SGSS 4N Prelim 2023 P1

[Turn over Mathematical Formulae Compound interest Total amount = 1 100 n rP+ Mensuration Curved surface area of a cone = πrl Surface area of a sphere = 4πr2 Volume of a cone = 1 3 πr2h Volume of a sphere = 4 3 πr3 Area of triangle ABC = 1 2 ab sin C Arc length = rθ, where θ is in radians Sector area = 1 2 r2θ, where θ is in radians Trigonometry sin sin sin a b c A B C== a2 = b2 + c2 – 2bc cos A Statistics Mean = fx f   Standard deviation = 22fx fx ff  − 

2 SGSS/MathP1/4NA4NT(OOS)/Prelim/2023 Answer all the questions. 1 Solve 4( 5) 3 2xx− = + . Answer x = …………………………… [2] __________________________________________________________________________________ 2 Factorise completely 8 10 12 15ab ay bx xy+ − − . Answer ……………………………….. [2] __________________________________________________________________________________ 3 By writing each number correct to 1 significant figure, estimate the value of 34.5 6.3 8.76 − . Show your working. Answer ……………………………….. [2] __________________________________________________________________________________

3 SGSS/MathP1/4NA4NT(OOS)/Prelim/2023 [Turn over 4 On the grid, draw an enlargement of this quadrilateral using the scale factor 3 2 . [2] __________________________________________________________________________________ 5 (a) Write 34 2 55 5−  as a single power of 5. Answer ……………………………….. [1] (b) Given that 1 393 n= , find n. Answer n = …………………………… [1] __________________________________________________________________________________

4 SGSS/MathP1/4NA4NT(OOS)/Prelim/2023 6 (a) Simplify 10 3(7 4 )xx−− . Answer ……………………………….. [1] (b) Make m the subject of the formula 2h k m=− . Answer m = …………………………… [2] __________________________________________________________________________________ 7 (a) Find p, giving a reason for your answer. p = ………….  because ………………………………………………………………... [2] (b) Determine if triangle ABC is an equilateral triangle. Answer ………………………………………………………………………………….. [2] …………………………………………………………………………………………… [2] …………………………………………………………………………………………… [2] __________________________________________________________________________________ A B C100 ° 60 ° p

5 SGSS/MathP1/4NA4NT(OOS)/Prelim/2023 [Turn over 8 The stem-and-leaf diagram shows the age, in years, of 50 performers in the National Day parade. 0 8 9 1 0 2 2 5 6 7 7 7 9 2 3 5 5 6 6 6 7 8 8 8 8 3 1 1 2 4 4 7 8 9 9 4 2 3 3 4 5 6 7 8 5 0 0 3 3 5 5 9 6 1 4 6 7 Key 1 | 2 represents 12 years (a) Find the modal age. Answer …………………………. years [1] (b) Find the median age. Answer …………………………. years [1] (c) One of the performers is selected at random. Find the probability that the performer is younger than 30 years old. Give your answer as a fraction in its lowest terms. Answer ……………………………….. [1] __________________________________________________________________________________

6 SGSS/MathP1/4NA4NT(OOS)/Prelim/2023 9 Solve these simultaneous equations. 4 13 7 33 xy xy −= += Show your working. Answer x = …………………………… [2] Answer y = …………………………… [3] __________________________________________________________________________________

7 SGSS/MathP1/4NA4NT(OOS)/Prelim/2023 [Turn over 10 y is inversely proportional to the square of x. (a) Given that y = 45 when x = 3, find a formula for y in terms of x. Answer ……………………………….. [2] (b) Find y when x = 6. Answer y = …………………………… [1] __________________________________________________________________________________ 11 The line l1 has equation 43yx=− . (a) Show that the point (2, 5) lies on the line l1. Answer [1] (b) Find the equation of the line l2 with the same gradient as line l1 and passing through the point (−1, 5). Answer ……………………………….. [2] __________________________________________________________________________________

8 SGSS/MathP1/4NA4NT(OOS)/Prelim/2023 12 P and Q are points on a circle with radius 15 cm and centre O. Reflex angle POQ = 200. Calculate the area of the shaded segment. Answer …………………………... cm2 [3] __________________________________________________________________________________ 13 Solve 42 5x x= − , giving your answers correct to 3 significant figures. Show your working. Answer x = ………… or x = ………… [4] __________________________________________________________________________________ P QO 200 ° 15 cm

9 SGSS/MathP1/4NA4NT(OOS)/Prelim/2023 [Turn over 14 (a) Express 2 10 9xx+− in the form 2()x a b++ . Answer ……………………………….. [2] (b) Hence solve 2 10 9 0xx+ − = . Give your answers correct to 2 decimal places. Answer x = ………… or x = ………… [2] __________________________________________________________________________________ 15 The diagram shows how 3 regular polygons, A, B and C, are joined together. Shape A has 3 sides and shape B has 10 sides. How many sides does shape C have? Show your working. Answer …………………………. sides [4] __________________________________________________________________________________ A B C

10 SGSS/MathP1/4NA4NT(OOS)/Prelim/2023 16 A map is drawn to a scale of 1 : 50 000. (a) This scale can be written as 1 cm to n km. Find n. Answer n = …………………………… [1] (b) Island A is 10 km away from Island B. Find the distance, in cm, between these two islands on the map. Answer …………………………… cm [1] (c) Island A has an area of 20 cm2 on the map. Find the actual area, in km2, of Island A. Answer …………………………... km2 [2] __________________________________________________________________________________