2023 BECE Candidates at Risk of Failing Mathematics If they are Weak in these Topics
![2023 BECE candidates who cannot solve Mathematics questions from these topics may fail 2022 BECE Mathematics Questions](https://ghanaeducation.org/wp-content/uploads/2022/10/mathematics-ga0cc9241c_640-1.webp)
As candidates get ready for the 2023 BECE, we are sharing this as an alert to help them put final touch to their readiness.
The topics and issues raised in this post were the reasons why some BECE candidates failed the 2021 BECE as revealed by WAEC.
It turned out that students could not answer questions related to these topics leading to failure. Once a candidate cannot solve such questions, it also means the mathematical foundation is weak.
The 2021 BECE examiner’s report is the latest report. It indicates that candidates’ weaknesses were found in the following areas:
- Applying laws of indices to simplify given expression.
How to Apply laws of indices to simplify given expressions in mathematics
The laws of indices, also known as exponent rules, are fundamental rules that allow us to simplify expressions involving exponents. Here’s a step-by-step guide on applying the laws of indices to simplify given expressions in mathematics:
Multiplication Rule: When multiplying terms with the same base, we can add their exponents. For example, a^m * a^n = a^(m + n). Similarly, (a^m) * (b^m) = (a * b)^m.
Division Rule: When dividing terms with the same base, we can subtract their exponents. For example, a^m / a^n = a^(m – n). Similarly, (a^m) / (b^m) = (a / b)^m.
Power Rule: When raising a power to another power, we can multiply the exponents. For example, (a^m)^n = a^(m * n).
Zero Exponent Rule: Any non-zero number raised to the power of zero is equal to 1. For example, a^0 = 1, where ‘a’ is any non-zero number.
Negative Exponent Rule: A term with a negative exponent can be rewritten as the reciprocal of the term with the positive exponent. For example, a^(-m) = 1 / a^m.
Simplifying Radicals: Rational exponents can be used to simplify radicals. For example, the square root of a number can be expressed as a^(1/2), and the cube root can be expressed as a^(1/3).
Combining Like Terms: In expressions with multiple terms, simplify by combining like terms. For example, 2a^2 * 3a^3 = 6a^(2 + 3) = 6a^5.
Parentheses and Order of Operations: Apply the laws of indices within parentheses first before applying other operations like addition or subtraction.
- clearing fraction and solving of linear equation;
To clear fractions when solving linear equations, follow these steps:
Identify the fractions: Identify any fractions present in the equation. These can be in the form of numerator/denominator or as decimals.
Multiply by the least common denominator (LCD): Find the least common denominator for all the fractions in the equation. This is the smallest number that all the denominators can divide evenly into. Multiply both sides of the equation by the LCD to eliminate the fractions.
Distribute the LCD: Distribute the LCD to every term in the equation, both on the left and right sides. This ensures that every term is multiplied by the same value, maintaining the equality of the equation.
Simplify the equation: Simplify both sides of the equation by performing any necessary operations, such as combining like terms or simplifying fractions if possible.
Solve the resulting equation: After clearing the fractions, you will have an equation without any fractions. Solve the resulting equation using standard techniques, such as isolating the variable on one side and performing inverse operations.
Check the solution: After solving for the variable, substitute the solution back into the original equation to verify its correctness. Ensure that the solution satisfies the equation and yields a true statement.
By following these steps, you can effectively clear fractions when solving linear equations, making it easier to find the solution. Remember to pay attention to each step and perform the necessary calculations accurately.
Here’s a practical linear equation with fractions that we can solve by clearing the fractions:
Question:
Solve the equation: (3/4)x – (1/2) = (2/3)x + (1/6)
Example:
Step 1: Identify the fractions:
In the given equation, we have fractions (3/4), (1/2), (2/3), and (1/6).
Step 2: Find the LCD:
The least common denominator (LCD) for the fractions 4, 2, 3, and 6 is 12.
Step 3: Multiply by the LCD:
Multiply both sides of the equation by 12 to clear the fractions:
12 * [(3/4)x – (1/2)] = 12 * [(2/3)x + (1/6)]
Step 4: Distribute the LCD:
Distribute the LCD to each term on both sides of the equation:
(12 * (3/4))x – (12 * (1/2)) = (12 * (2/3))x + (12 * (1/6))
Simplifying, we get:
(9/4)x – 6 = (8/3)x + 2
Step 5: Solve the resulting equation:
To solve the equation, let’s isolate the variable terms on one side and the constant terms on the other side:
(9/4)x – (8/3)x = 2 + 6
Common denominator for (9/4) and (8/3) is 12.
(27/12)x – (32/12)x = 8
(-5/12)x = 8
To solve for x, we can multiply both sides by the reciprocal of (-5/12), which is (-12/5):
((-12/5) * (-5/12))x = (8 * (-12/5))
Simplifying, we get:
x = -96/5
Step 6: Check the solution:
Substitute the value of x back into the original equation to verify if it satisfies the equation:
(3/4)(-96/5) – (1/2) = (2/3)(-96/5) + (1/6)
After performing the calculations, both sides of the equation should be equal. If they are, then the solution is valid.
By following these steps, we can successfully clear fractions and solve linear equations, ensuring accurate solutions to the given problem.
- solving word-problems;
- How to solve word-problems in mathematics plus step by step guide.
- Solving word problems in mathematics requires a systematic approach and careful analysis of the given information. Here’s a step-by-step guide to help you solve word problems effectively:
- Step 1: Read the Problem Carefully: Read the word problem carefully and identify the key information, including the given values, what is being asked, and any conditions or constraints mentioned.
- Step 2: Define Variables: Assign variables to the unknown quantities mentioned in the problem. It helps to use letters or symbols to represent these unknowns, making it easier to set up equations or expressions.
- Step 3: Translate into Mathematical Expressions or Equations: Based on the information given, translate the word problem into mathematical expressions or equations. Break down the problem into smaller steps if necessary and determine the relationship between the known and unknown quantities.
- Step 4: Solve the Equations: Solve the mathematical equations or expressions to find the values of the unknown variables. Utilize appropriate mathematical techniques, such as simplifying expressions, applying formulas, or solving systems of equations.
- Step 5: Check Your Solution: Once you have obtained the values for the unknown variables, double-check your solution. Substitute the values back into the original problem to ensure they satisfy the given conditions and provide the correct answer.
- Step 6: Communicate Your Answer: Clearly state the final answer, including the correct units or measurements if applicable. Use proper mathematical notation and provide a clear explanation of your solution, ensuring it aligns with the context of the word problem.
- Step 7: Reflect and Practice: After solving the word problem, reflect on your approach and identify areas for improvement. Practice solving a variety of word problems to enhance your problem-solving skills and familiarize yourself with different problem-solving techniques.
- Remember, word problems often require critical thinking, logical reasoning, and application of mathematical concepts. Regular practice and exposure to different types of word problems will help improve your ability to solve them efficiently.
Question:
An ice cream vendor sold 65 ice creams on Monday and 82 ice creams on Tuesday. If he sold 3 times as many ice creams on Wednesday as he did on Monday, and he sold 10 more ice creams on Thursday than he did on Tuesday, how many ice creams did the vendor sell in total from Monday to Thursday?
Solution:
Step 1: Calculate the number of ice creams sold on Wednesday:
The number of ice creams sold on Wednesday is 3 times the number sold on Monday.
Ice creams sold on Wednesday = 3 * 65 = 195
Step 2: Calculate the number of ice creams sold on Thursday:
The number of ice creams sold on Thursday is 10 more than the number sold on Tuesday.
Ice creams sold on Thursday = 82 + 10 = 92
Step 3: Calculate the total number of ice creams sold:
Add up the number of ice creams sold on each day.
Total ice creams sold = Monday + Tuesday + Wednesday + Thursday
Total ice creams sold = 65 + 82 + 195 + 92
Total ice creams sold = 434
Answer:
The ice cream vendor sold a total of 434 ice creams from Monday to Thursday.
(d) finding rule of a given mapping;
To find the rule of a given mapping, follow these step-by-step instructions:
Step 1: Identify the Inputs and Outputs:
Look at the given mapping and identify the inputs (also known as the domain) and the corresponding outputs (also known as the range). Write them down in a clear and organized manner.
Step 2: Analyze the Pattern:
Examine the relationship between the inputs and outputs to identify any patterns or rules that govern the mapping. Look for consistent changes or transformations that occur as you move from one input to the next.
Step 3: Look for Common Operations:
Determine if there are any common mathematical operations applied to the inputs to obtain the corresponding outputs. Examples of common operations include addition, subtraction, multiplication, division, or raising to a power.
Step 4: Test the Rule:
Based on your analysis of the pattern and common operations, formulate a rule that describes the relationship between the inputs and outputs. Use this rule to test whether it accurately predicts the outputs for other inputs in the mapping.
Step 5: Refine and Confirm the Rule:
Check if the rule works consistently for all inputs and outputs in the mapping. If it does, you have successfully identified the rule. If not, reanalyze the pattern and adjust your rule accordingly until it accurately predicts all the outputs.
Step 6: Express the Rule:
Once you have confirmed the rule, express it in a clear and concise manner using mathematical notation or plain language, depending on the context.
Step 7: Verify the Rule:
Double-check your rule by applying it to additional inputs and confirming that it consistently produces the correct corresponding outputs. This helps ensure the accuracy of the identified rule.
By following these steps, you can systematically analyze a given mapping and determine the rule that governs its relationship between inputs and outputs. Remember, practice and exposure to different mappings will help develop your pattern recognition skills and improve your ability to identify rules efficiently.
(e) simplifying fractions and converting to the nearest whole numbers.
To simplify fractions and convert them to the nearest whole numbers, you can follow these steps:
Simplifying Fractions:
Step 1: Identify the fraction that needs to be simplified.
Step 2: Find the greatest common divisor (GCD) of the numerator and denominator. This is the largest number that divides evenly into both.
Step 3: Divide both the numerator and denominator by their GCD.
Step 4: If the resulting fraction is still a proper fraction (numerator is smaller than the denominator), simplify it further if possible. If it’s an improper fraction (numerator is equal to or larger than the denominator), proceed to the next step.
Converting to Nearest Whole Numbers:
Step 5: Divide the numerator by the denominator.
Step 6: If the division results in a decimal value, round it to the nearest whole number using rounding rules (e.g., rounding up if the decimal is 0.5 or greater).
Step 7: The whole number obtained is the converted value.
Example:
Let’s work through an example using the fraction 15/6.
Step 1: Identify the fraction: 15/6
Step 2: Find the GCD of 15 and 6. The GCD is 3.
Step 3: Divide both numerator and denominator by 3: 15/3 ÷ 6/3 = 5/2
Step 4: The resulting fraction is improper. Proceed to the next step.
Step 5: Divide the numerator by the denominator: 5 ÷ 2 = 2.5
Step 6: Round 2.5 to the nearest whole number, which is 3.
Step 7: The converted value is 3.
So, simplifying 15/6 results in 3 when converted to the nearest whole number.
By following these steps, you can simplify fractions and convert them to the nearest whole numbers, making them easier to work with and understand.