{"id":2273,"date":"2025-02-20T11:42:53","date_gmt":"2025-02-20T11:42:53","guid":{"rendered":"https:\/\/www.explico.sg\/blog\/?p=2273"},"modified":"2025-02-20T11:42:53","modified_gmt":"2025-02-20T11:42:53","slug":"top-5-hardest-psle-math-questions-solved-step-by-step-solutions-for-2023-psle","status":"publish","type":"post","link":"https:\/\/www.explico.sg\/blog\/top-5-hardest-psle-math-questions-solved-step-by-step-solutions-for-2023-psle\/","title":{"rendered":"Top 5 Hardest PSLE Math Questions Solved: Step-by-Step Solutions for 2023 PSLE"},"content":{"rendered":"<p><span style=\"font-weight: 400;\">Welcome to Explico, your trusted resource for mastering PSLE Math! Today, we\u2019re diving deep into some of the toughest PSLE Math questions from the 2023 paper, providing you with detailed, step-by-step solutions that will help you understand the underlying concepts. Whether you&#8217;re a student preparing for the exam or a parent helping your child, this blog will break down the most challenging questions to ensure you&#8217;re well-prepared for the PSLE Math.<\/span><\/p>\n<h2><b>Introduction to PSLE Math Challenges<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">The Primary School Leaving Examination (PSLE) is a significant milestone in a Singaporean student\u2019s academic journey. Among the various subjects tested, Math is often seen as one of the most challenging due to its complex problem-solving nature. However, with the right approach and strategy, even the toughest problems can be solved!<\/span><\/p>\n<p><span style=\"font-weight: 400;\">In this blog, we will focus on the <\/span><b>Top 5 Hardest PSLE Math Questions from 2023<\/b><span style=\"font-weight: 400;\">. These questions are known for testing both basic arithmetic and higher-order thinking skills, such as critical reasoning and problem analysis. We will guide you through each problem step by step, highlighting the key concepts involved.<\/span><\/p>\n<h3><b>Question 1: Fractions and Percentage Problem<\/b><\/h3>\n<h4><b>Problem:<\/b><\/h4>\n<p><span style=\"font-weight: 400;\">In a school, 3\/5 of the students are girls. Of the girls, 40% attend the Science Club, and the rest attend the Math Club. If the total number of students in the school is 600, how many girls are in the Math Club?<\/span><\/p>\n<h4><b>Solution:<\/b><\/h4>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Find the total number of girls in the school:<\/b>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"2\"><span style=\"font-weight: 400;\">Since 3\/5 of the students are girls, we multiply 3\/5 by the total number of students (600).<\/span><\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\\text{Number of girls} = \\frac{3}{5} \\times 600 = 360 ]<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Calculate the number of girls in the Science Club:<\/b>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"2\"><span style=\"font-weight: 400;\">40% of the girls attend the Science Club.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"2\"><\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\\text{Girls in Science Club} = 40% \\times 360 = 0.4 \\times 360 = 144 ]<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Find the number of girls in the Math Club:<\/b>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"2\"><span style=\"font-weight: 400;\">The remaining girls must be in the Math Club. Subtract the girls in the Science Club from the total number of girls.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"2\"><\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\\text{Girls in Math Club} = 360 &#8211; 144 = 216 ]<\/span><\/li>\n<\/ol>\n<p><b>Answer:<\/b><span style=\"font-weight: 400;\"> There are <\/span><b>216 girls in the Math Club<\/b><span style=\"font-weight: 400;\">.<\/span><\/p>\n<h2><b>Question 2: Ratio and Proportion Problem<\/b><\/h2>\n<h4><b>Problem:<\/b><\/h4>\n<p><span style=\"font-weight: 400;\">The ratio of the number of red balls to blue balls in a box is 3:4. If there are 84 balls in total, how many red balls are there?<\/span><\/p>\n<h4><b>Solution:<\/b><\/h4>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Represent the ratio:<\/b>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"2\"><span style=\"font-weight: 400;\">The ratio of red balls to blue balls is 3:4, which means for every 3 red balls, there are 4 blue balls.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"2\"><span style=\"font-weight: 400;\">The total parts in the ratio = 3 + 4 = 7 parts.<\/span><\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Set up the equation:<\/b>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"2\"><span style=\"font-weight: 400;\">Let the total number of balls be 84.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"2\"><span style=\"font-weight: 400;\">Since the ratio is divided into 7 parts, each part represents 847=12\\frac{84}{7} = 12784\u200b=12 balls.<\/span><\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Calculate the number of red balls:<\/b>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"2\"><span style=\"font-weight: 400;\">The red balls are represented by 3 parts.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"2\"><\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\\text{Number of red balls} = 3 \\times 12 = 36 ]<\/span><\/li>\n<\/ol>\n<p><b>Answer:<\/b><span style=\"font-weight: 400;\"> There are <\/span><b>36 red balls<\/b><span style=\"font-weight: 400;\">.<\/span><\/p>\n<h3><b>Question 3: Speed, Time, and Distance Problem<\/b><\/h3>\n<h4><b>Problem:<\/b><\/h4>\n<p><span style=\"font-weight: 400;\">Two trains, Train A and Train B, start from the same point at the same time. Train A travels at 60 km\/h, and Train B travels at 80 km\/h. After how many hours will Train B be 60 km ahead of Train A?<\/span><\/p>\n<h4><b>Solution:<\/b><\/h4>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Set up the relationship between the two trains:<\/b>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"2\"><span style=\"font-weight: 400;\">The relative speed between the two trains is the difference in their speeds.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"2\"><\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\\text{Relative speed} = 80 , \\text{km\/h} &#8211; 60 , \\text{km\/h} = 20 , \\text{km\/h} ]<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Use the formula for distance:<\/b>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"2\"><span style=\"font-weight: 400;\">Distance = Speed \u00d7 Time.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"2\"><span style=\"font-weight: 400;\">The distance Train B needs to be ahead of Train A is 60 km. Using the relative speed:<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"2\"><\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\\text{Time} = \\frac{\\text{Distance}}{\\text{Relative speed}} = \\frac{60 , \\text{km}}{20 , \\text{km\/h}} = 3 , \\text{hours} ]<\/span><\/li>\n<\/ol>\n<p><b>Answer:<\/b><span style=\"font-weight: 400;\"> Train B will be 60 km ahead of Train A after <\/span><b>3 hours<\/b><span style=\"font-weight: 400;\">.<\/span><\/p>\n<h3><b>Question 4: Algebraic Expression Problem<\/b><\/h3>\n<h4><b>Problem:<\/b><\/h4>\n<p><span style=\"font-weight: 400;\">The sum of three consecutive integers is 57. What are the three integers?<\/span><\/p>\n<h4><b>Solution:<\/b><\/h4>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Represent the integers algebraically:<\/b>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"2\"><span style=\"font-weight: 400;\">Let the first integer be xxx, the second integer be x+1x + 1x+1, and the third integer be x+2x + 2x+2.<\/span><\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Set up the equation:<\/b>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"2\"><span style=\"font-weight: 400;\">The sum of the three integers is 57.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"2\"><\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">x + (x + 1) + (x + 2) = 57 ]<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Simplify and solve for xxx:<\/b>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"2\"><\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">3x + 3 = 57 ]<\/span>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"2\"><span style=\"font-weight: 400;\">Subtract 3 from both sides:<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"2\"><\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">3x = 54 ]<\/span>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"2\"><span style=\"font-weight: 400;\">Divide by 3:<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"2\"><\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">x = 18 ]<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Find the three integers:<\/b>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"2\"><span style=\"font-weight: 400;\">The first integer is x=18x = 18x=18, the second is x+1=19x + 1 = 19x+1=19, and the third is x+2=20x + 2 = 20x+2=20.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<p><b>Answer:<\/b><span style=\"font-weight: 400;\"> The three consecutive integers are <\/span><b>18, 19, and 20<\/b><span style=\"font-weight: 400;\">.<\/span><\/p>\n<h3><b>Question 5: Geometry Problem (Area of Triangle)<\/b><\/h3>\n<h4><b>Problem:<\/b><\/h4>\n<p><span style=\"font-weight: 400;\">A triangle has a base of 10 cm and a height of 6 cm. What is the area of the triangle?<\/span><\/p>\n<h4><b>Solution:<\/b><\/h4>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Use the area formula for a triangle:<\/b>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"2\"><span style=\"font-weight: 400;\">The area AAA of a triangle is given by the formula:<\/span><\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">A=12\u00d7Base\u00d7HeightA = \\frac{1}{2} \\times \\text{Base} \\times \\text{Height}A=21\u200b\u00d7Base\u00d7Height<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><b>Substitute the given values:<\/b>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"2\"><span style=\"font-weight: 400;\">Base = 10 cm, Height = 6 cm.<\/span><\/li>\n<li style=\"font-weight: 400;\" aria-level=\"2\"><\/li>\n<\/ul>\n<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">A = \\frac{1}{2} \\times 10 \\times 6 = \\frac{1}{2} \\times 60 = 30 , \\text{cm}^2 ]<\/span><\/li>\n<\/ol>\n<p><b>Answer:<\/b><span style=\"font-weight: 400;\"> The area of the triangle is <\/span><b>30 cm\u00b2<\/b><span style=\"font-weight: 400;\">.<\/span><\/p>\n<h5><b>Final Words\u00a0<\/b><\/h5>\n<p><span style=\"font-weight: 400;\">These five problems from the 2023 <\/span><a href=\"https:\/\/www.explico.sg\/psle-exam\/psle-maths\"><span style=\"font-weight: 400;\">PSLE Math paper<\/span><\/a><span style=\"font-weight: 400;\"> demonstrate the diverse range of skills required to excel in the exam. From fractions and percentages to geometry and algebra, each question tests different areas of mathematical knowledge. The key to success in PSLE Math is practice, understanding the concepts, and applying logical steps to solve each problem.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">We hope this walk-through helps you feel more confident in tackling even the hardest questions. Keep practicing and reviewing, and remember that every mistake is just a step closer to mastering the subject.<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Stay tuned to <\/span><a href=\"https:\/\/www.explico.sg\/\"><span style=\"font-weight: 400;\">Explico<\/span><\/a><span style=\"font-weight: 400;\"> for more in-depth explanations, sample solutions, and tips to ace your PSLE Math!<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Welcome to Explico, your trusted resource for mastering PSLE Math! Today, we\u2019re diving deep into some of the toughest PSLE Math questions from the 2023 paper, providing you with detailed, step-by-step solutions that will help you understand the underlying concepts. Whether you&#8217;re a student preparing for the exam or a parent helping your child, this [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":2275,"comment_status":"open","ping_status":"open","sticky":true,"template":"","format":"standard","meta":[],"categories":[41],"tags":[115,116,122],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v18.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Top 5 Hardest PSLE Math Questions Solved | Blog - Explico<\/title>\n<meta name=\"description\" content=\"Do you want to master PSLE Maths for 2025? Practice the most challenging questions to make the subject easier and score high. 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