Explore the 2018 Elective Maths WASSCE Questions and Solutions

Sample Questions and Answers

1. If the quadratic equation is x² – 5x + 6 = 0, find the roots.
   The roots of the equation x² – 5x + 6 = 0 are 2 and 3. These are the values of x that satisfy the equation.

2. Solve for x: 2x + 3 = 11.
   By subtracting 3 from both sides, we get 2x = 8. Dividing both sides by 2, x = 4.

3. Find the sum of the first 10 terms of the arithmetic sequence: 5, 8, 11, 14…
   The sum of the first 10 terms is 10/2 * (5 + 32) = 185. This is calculated using the formula for the sum of an arithmetic series.

4. A right-angled triangle has legs of lengths 3 cm and 4 cm. What is the length of the hypotenuse?
   By applying the Pythagorean theorem, the length of the hypotenuse is √(3² + 4²) = 5 cm.

5. Solve for y: 4y – 7 = 9.
   Adding 7 to both sides gives 4y = 16. Dividing both sides by 4, y = 4.

6. Find the area of a circle with radius 7 cm.
   The area of the circle is π * 7² = 49π cm², approximately 153.94 cm².

7. Factorize the expression: x² – 9.
   The expression x² – 9 can be factorized as (x – 3)(x + 3).

8. Solve for x: 3x² – 12 = 0.
   By dividing the equation by 3, we get x² – 4 = 0. Factoring it gives (x – 2)(x + 2) = 0, so x = 2 or x = -2.

9. If the perimeter of a rectangle is 24 cm, and one side is 7 cm, find the length of the other side.
   The perimeter of a rectangle is given by P = 2(length + width). So, 24 = 2(x + 7), and solving for x gives the width as 10 cm.

10. A car travels 60 kilometers per hour. How far will it travel in 5 hours?
    The car will travel 60 * 5 = 300 kilometers in 5 hours.

11. Solve for z: 2z + 6 = 18.
    Subtracting 6 from both sides gives 2z = 12. Dividing both sides by 2, z = 6.

12. Find the volume of a cylinder with radius 3 cm and height 10 cm.
    The volume of the cylinder is π * 3² * 10 = 90π cm³, approximately 282.74 cm³.

13. A number is increased by 25% to get 125. What was the original number?
    Let the original number be x. So, x + 0.25x = 125, which simplifies to 1.25x = 125, and x = 100.

14. If the length of a rectangle is 8 cm and its area is 56 cm², find the width.
    The area of a rectangle is length × width, so 56 = 8 * width, and solving for width gives 7 cm.

15. Solve for t: 5t – 9 = 21.
    By adding 9 to both sides, we get 5t = 30. Dividing both sides by 5, t = 6.

16. A cylinder has a radius of 5 cm and a height of 12 cm. What is its surface area?
    The surface area of the cylinder is 2πr(h + r), so the surface area is 2π * 5 * (12 + 5) = 2π * 5 * 17 = 170π cm², approximately 534.07 cm².

17. If a bag contains 7 red balls and 5 green balls, what is the probability of drawing a green ball?
    The total number of balls is 7 + 5 = 12. The probability of drawing a green ball is 5/12.

18. Find the square root of 144.
    The square root of 144 is 12.

19. If x + y = 10 and x = 3, what is the value of y?
    Substituting x = 3 into the equation, we get 3 + y = 10, and solving for y gives y = 7.

20. A sphere has a radius of 6 cm. What is its volume?
    The volume of a sphere is 4/3πr³. So, the volume is 4/3π * 6³ = 4/3π * 216 = 288π cm³, approximately 904.32 cm³.

These questions cover a range of mathematical concepts such as algebra, geometry, and arithmetic, which would be found in the 2018 Elective Maths WASSCE.

Recommended Indian Books for 2018 Elective Maths WASSCE Preparation

1. “Mathematics for Class 12” by R.D. Sharma
   Publication: Dhanpat Rai Publications
   This book offers a thorough explanation of all topics covered in the syllabus, including algebra, calculus, and trigonometry. It is designed for students preparing for board exams and competitive exams. The exercises range from basic to advanced, allowing students to practice a wide range of problems.

2. “Problems in Calculus of One Variable” by I.A. Maron
   Publication: K.K. Gupta & Co.
   This book is excellent for mastering calculus, one of the core topics in Elective Maths. It includes numerous practice problems and solutions related to limits, continuity, differentiation, and integration, which are crucial for understanding the subject in depth.

3. “Higher Algebra” by Hall and Knight
   Publication: S. Chand Publishing
   A classic book for mastering algebra, this book provides detailed explanations on topics such as quadratic equations, theory of polynomials, and progressions. The problem sets are extensive, covering a variety of question types that are common in WASSCE exams.

4. “Objective Mathematics” by R.D. Sharma
   Publication: Dhanpat Rai Publications
   This book is perfect for practicing objective-type questions. It includes questions on topics such as matrices, sets, and relations, providing a comprehensive approach for students aiming to excel in competitive exams.

5. “Problems in Differential Equations” by A. R. Vasishta
   Publication: Krishna Prakashan Media
   This book focuses on the differential equations portion of the syllabus. It provides clear explanations of first and second-order differential equations, with an ample number of problems to help build problem-solving skills.

6. “Trigonometry” by S.L. Loney
   Publication: S. Chand Publishing
   A go-to book for students struggling with trigonometry, it covers all essential topics with clear, step-by-step solutions. Students will find a variety of problems related to angles, identities, and equations.

7. “Integral Calculus” by Amit M Agarwal (Aakash Institute)
   Publication: Aakash Educational Services
   This book is ideal for mastering integral calculus, including integration techniques, definite integrals, and applications of integrals. It also includes a set of problems that prepare students for exams like WASSCE.

8. “Advanced Problems in Mathematics for JEE Main & Advanced” by Vikas Gupta and P.K. Agarwal
   Publication: Dhanpat Rai & Co
   Though primarily focused on JEE preparation, this book is filled with advanced-level problems in areas like calculus, algebra, and geometry, which can help students strengthen their mathematical foundation for WASSCE exams.

9. “Mathematics Class 12” by R.S. Aggarwal
   Publication: S. Chand Publishing
   A comprehensive guide, R.S. Aggarwal’s book focuses on topics from algebra, coordinate geometry, and calculus. It is well-suited for WASSCE preparation as it provides practice exercises and previous exam questions.

10. “Coordinate Geometry” by S.L. Loney
    Publication: S. Chand Publishing
    This book is highly recommended for understanding and practicing coordinate geometry. It covers all important topics like straight lines, circles, and conic sections with well-explained solutions and plenty of problems to practice.

11. “Mathematics for Class 12 (Part I & II)” by M.L. Khanna
    Publication: Dhanpat Rai Publications
    A thorough book for Class 12 maths, it covers all the essential topics with deep insights and a wide range of questions, helping students to improve both conceptual clarity and problem-solving speed.

12. “Algebra for JEE (Main & Advanced)” by Dr. S.K. Goyal
    Publication: Arihant Publications
    Focuses on the algebraic concepts that are fundamental to both WASSCE and other competitive exams. It covers various types of algebraic expressions, equations, and inequalities.

13. “Mathematics for Class 12 (Vol. 1 & 2)” by P. K. Mittal
    Publication: S. Chand Publishing
    This book offers in-depth coverage of the core subjects like probability, integration, and differentiation. Its exhaustive set of questions includes various question formats to give students a well-rounded preparation.

14. “Integral Calculus for JEE” by Amit M Agarwal
    Publication: Aakash Educational Services
    This is a focused book on integral calculus, perfect for students seeking to strengthen their integration skills. It contains detailed solutions and plenty of exercises tailored to WASSCE-level exams.

15. “Advanced Level Problems in Algebra” by V. K. Ahuja
    Publication: Vikas Publications
    An excellent resource for students wishing to develop a deep understanding of algebraic expressions, equations, and theorems. This book provides advanced-level problems similar to those found in elective maths exams.

16. “CBSE All In One Mathematics Class 12” by Sandeep Garg
    Publication: Arihant Publications
    This book covers all topics systematically and includes previous year’s solved questions and sample papers. It provides a balanced approach for students preparing for board exams and WASSCE.

17. “Mathematics – Class 12” by R. S. Aggarwal
    Publication: S. Chand Publishing
    This book covers all core topics like functions, matrices, vectors, and complex numbers, with a vast collection of practice questions, making it ideal for WASSCE preparation.

18. “Integral Calculus for Class 12” by Amit M Agarwal
    Publication: Aakash Educational Services
    Aimed at providing clarity in integral calculus, this book includes solved examples and practice questions to help students grasp difficult concepts effectively.

19. “Problems in Higher Algebra” by Loney
    Publication: S. Chand Publishing
    This book is a great resource for students aiming to master algebra. It includes a wide range of problems covering all essential topics required for WASSCE exams.

20. “Mathematics Class 12” by D.C. Sharma
    Publication: S. Chand Publishing
    This book covers all the topics necessary for Class 12 maths with clear explanations and a variety of problems. The exercise sets include problems from previous years, which are crucial for WASSCE preparation.

These books provide a rich variety of content, including problem-solving techniques, step-by-step solutions, and ample practice questions, tailored to help students prepare for the 2018 Elective Maths WASSCE exam.

2018 Elective Maths WASSCE Questions: A Complete Guide for Students

The 2018 Elective Mathematics WASSCE exam was a pivotal challenge for many students, aiming to assess their knowledge of advanced mathematical concepts. Preparing for this exam involves understanding the topics covered, practicing various types of questions, and knowing how to approach them efficiently. In this guide, we will break down key areas of the syllabus, offer expert-backed recommendations, and provide tips to tackle the exam confidently.

Key Topics in the 2018 Elective Maths WASSCE Exam

The 2018 Elective Maths WASSCE exam covered a variety of topics from algebra, geometry, calculus, and statistics. One of the primary areas of focus was the application of mathematical theories to solve real-life problems. Students were expected to be proficient in topics like quadratic equations, integration, differentiation, vectors, and complex numbers. These areas required a clear understanding of both fundamental concepts and advanced problem-solving techniques.

For algebra, questions related to quadratic equations, progressions, and inequalities were common. In calculus, students needed to demonstrate their ability to differentiate and integrate functions effectively, and apply these concepts to solve practical problems. Geometry questions often tested students’ understanding of conic sections, circles, and coordinate geometry, with a heavy emphasis on proofs and logical reasoning.

Effective Study Tips for 2018 Elective Maths WASSCE Questions

1. Understand Core Concepts: It’s essential to have a strong grasp of the fundamentals. For topics like calculus, algebra, and geometry, mastering the basic rules and formulas will make solving complex problems easier. Practice these concepts regularly through various problem sets.

2. Solve Previous Year Papers: Practicing previous year’s papers, especially from 2018, will give you an idea of the types of questions asked in the WASSCE exam. It helps you get used to the exam format and time management.

3. Focus on Application-Based Problems: The 2018 exam emphasized applying mathematical concepts to solve real-life scenarios. So, pay attention to word problems and practice applying theories to these types of questions.

4. Practice with Timed Mock Tests: Time management plays a key role in WASSCE exams. Taking mock tests under timed conditions will help improve your speed and accuracy.

5. Seek Expert Guidance: If you’re stuck on a particular topic, it’s always a good idea to seek help from a teacher or mentor who can explain difficult concepts in simpler terms. Join study groups or online forums where you can discuss doubts with fellow students.

FAQ for 2018 Elective Maths WASSCE Questions

1. What are the most important topics to focus on for the 2018 Elective Maths WASSCE?
   Focus on algebra, calculus, and geometry, as these areas are heavily tested. Ensure that you understand quadratic equations, differentiation, integration, and conic sections. Additionally, practice statistics and probability problems.

2. How can I manage my time effectively during the exam?
   Time management is critical. Allocate specific time limits for each section based on its weightage. Start with the questions that you find easiest, and then move on to more challenging ones. Practice mock exams to improve your speed.

3. What type of questions should I expect in the Elective Maths WASSCE exam?
   Expect a mix of multiple-choice, short-answer, and long-answer questions. Topics like algebraic manipulations, solving calculus problems, and geometry proofs are commonly tested. You may also encounter application-based questions that require the use of real-life scenarios.

4. How should I prepare for complex calculus problems?
   Break down each problem into smaller, manageable parts. Start by practicing basic differentiation and integration problems before moving on to complex ones. Ensure you understand the various techniques such as substitution and integration by parts.

5. Are there any recommended books or resources to aid my preparation?
   Yes, there are numerous books dedicated to Elective Maths preparation. Look for resources that focus on previous year’s papers, practice problems, and comprehensive explanations. Books by well-known authors in the subject like R.D. Sharma and S.L. Loney are excellent starting points.

6. How can I improve my understanding of geometric proofs and theorems?
   To improve your geometry skills, start by reviewing the basic theorems and practicing their applications. Work through problems that require geometric reasoning, such as proving properties of triangles, circles, and other shapes. Regular practice will help you build confidence in solving proofs.

7. Is it necessary to memorize formulas for the exam?
   While it’s important to know key formulas, understanding their derivations and applications is even more crucial. Focus on conceptual clarity rather than rote memorization. Practice applying formulas in different problem contexts.

8. How can I ensure that I don’t make careless mistakes in the exam?
   Double-check your calculations, especially in algebra and calculus. Ensure that you understand the question fully before starting. Practice taking exams under timed conditions to reduce the likelihood of making careless errors due to time pressure.

By following these expert-backed strategies and preparing effectively, you can enhance your chances of performing well in the 2018 Elective Maths WASSCE exam.