Nepal SEE Mathematics common mistakes
Nepal SEE Mathematics · Understand the traps and how to avoid them.
In a two-set word problem, writes n(A∪B) = n(A) + n(B) and then cannot place the 'both' value, or reports 'only A' as n(A).
The formula is memorized as symbols without attaching meaning to each Venn region, so the overlap is added twice and the 'only' regions are never separated.
What to do instead
Draw two overlapping circles and fill the intersection first. Subtract it from each set to get 'only A' and 'only B', then use n(U) to place 'neither'. Check that all four regions sum to n(U).
Computes the discount on marked price, then adds 13% VAT to the marked price instead of to the discounted price, or applies VAT before the discount.
Discount, selling price and VAT are memorized as separate formulas rather than one ordered chain, so the VAT base is chosen incorrectly.
What to do instead
Write the chain explicitly: MP → discount amount → price after discount → VAT → final amount. Keep the VAT base as the price after discount, and sanity-check that the final amount is greater than the discounted price.
For interest compounded half-yearly, halves the annual rate but keeps n as the number of years.
The rate adjustment R/2 is remembered, but the matching time adjustment is forgotten, so too few conversion periods are used.
What to do instead
Convert both quantities together: rate per half-year = R/2 and number of periods = 2T; for quarterly use R/4 and 4T. Test with T = 1 year and confirm two half-yearly periods are applied.
Adds the full surface areas of a cylinder and hemisphere in a combined solid, counting the circular joint twice.
Each solid's formula is learned separately and then simply added; the hidden joined faces are never subtracted.
What to do instead
List only exposed surfaces before calculating. Subtract one circle area for every joint; for a capsule use curved cylinder + two curved hemisphere surfaces and no base circles. Sketch and shade the exposed surface first.
Rationalizes 1/(√7 − √2) by multiplying by (√7 − √2) again, or writes the new denominator as 7 + 2.
The conjugate is confused with squaring a binomial, and the sign change in the middle term is not applied.
What to do instead
The conjugate flips only the middle sign: multiply by (√7 + √2)/(√7 + √2). Then (√a − √b)(√a + √b) = a − b, so the denominator is 7 − 2 = 5. Verify with a decimal approximation.
In a circle proof, states '∠A = ∠B because they are angles in the same segment' when the points lie on different arcs, or assumes a quadrilateral is cyclic because it looks so.
The reason is chosen from the diagram's appearance rather than from checking which chord and arc actually subtend each angle.
What to do instead
Before writing each reason, name the chord or arc and the two points on the circumference. For a cyclic quadrilateral, prove all four vertices lie on the circle or prove a pair of opposite angles is supplementary.
Draws the angle of depression at the object on the ground instead of at the observer's eye, then substitutes the wrong angle into tan θ = height/horizontal distance.
Elevation and depression are treated as unrelated angles, and the alternate-angle relationship created by the horizontal line through the eye is not visualized.
What to do instead
Draw a horizontal line through the observer's eye and mark the depression below it. Mark the equal alternate angle at the object, label opposite and adjacent sides, then choose the ratio. Never place the depression angle at the ground point.
For grouped data, locates the median class using N/2 but then substitutes the class's lower limit and frequency without the cumulative frequency of the previous class.
The median formula is memorized as a string of symbols without understanding that the fraction measures position inside the median class.
What to do instead
Build a cumulative-frequency column, find N/2, and identify the first class whose cf reaches N/2. Then use L + [(N/2 − cf before)/f] × h, checking that the answer lies inside the median class.
Describes an enlargement as 'enlarged by 2' only, omitting the centre, or describes a rotation without giving the angle and direction.
The transformation is treated as a size change rather than a complete mapping, and full-description mark requirements are not practised.
What to do instead
Always give the full description: enlargement needs centre and scale factor; rotation needs centre, angle and direction; reflection needs the mirror line; translation needs a column vector. State the type first, then all required data.
In the section formula, swaps the ratio and uses (m x₁ + n x₂)/(m + n) for the point dividing AB in the ratio m:n.
The formula is recalled without linking m to the segment adjacent to A, so the coordinates are paired with the wrong ratio part.
What to do instead
Mark AP:PB = m:n on the diagram. The part adjacent to A multiplies B's coordinate: x = (m x₂ + n x₁)/(m + n). Test with m = n to confirm the result reduces to the midpoint formula.