2023 VS Prelim P1

This paper consists of 18 printed pages, including the cover page. [Turn over Class Register Number Name 4052/01 23/S4PR/EM/1 MATHEMATICS PAPER 1 Wednesday 23 August 2023 2 hours 15 minutes VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHO OL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHO OL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHO OL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL PRELIMINARY EXAMINATION SECONDARY FOUR Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, class and register number 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. The number of marks is given in brackets [ ] at the end of each question or part question If working is needed for any question, it must be shown with the answer. The omission of essential working will result in loss of marks. The total number of marks for this paper is 90. 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. Gives answers in degrees to one decimal place. For π, use either your calculator value or 3.142.

2 VICTORIA SCHOOL 23/S4PR/EM/1 Mathematical Formulae Compound interest Total amount = 1 100 nrP+ Mensuration Curved surface area of a cone = πrl Surface area of a sphere = 24πr Volume of a cone = 21 π3 rh Volume of a sphere = 34 π3 r Area of triangle ABC = 1 sin2 ab C Arc length = r , where  is in radians Sector area = 21 2 r  , where  is in radians Trigonometry sin sin sin a b c A B C== 2 2 2 2 cosa b c bc A= + − Statistics Mean = fx f   Standard deviation = 22fx fx ff  −  

3 VICTORIA SCHOOL 23/S4PR/EM/1 1 Solve 347 0. 5 x−−= Answer x= ................................................ [2] 2 (a) Express 24 and 2160 as a product of their prime factors. Leave your answers in index notation. Answer 24= ..................................................... 2160= ............................................... [2] (b) Find the smallest integer x such that the lowest common multiple of 24x and 2160 is 4320. Answer x= ................................................ [1]

4 VICTORIA SCHOOL 23/S4PR/EM/1 3 (a) Calculate 3 3 71.5 8150 . 6.01 6 −− + Write your answer correct to 4 significant figures. Answer ............................................................... [1] (b) Write your answer to part (a) in standard form. Answer ............................................................... [1] 4 Expand and simplify ( )( ) ( ) 2 3 2 3 5 .x y x y x y+ − − − Answer ................................................................. [2] 5 y is inversely proportional to 2.x It is given that 7y = for a particular value of .x Find the value of y when this value of x is increased by 250%. Answer ................................................................. [2]

5 VICTORIA SCHOOL 23/S4PR/EM/1 6 (a) Express 212 4y x x= + − in the form of ( ) 2 .y p x q= − − Answer ................................................................. [2] (b) Sketch the graph of 212 4 .y x x= + − Indicate clearly the coordinates of the points where the graph crosses the axes (where applicable) and the maximum point on the curve. Answer [3] (c) Explain why the equation 212 4 16.5xx+ − = does not have any solutions. [1] y x O

6 VICTORIA SCHOOL 23/S4PR/EM/1 7 The diagram shows the positions of three points A, B and C. (a) Construct the perpendicular bisector of AB. [1] (b) Construct the bisector of angle .ABC [1] (c) Point P is equidistant from A and B and equidistant from AB and BC. Mark the point P on the diagram and measure the length BP. Answer BP= ..................................................cm [1] (d) Construct the parallelogram ABCD by completing the diagram. [1] 8 At an event, 1 3 of the participants are children. 37.5% of the remaining participants are adults wearing spectacles and the remaining 50 participants are adults not wearing spectacles. Find the total number of participants at the event. Answer ............................................................... [2] A B C

7 VICTORIA SCHOOL 23/S4PR/EM/1 9 In the diagram, A, B, C and D are points on a circle, centre O. EAF is a tangent to the circle at A. DOGF is a straight line. Angle 20 and angle 42 .OAD OAB=  =  (a) Find angle .ABG Give reasons for each step of your working. Answer Angle ABG= .......................................  [2] (b) Show that angle 118 .BCD= Give reasons for each step of your working. [2]

8 VICTORIA SCHOOL 23/S4PR/EM/1 10 Two bags A and B contain some blue and yellow marbles. The ratio of the number of blue marbles in bag A to bag B is 5 : 3. The ratio of the number of yellow marbles in bag A to bag B is 3 : 7. If both bags contain the same number of marbles, find the ratio of the number of blue marbles in bag A to the number of yellow marbles in bag A. Answer ............................................................... [3] 11 A group of 80 students took part in a challenge. The table below shows the distribution of the time taken to complete the challenge. Time (t minutes) 30 40t 40 50t 50 60t 60 70t 70 80t Number of students 12 32 23 9 4 (a) Calculate the estimate of the mean time taken. Answer ........................................................ mins [1] (b) Calculate the estimate of the standard deviation of the time taken.