Mie Entrance Mathematics common mistakes
Mie Entrance Mathematics · Understand the traps and how to avoid them.
When solving 3(x − 2) = 4x + 5, expanding only the first term and writing 3x − 2 = 4x + 5, so the final answer comes out one unit off.
The candidate treats the bracket as attached only to the number in front of it, forgetting that the multiplier must reach every term inside. In earlier drill the bracket often contained a single term, so the habit was never corrected.
What to do instead
Before solving, draw an arrow from the multiplier to each term inside the bracket and rewrite the line aloud: '3 times x, 3 times −2.' Do five expansions with two- and three-term brackets daily for a week, then check by substituting the answer back into the original equation.
Solving −2x < 6 by writing x < −3, keeping the inequality sign unchanged after dividing by a negative number.
The rule about flipping the sign is memorised as a sentence without a picture, so it drops out under time pressure. Candidates also confuse it with the rule for moving terms across the inequality.
What to do instead
Re-derive the rule once with numbers: 2 < 4, multiply by −1, get −2 > −4. Then adopt a routine: after isolating x, always ask 'did I multiply or divide by a negative?' and mark the flip with a circled arrow. Verify the boundary value and one interior value in the original inequality.
Adding fractions such as 1/2 + 1/3 by writing 2/5, adding numerators and denominators straight across.
The visual layout invites treating the fraction bar as a separator between two independent numbers. Whole-number addition has been practised far longer, so the automatic response carries over.
What to do instead
Replace every fraction addition with a picture: one half of a cake plus one third cannot be two fifths. Practise converting to a common denominator by listing multiples, and finish by estimating the answer (about 0.8) to catch impossible results.
Answering a 'find the value of x' question with the value of the expression, or stopping after finding x when the question asks for the length of a side or the value of 2x + 1.
The candidate works forward mechanically and treats the first number produced as the goal. Reading of the final demand is skipped because the algebra felt difficult and the relief of solving ends the thinking.
What to do instead
Underline the actual request in the question before starting. After solving, write a one-line answer sentence that names the quantity ('the side length is … cm') and check that the units and magnitude are plausible for the figure or context.
Reading a gradient from a graph by counting squares along the axes rather than dividing the vertical change by the horizontal change, or taking the gradient of a line with negative slope as positive.
The candidate confuses 'how steep it looks' with the ratio rise over run, and the axis scales are assumed equal when one axis is stretched. The sign of the gradient is not connected to the direction of the line.
What to do instead
Always write the two chosen points as coordinates, compute (y2 − y1)/(x2 − x1), and state the scale of each axis first. Check the sign by asking 'as x increases, does y go up or down?' and match the answer against the drawn line.
Using a similarity ratio of 1:3 for areas and volumes, so a triangle enlarged three times is said to have nine times the perimeter, or a solid tripled in length is said to have three times the volume.
The candidate applies the linear scale factor to every measurement. The separate rules for length, area and volume are remembered as one rule, and there is no mental model of squares and cubes behind the factors.
What to do instead
Build the rule from a square and a cube: double the side of a square and draw four copies; double the edge of a cube and count eight small cubes. Record the ladder length k, area k², volume k³ and test it on one numerical example before answering.
Applying the circle theorems with the wrong arc, for example saying the angle at the centre equals the inscribed angle on the same arc, or treating opposite angles of a cyclic quadrilateral as equal rather than supplementary.
Theorem statements are recalled as isolated sentences without the diagram that gives them meaning, and the candidate does not identify which arc each angle subtends before substituting.
What to do instead
Redraw the figure and colour the arc that each angle stands on. Write the theorem next to the relevant angle pair before calculating. Keep a one-page sheet where each theorem is a small labelled sketch, and rehearse identifying the arc first, the rule second.
Computing the surface area of a prism or cylinder by adding only the two end faces, or using the diameter instead of the radius in the circle formulas.
The candidate pictures the solid as flat and forgets the lateral surface, and the words radius and diameter are read quickly without checking which is given.
What to do instead
Before calculating, sketch the net of the solid and number each face. Write 'r = d ÷ 2' as an explicit line whenever a diameter appears. Estimate the answer roughly (a cylinder's curved surface is about three times the rectangle around it) to catch a missing face.
Treating mutually exclusive events as independent and multiplying their probabilities, for example giving the chance of drawing a red then a blue marble with replacement as the product of the separate probabilities when the draws are without replacement.
The multiplication rule is over-applied because the distinction between 'and' and 'or', and between with and without replacement, is not tied to a physical picture of the bag changing.
What to do instead
For every probability question, state the sample space and whether items are returned. Draw the tree diagram with the second-branch denominators updated. Add the branches for 'or' and multiply along a path for 'and', then check that all branch probabilities sum to one.
Writing a 'prove that' answer as a numerical example, such as showing that 3² + 4² = 5² and concluding that the statement holds for all right-angled triangles.
The candidate has practised calculation far more than deduction and does not distinguish verifying one case from proving a general claim. The expected structure of a proof (given, construction, reasoning, conclusion) has never been made explicit.
What to do instead
Practise the template: state what is given, what must be shown, the construction or known theorem used, each step with a reason, and a closing sentence. Learn one counterexample kills a general claim, while one example never proves it, and label each line 'given', 'theorem' or 'reasoning'.