SPS EM 2026 4G3 P1 Final

NAME FORM CLASS ACAD CLASS ST. PATRICK’S SCHOOL PRELIMINARY EXAMINATION 2026 SUBJECT : Mathematics DATE : 17 August 2026 (4052/01) LEVEL : Secondary 4EXP/5NA DURATION : 2 hours 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your Name, Form Class and Acad Class in the spaces at the top of the page. 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 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 of the 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. Give answers in degrees to one decimal place. For  , use either your calculator value or 3.142. For Examiner’s Use Type of Penalties Question Number 90 Presentation 1− 2− This paper consists of 23 printed pages including this cover page.

2 Mathematical Formulae Compound Interest Total amount = 1 100 n rP+ Mensuration Curved surface area of a cone = rl Surface area of a sphere = 24 r Volume of a cone = 21 3 rh Volume of a sphere = 34 3 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 4052/01 [Turn over Answer all the questions. 1 Calculate 23 9.415.6 0.028− . Answer …............................................. [1] 2 Simplify. (a) 4526pp − Answer …............................................. [1] (b) 4(3x – 2) – 5 Answer …............................................. [1] 3 (a) Express 0.00047 in standard form. Answer …............................................. [1] (b) Express 1 km as a percentage of 0.4 nm, where 1 nm = 1 × 10⁻⁹ m. Give your answer in standard form. Answer …............................................ % [1]

4 4052/01 [Turn over 4 The magnetic force, F, between two magnets is inversely proportional to the square of the distance, d, between them. At a certain distance the force is 0.8 N. Find the increase in the magnetic force when the distance is halved. Answer …..................................... N [2] 5 A bag of sand has a mass of x kg and a bag of cement has a mass of y kg. Two bags of sand have a mass that is 10 kg more than one bag of cement. A delivery of 4 bags of sand and 3 bags of cement has a total mass of 220 kg. Find the value of x and y. Answer x = …..................... …. y = …..................... [3]

5 4052/01 [Turn over 6 A toy building block is a cuboid measuring 24 mm by 16 mm by 10 mm. Identical blocks are stacked together to form a cube. Find the length of the smallest possible cube that can be formed, and the number of blocks needed. Answer length of cube …............... mm Number of blocks …............... [3] 7 In Class A, the ratio of boys to girls is 5 : 2. In Class B, the ratio of boys to girls is 7 : 4. The two classes have the same number of boys. Express as a fraction, the total number of girls in both classes. Answer …............................................. [3]

6 4052/01 [Turn over 8 Solve the equation 3x2 – 7x + 1 = 0, giving your answers correct to 2 decimal places. Answer x = …........... or x = …........... [3] 9 In the diagram, AC and BD intersect at M. M is the midpoint of both AC and BD. Show that AB is parallel to CD. Answer …...................................................................................................................................... . ….................................................................................................................................... ......................................................................................................................................... …...................................................................................................................................... . ….............................................................................................................................. [3]

7 4052/01 [Turn over 10 The table shows the times, t minutes, taken by 40 students to complete a Mathematics quiz. Time, t (minutes) Frequency 30 ≤ t < 40 6 40 ≤ t < 50 10 50 ≤ t < 60 16 60 ≤ t < 70 8 (a) Calculate an estimate for (i) the mean time, Answer …............................... min [1] (ii) the standard deviation of the times. Answer …............................... min [1] (b) Each recorded time was 5 minutes less than the actual time, so 5 minutes is added to each time to correct it. Explain how the mean and standard deviation of the corrected times compare with the values in (a). ….......................................................................................................................... ........................................................................................................................ [2]

8 4052/01 [Turn over 11 Two fair four-sided dice, each with faces numbered 1, 2, 3 and 4, are thrown. The two numbers shown are multiplied to give the score. In a game, Aisha wins if the score is even and Ben wins if the score is odd. (a) Explain why the game is unfair. ….......................................................................................................................... ........................................................................................................................ [1] (b) Aisha claims that she is twice as likely to win as Ben. Determine whether Aisha is correct. ….......................................................................................................................... .............................................................................................................................. .............................................................................................................................. .............................................................................................................................. ....................................................................................................................... [2] 12 The area of triangle PQR is 67.67 cm2. Given that QP = 9.8 cm and QR = 15 cm, find the possible values of angle PQR. Answer Angle PQR = ................ or ................ [3]

9 4052/01 [Turn over 13 A closed cylinder fits two identical spheres exactly, as shown. Each sphere touches the curved surface of the cylinder, and the spheres touch each other and the two flat ends. Find the fraction of the volume of the cylinder that is not occupied by the spheres, giving your answer in its simplest form. Answer ........................................ [3]

10 4052/01 [Turn over 14 A, B and C are points on a circle with centre O. AOC and ABD are straight lines, Angle CAB = 28° and Angle BDC = 60°. (a) Find angle DCB. Give a reason for each step of your working. Answer Angle DCB = ……………………………. [2] (b) Explain why DC is not a tangent to the circle. Answer .......