2024 4NA Prelim Peirce Secondary P1

ClassRegister No. Candidate Name PEIRCE SECONDARY SCHOOL PRELIMINARY EXAMINATION 2024 SECONDARY 4 NORMAL ACADEMIC MATHEMATICS 4045/01 Paper 1 31 July 2024 2 hours Additional Materials: Plain Paper (for rough work) INSTRUCTIONS TO CANDIDATES Candidates answer on the Question Paper. 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 pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all 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. Forπ, use either your calculator value or 3.142, unless the question requires the answer in terms of π. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 70. For Examiner’s Use PARENT’S SIGNATURE Total This paper consists of 18 printed pages and 0 blank page. Setter: Mr Goh [TURN OVER 2 Mathematical Formulae Compound interest

67 58 41 32 Total amount = (1)100nrP+ Mensuration Curved Surface area of a cone = prl Surface area of a sphere = 24rπV olume of a cone = 213rhπV olume of a sphere = 343rπArea of triangle ABC = 1sin2abCArc length = rθ, where θ is in radians Sector area = 212rθ, where θ is in radians Trigonometry sinsinsinabcABC== 2222cosabcbcA=+− Statistics Mean = fxf∑∑Standard deviation = 22fxfxff⎛⎞∑∑−⎜⎟∑∑⎝⎠ Answer all the questions. 1 The spinner in the diagram has an equal chance of landing on each of the numbers 1, 2, 3, 4, 5, 6, 7 and 8. Find the probability that the spinner lands on (a) a prime number, A D C B21 cm 9 cm L N M K3 cm y xO B A 8 – 6 0 1 2 3 Number of Pets Q (4, k)

Answer ……………………… ….. [1] (b) a number more than 3. Answer ……………………… ….. [1] 2 Find the obtuse angles A and B such that (a) sin A = 0.65, Answer ………………… ….. [1] (b) cos B = 0.2−. Answer ………………… ….. rad [1] 3 By writing each value correct to 1 significant figure, estimate the value of 2.2419.89.83×without the use of calculator. Show all workings clearly. Answer…..…...…………...…………....[2]

4 Arrange the following numbers in descending order. 9.2•32.13π9.22 Answer…..…...………………………….. ……...…………..........................................[2] 5 Trapezium NMLK is a reduction of trapezium ABCD. (a) Find the length of NM. Answer …………………………...cm [ 1]

(b) Write down the scale factor for the reduction of trapezium ABCD to trapezium NMLK. Answer ……………………………… [1] 6 Expand and simplify (24)(5)yy+−. Answer ……………………………………………………… [2] 7 Solve the equation 322915pp++=−. Answer ……………………………………………………… [2] 8 The first 3 terms of a sequence are 58, 51, 44. (a) Find the next 2 terms.

Answer…..…...…………...…………..........................................[1] (b) Find the nth term of the sequence. Answer…..…...…………...…………...............................[1] (c) Determine if 4− is in the sequence.Show all workings clearly. Answer [2] 9 (a) Solve the inequality 10218y−≤. Answer…..…...…………...…………...................................................................................[2] (b) Find the smallest integer that satisfy 10218y−≤. Answer…..…...…………...………….......................................[1] 10 Make g the subject of the formula 2tgh=−.

Answer…..…...…………...………….......................................[3] 11 2617xx+− can be written as 2()xab++, where a and b are constants. (a) Find a and b. Answera = .…...…………., b = ..………….........[2] (b) Hence, solve the equation 26170xx+−=, leaving your answers to 3 decimal places.

Answer……………………………………………………………………. [2] 12 The diagram below shows the graph of (4)yxx=−. The graph passes through the x-axis at A(0, 0) and B(k, 0). (a) State the value of k. Answer ..................................... [1] (b) Find the equation of the line of symmetry. Answer ..................................... [1] (c) Find the coordinates of the minimum point of the graph.

12 cm QP 7 cm S R QP Answer ..................................... [1] 13 The following shows the sketch of a parallelogram PQRS. (a) Complete the construction of the parallelogram. PQ has already been drawn for you. [2] (c) Construct the perpendicular bisector of SR. [1] (d) Construct the angle bisector of angle

PQR. [1] (e) The perpendicular bisector of SR intersects the angle bisector of PQR at point Y. Measure the length QY. Answer ……………………… cm [1] 14 y is inversely proportional to x2 and y = 0.5 when x = 3. (a) Express y in terms of x. Answer ……………………………………. [ 2] (b) Find the value of y when x = 2−. Answer ……………………………………. [1] (c) Find the value(s) of x when y = 8.