Jan 2025 Paper 2 number 1 Solution

Summary

In this educational video, the presenter walks viewers through a series of mathematics problems from the January 2025 paper. The content covers fraction operations using BODMAS, ratio calculations for juice boxes in different varieties, and the calculation of profit margins from sales. Key steps include simplifying complex fractions, using ratios to determine quantities, and understanding profit percentages. The presenter also highlights an error in a profit calculation question, pointing out missing details needed for a correct solution. Ultimately, viewers gain insights into handling fractions, ratios, and percentage profit calculations effectively.

Takeaways

• 😀 The script explains how to solve a math problem from the January 2025 Paper 2, specifically focusing on operations with fractions and the correct application of BODMAS.
• 😀 The first part of the problem involves simplifying a complex fraction involving addition and division, using BODMAS principles to solve step by step.
• 😀 The BODMAS rule suggests solving operations inside brackets first, followed by division, and then addition to correctly simplify the expression.
• 😀 The script emphasizes converting improper fractions to mixed numbers to make the final result easier to understand.
• 😀 For fraction operations, the Least Common Multiple (LCM) is used when denominators are different to add fractions correctly.
• 😀 The solution shows how to use a calculator for easier computation, highlighting the use of the over button for fraction division.
• 😀 Part B of the question discusses ratios, explaining how to interpret the ratio of apple, orange, and pineapple juice, and the calculation of pineapple juice boxes in a case.
• 😀 The script clarifies that the ratio of apple, orange, and pineapple juices is 2:5:1, meaning 2 parts apple, 5 parts orange, and 1 part pineapple.
• 😀 The cost price of a box of juice is derived from the profit calculation, but the script points out a possible error in the question that leads to an incorrect profit figure.
• 😀 The final part calculates the percentage profit on the sale of the juice, using the formula (Profit / Cost Price) × 100 to get the exact percentage.

Q & A

What mathematical rule is used to determine the order of operations in the script?

The BODMAS rule is used, which stands for Brackets, Orders (powers and roots), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).

How did the speaker simplify the complex fraction involving 1/8 + 5/12 divided by 1/9?

The speaker first simplified the division of fractions 5/12 ÷ 1/9 by converting the division into multiplication by 9/1, resulting in 15/4. Then, 1/8 was added to this, and the fractions were made compatible by finding the least common multiple (LCM) of 8 and 4, which is 8.

How was the improper fraction 31/12 converted into a mixed number?

The improper fraction 31/12 was converted into a mixed number by dividing 31 by 12, resulting in 2 as the quotient and 7 as the remainder. This gives the mixed number 2 7/12.

What did the speaker demonstrate regarding how to use a calculator to solve the fraction problem?

The speaker showed how to input the expression into a calculator and confirmed that the result would be 2 7/12, the same as the manual calculation, verifying the correctness of the answer.

In the ratio problem about fruit juice, what does the ratio 2:5:1 represent?

The ratio 2:5:1 represents the number of parts of apple juice, orange juice, and pineapple juice, respectively, in each case. Apple juice is 2 parts, orange juice is 5 parts, and pineapple juice is 1 part.

How did the speaker calculate the number of pineapple juice boxes in a case?

The speaker first determined that there are 8 total parts (2 + 5 + 1). Since 8 parts correspond to 24 boxes, each part is equivalent to 3 boxes. Therefore, pineapple juice, which is 1 part, is equal to 3 boxes per case.

What error did the speaker identify in the question regarding the profit from selling pineapple juice boxes?

The speaker pointed out that there is an inconsistency in the question because it claims a profit of $356 from selling only 3 boxes, which is not mathematically possible. The question does not provide sufficient information to make this calculation.

How did the speaker suggest correcting the error in the profit question?

The speaker suggested that the problem could have been solved if the number of boxes sold was given, such as 36 boxes, instead of the vague reference to 'several cases.' With that information, the profit could be accurately calculated.

What formula did the speaker use to calculate the percentage profit from selling pineapple juice?

The speaker used the formula for profit percentage: (Profit ÷ Cost Price) × 100%. The profit per box was $0.99, and the cost price per box was $2.35, leading to a profit percentage of 42.6%.

What was the final percentage profit calculated in the script?

The final percentage profit calculated in the script was 42.6%, derived from the profit of $0.99 and the cost price of $2.35.