LC Foundation Maths common mistakes
LC Foundation Maths · Understand the traps and how to avoid them.
For a 15% increase on €80, writes €95 by adding 15 to 80 instead of calculating 80 × 1.15.
Treats the percentage as a fixed money amount and does not convert it to a decimal or multiplier.
What to do instead
Write the multiplier first: increase = ×1.15, decrease = ×0.85. Estimate that the answer must be between €80 and €100, then calculate 80 × 1.15 = €92.
Solves 5x − 3 = 17 by writing 5x = 17 − 3 instead of 5x = 17 + 3.
Uses a remembered 'change side, change sign' rule without applying the inverse operation to both sides.
What to do instead
Show the same operation on both sides: add 3 to both sides to get 5x = 20, then divide both sides by 5. Substitute x = 4 back into the original equation to check.
Shares €60 in the ratio 2:3 by calculating 60 ÷ 2 = 30 and 60 ÷ 3 = 20, giving €30 and €20.
Treats each ratio number as a separate divisor rather than as parts of one total.
What to do instead
Add the ratio parts: 2 + 3 = 5. One part is €60 ÷ 5 = €12, so the shares are 2 × 12 = €24 and 3 × 12 = €36. Check that €24 + €36 = €60.
Given a circle with diameter 10 cm, substitutes r = 10 into πr² and gets 100π cm².
Reads the diameter as the radius because the formula uses r and the diagram labels the full width.
What to do instead
Mark the radius on the diagram: r = diameter ÷ 2 = 5 cm. Then use area = π × 5² = 25π ≈ 78.5 cm². Check that the area is less than a 10 cm by 10 cm square.
For a grouped frequency table, calculates the mean by averaging the class midpoints and ignores the frequency column.
Sees the mean as an ordinary average of the x-values and forgets that each midpoint represents many data values.
What to do instead
Make an f × x column and use mean = Σfx ÷ Σf. Check that the answer lies between the smallest and largest midpoint; if it does not, the weighting has been missed.
For two independent coin tosses, calculates P(two heads) = 1/2 + 1/2 = 1.
Confuses 'and' with 'or' and adds probabilities for events that must both happen.
What to do instead
Draw a tree diagram or two-way table. Multiply along branches for 'and': 1/2 × 1/2 = 1/4. Add only for mutually exclusive alternatives such as 'one head and one tail'.
Rounds every intermediate calculator value to two decimal places during a multi-step money or percentage calculation, so the final answer is off by several cent.
Believes each displayed calculator value is the final answer and copies the rounded value into the next step.
What to do instead
Keep the full value in the calculator using the Ans key or memory. Write down the unrounded value until the final line, then round only the final answer to the requested accuracy.
Evaluates x² − 2x for x = −3 by entering −3² on the calculator and getting −9, then obtains −9 + 6 = −3.
Omits brackets around a negative number when squaring, so the calculator applies the minus sign after squaring.
What to do instead
Substitute with brackets: (−3)² − 2(−3) = 9 + 6 = 15. Enter (−3)² with brackets on the calculator and check the sign of each term.
For a 120 km journey made of 60 km at 60 km/h and 60 km at 120 km/h, averages the two speeds to get 90 km/h instead of 80 km/h.
Treats average speed as the arithmetic mean of the speeds and ignores that the faster section takes less time.
What to do instead
Find each time: 60 ÷ 60 = 1 h and 60 ÷ 120 = 0.5 h. Total time = 1.5 h, so average speed = total distance ÷ total time = 120 ÷ 1.5 = 80 km/h.
Converts 3 m² to cm² by multiplying by 100 and writes 300 cm².
Applies the linear conversion factor to an area and forgets that both length and width change units.
What to do instead
Convert the length unit first: 1 m = 100 cm, so 1 m² = 100² cm² = 10,000 cm². Therefore 3 m² = 30,000 cm². For volume use the cube of the length factor.