Botswana BGCSE General Mathematics 1236 common mistakes
Botswana BGCSE General Mathematics 1236 · Understand the traps and how to avoid them.
In a percentage change question, divides the change by the new value or by the larger value instead of the original value; for example, a price rise from P80 to P100 is written as 20/100 = 20%.
Candidates memorise 'difference over one of the numbers' and choose the final or most prominent figure, especially when the original value was mentioned earlier and is no longer in view.
What to do instead
Before calculating, write 'original = ...' and 'change = new − original'. Then use change/original × 100. Check by reversing the change: a 25% increase from P80 should return P100.
Writes 0.00036 in standard form as 3.6 × 10^-3 instead of 3.6 × 10^-4, or gives a positive index for a number that has become smaller.
Counts zeros after the decimal point rather than counting decimal-place moves, and does not check the size of the result against the original number.
What to do instead
Move the decimal point to sit immediately after the first non-zero digit and count each jump. For numbers less than 1 the index is negative. Substitute back to check: 3.6 × 10^-4 = 0.00036.
For two sets A and B, calculates n(A ∪ B) as n(A) + n(B) and ignores the overlap, or writes n(A ∩ B) as the number of elements in either circle.
Treats 'union' as simple addition and does not link the words and symbols to the separate Venn regions, so 'both' and 'either' are confused.
What to do instead
Write n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Sketch and label three regions: only A, only B, and both. Check that the region totals equal the universal set count.
When solving x/3 + 2 = 5, multiplies only the fraction x/3 by 3 and obtains x + 2 = 5, instead of multiplying every term by 3.
Sees the denominator as attached only to the fraction and applies the inverse operation locally rather than to the whole equation.
What to do instead
Multiply every term on both sides by the LCM of the denominators and bracket each term: 3(x/3 + 2) = 3(5), so x + 6 = 15. Substitute the answer into the original equation to check.
Expands −(2x − 5) as −2x − 5, or 3 − (x + 4) as 3 − x + 4, by distributing the minus sign only to the first term inside the bracket.
Reads the minus as a subtraction sign rather than as a multiplier of −1 across the whole bracket.
What to do instead
Rewrite the expression as −1(2x − 5), or draw arrows showing that every term changes sign. For 3 − (x + 4), write 3 − x − 4 before collecting. Test with x = 1 numerically.
Marks two angles as equal because they look like corresponding or alternate angles, without checking that the two lines cut by the transversal are marked parallel; also quotes 'alternate angles' for a pair that is co-interior.
Relies on the visual layout of the diagram and memorised angle names rather than on the parallel-line condition and the exact position of the angles.
What to do instead
First write 'given: AB ∥ CD'. Then name the pair precisely, such as alternate interior angles, and state the reason. If parallel marks are absent, do not assume equality; use the triangle angle sum or other given facts.
Uses the diameter in A = πr², or calculates circumference when the question asks for area; also gives an area in cm rather than cm².
Recalls a mixture of the circle formulas and takes the number labelled on the diagram without converting diameter to radius.
What to do instead
Write r = d/2 as a separate line before substituting. Write the formula with its units: A = πr² gives square units. Check whether the question asks for the distance around the circle or the space inside it.
For a grouped frequency table, calculates the mean as Σfx divided by the number of class rows rather than by the total frequency Σf.
Confuses the number of categories with the number of data values; the frequency column is treated as a label rather than as a count of items.
What to do instead
Add a total row and write Σf explicitly. Compute mean = Σfx/Σf, using class midpoints for x. Sanity-check that the mean lies between the smallest and largest midpoints.
For two independent events, adds their probabilities to find the probability that both occur, writing P(A and B) = P(A) + P(B); or adds probabilities for 'at least one' without using the complement.
The words 'or' and 'and' are not linked to addition and multiplication, and tree-diagram branch rules are not applied consistently.
What to do instead
For independent events use P(A and B) = P(A) × P(B); for mutually exclusive alternatives use addition. For 'at least one', calculate 1 − P(none). Draw a tree: multiply along branches and add across branches.
In a right-angled triangle, identifies the side adjacent to the chosen angle as the opposite side, or vice versa, and therefore selects the wrong ratio from SOHCAHTOA.
Uses a fixed picture of 'opposite = vertical side' instead of locating the side relative to the marked angle, especially when the triangle is rotated or the angle is at the top.
What to do instead
Mark the angle with an arc, trace the side opposite it across the triangle, and identify the hypotenuse as the side opposite the right angle. Label O, A and H on the diagram before choosing sine, cosine or tangent.