essential working will result in loss of marks. The use of an approved scientific calculator is expected, where appropriate. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For  , use either your calculator value or 3.142, unless the question requires the answer in terms of  . 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 90. For Examiner’s Use Total /90 Do not turn over this question paper until you are told to do so. ______________________________________________________________________________________________________ This question paper consists of 21 printed pages.

2 Mathematical Formulae Compound Interest Total amount = n rP      + 1001 Mensuration Curved surface area of a cone = rl Surface area of a sphere = 4 2r Volume of a cone = hr 2 3 1 Volume of a sphere = 3 3 4 r Area of triangle ABC = Cabsin2 1 Arc length = rθ, where θ is in radians Sector area = 2 2 1 r , where θ is in radians Trigonometry C c B b A a sinsinsin == Abccba cos2222 −+= Statistics Mean = f fx   Standard deviation = 22        −  f fx f fx

3 [Turn Over Answer all the questions 1 (a) By prime factorization, explain why 484 is a perfect square. Answer ……………………………………………………………………………………… ……………………………………………………………………………………… ……………………………………………………………………………………… ……………………………………………………………………………………… [2] (b) Find the highest common factor (HCF) of 66 and 150. Answer ................................... [2] 2 The expression 2 62xx−− can be written in the form ( ) 2 3xb−+ . (a) Find the value of b. Answer b = ................................... [2] (b) Explain whether the y value at x = 3 is a maximum or minimum value. Answer [1] ……………………………………………………………………………………….. ……………………………………………………………………………………….. ……………………………………………………………………………………….. ………………………………………………………………………………………..

4 3 Solve 23 216xx −=+− Answer x = ................................... [4] 4 Find the equation of the straight line passing through (1 , -3) and is parallel to the line 3 5 15yx+= . Answer ................................... [3]

5 [Turn Over 5 (a) Simplify 3 2 3a −   , leaving your answer in positive index notation. Answer ................................... [2] (b) Simplify 2 32 125 10xy xy−− Answer ................................... [2]

6 6 In the diagram, SW and RQ intersect at T and QSP, WRP, QTR and WTS are straight lines. Given that 90PSW PRQ = =  and SQ RW= . (a) Prove that triangle STQ is congruent to triangle RTW. Answer [3] (b) Find RTW if 62RPS =  Answer ...................................o [2] S Q W P R T

7 [Turn Over 7 In the circle, the ratio of the arc length of the minor arc AB to the circumference of the whole circle is 1:6. (a) Calculate the acute angle AOB in radians. Answer ................................... rad [2] (b) Given that the area of the minor sector AOB is 18 3 cm2. Calculate the radius of the circle. Answer ...................................cm [2] O A B C

8 (c) Find the perimeter of the minor sector OBA. Answer ...................................cm [2] 8 (a) Expand and simplify 5 3(2 7) 9xx− − + . Answer ................................... [2]

9 [Turn Over (b) Simplify 37 2 1 1xx −−+ . Answer ................................... [3] 9 In the diagram, XYZ is a straight line, XY = 4 cm, YZ = 5 cm, ZW = 12 cm and WY = 13 cm. (a) Explain why angle WZY is a right angle, Answer …..……………………………………………………………………………………. …..……………………………………………………………………………………. …..……………………………………………………………………………………. …..……………………………………………………………………………………. [2] W X Z Y 12 cm 13 cm 5 cm 4 cm

10 (b) Find the length of WX, Answer .........................................cm [2] (c) Find the value of cos XYW . Answer ......................................... [1] (d) the area of triangle WXY. Answer ...................................cm2 [1]