AQA GCSE Mathematics Past Papers

Common mistake: Multiplying or dividing the bases as well as the indices. For example, incorrectly calculating (3^6 \times 3^5) as (9^{11}), instead of (3^{11}), or (6^3 \times 5^3) as (11^9), instead of (30^3). Another common error is incorrectly "cancelling" the bases when dividing, such as calculating (\frac{3^{15}}{3^5}) as (1^5), instead of (3^{10}).

How to solve it: Remember that when multiplying or dividing terms with the same base, the base remains unchanged while you add or subtract the indices (e.g., (3^6 \times 3^5 = 3^{11})).

Common mistake: Many students use a direct proportion strategy, leading to answers where more workers result in more time taken, which fails a "common sense" check. Another frequent error is calculating the total number of workers needed but forgetting to answer the specific question of "how many more" workers are required.

How to solve it: Always check if your answer makes sense—in inverse proportion, as one variable increases, the other must decrease. Calculate the "total work" required (e.g., number of workers × days) and then divide by the new variable.

Common mistake: A common mistake is treating columns in a frequency table as independent sets of results or averaging the relative frequencies of different sets.

How to solve it: To find the best estimate for probability, you must use the total number of successes divided by the total number of trials across all sets combined, rather than calculating individual relative frequencies and finding their mean.

Common mistake: When dealing with similar shapes, students often use the linear scale factor for volume or area problems without squaring or cubing it first.

How to solve it: Always identify what dimension the question is asking for. If the linear scale factor is k, the area scale factor is k2 and the volume scale factor is k3.

Common mistake: Many students confuse the gradient formula, using change in x over change in y instead of the correct change in y over change in x. Students also struggle to identify when a gradient should be negative.

How to solve it: Memorize the formula m=x2−x1y2−y1. Draw a quick sketch of the points to visualize the line; if it goes "downhill" from left to right, your gradient must be negative.