YCSS 2024 4NA Prelim P1 - Qns

YUAN CHING SECONDARY SCHOOL Secondary Four Normal (Academic) Course Preliminary Examination 2024 CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS Paper 1 Candidates answer on the Question Paper. 4045/01 5 August 2024 2 hours READ THESE INSTRUCTIONS FIRST Write your name, class and index 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 staple, paper clips, highlighters, glue or correction fluid. Answer all 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. Omission of essential working will result in loss of marks. The total number of marks for this paper is 70. 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 π, use either your calculator value or 3.142. MARKS Total / 70 This paper consists of 20 printed pages. [Turn Over]

2 Mathematical Formulae Compound Interest Total amount = n rP       1001 Mensuration Curved surface area of a cone = lr 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 a triangle ABC = Cabsin2 1 Arc length = r , where  is in radians Sector area = 2 2 1 r , where  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 Answer all the questions. 1 2 3224.4 2.1 277 Write these numbers in order of size, starting with the smallest. Answer …………… , …………… , …………… , …………… , …………… [2] smallest 2 (a) Represent 13 x   on the number line below. Answer [1] (b) Solve the inequality 37x . Answer ……………………… [1] (c) State the smallest integer that satisfy 37x . Answer ……………………… [1]

4 3 2940 expressed as a product of its prime factors is 222 3 5 7   . (a) Express 504 as a product of its prime factors. Answer ……………………… [1] (b) Find the lowest common multiple of 2940 and 504. Answer ……………………… [1] (c) Find the smallest integer k such that 2940k is a perfect square. Answer ……………………… [1] 4 Which of these ratio(s) are equivalent to the ratio :ab ? 22 11: : 4 : 4 : 2 : 2baa b a b a b a b ba  Answer ………………………………………………………………… [2]

5 5 Gracia has a map drawn to a scale 1: 25 000 . (a) Rewrite the scale in the form 1 cm to x km. Answer ……………cm to ………….…km [1] (b) A road on the map is 13 cm long. Find the actual length of the road in kilometres. Answer …………………… km [1] (c) A plot of land has an area of 120 km2. Find the area of the plot of land on the map in square centimetres. Answer …………………… cm2 [2]

6 6   22 62x x x a b     (a) Find the value of a and b. Answer a = …………………, b = ………………… [2] (b) Hence, solve 2 6 2 0xx   . Give your answers correct to 2 decimal places. Answer x = …………………, x = ………………… [2]

7 7 238v w u (a) Find v when 4w and 2u . Answer v ……………………… [1] (b) Rearrange the formula to make u the subject. Answer …………………………… [2] 8 Solve 3 123 xx  . Answer x ……………………. [2]

8 9 P is the point ( 2, 1) and Q is the point (5,6) . (a) Find the length of PQ. Answer ………………… units [1] (b) R is the point (8, )k . Given that the gradient of QR is 3 , find the value of k. Answer k …………………… [2] x 2 4 6 8 0 2 4 6 -2 x x P Q y

9 (c) Find the equation of line QR. Answer ……………………… [2] 10 In the diagram below, ABCD is similar to WXYZ. AB is parallel to CD. (a) Find the value of r. Answer r = ………………  [1] (b) Find the value of s. Answer s = ………………  [1] (c) Find the length of WZ. Answer ………………… cm [2] A B C D 5 cm 4 cm 2 cm W X Y Z s r

10 11 ABC is a triangle with AB = 9 cm, angle 45BAC and angle 70ABC . (a) Construct triangle ABC. AB has been drawn for you. [2] (b) The perpendicular bisector of AB and the angle bisector of ACB meet at point T. Label point T. [2] A B