UAE TLS Mathematics Test common mistakes
UAE TLS Mathematics Test · Understand the traps and how to avoid them.
Evaluates a mixed addition/subtraction expression strictly left-to-right only when it suits them, or removes parentheses without distributing the negative, e.g. computes 8 − (3 + 2) as 8 − 3 + 2 = 7.
Overgeneralises the idea that operations are performed left-to-right, or treats a minus sign as detachable from the grouped quantity instead of as multiplication by −1.
What to do instead
Rewrite every subtraction as addition of the negative before simplifying: 8 − (3 + 2) = 8 + (−3) + (−2). Then evaluate and check with an estimate.
Solves x² = 3x by dividing both sides by x and reports only x = 3, losing x = 0.
Cancellation is treated as always valid, and the possibility that the divisor equals zero is not checked.
What to do instead
Move all terms to one side and factor: x² − 3x = x(x − 3) = 0, so x = 0 or x = 3. Explicitly state any variable restrictions before dividing.
Substitutes the diameter into A = πr² or C = 2πr as though it were the radius, e.g. uses r = 10 for a circle with diameter 10.
Formula recall is strong but the candidate does not pause to identify which circle measurement the problem supplies.
What to do instead
Before substituting, write a labelled line: diameter = ___ so radius = diameter ÷ 2. Then substitute and check that the answer has square units for area and linear units for circumference.
Calculates sin(30) or an inverse trigonometric value while the calculator is in radian mode, or mixes degree and radian measures within one problem.
Calculator mode is not checked, and the candidate relies on the display rather than on known reference values.
What to do instead
Check the mode indicator before every trigonometric calculation. For common angles, compare the result with exact values such as sin 30° = 0.5; if the display disagrees, reset the mode.
Reads P(A|B) as P(B|A), or multiplies P(A)P(B) for events that the problem shows are not independent.
Everyday language such as 'given that' is converted into the wrong conditional direction, and independence is assumed whenever two events are mentioned.
What to do instead
Write the conditional probability formula explicitly, label the given event, and use a two-way table or tree diagram. Check independence by comparing P(A|B) with P(A), not by assuming it.
Differentiates a composite function by differentiating only the outer function, e.g. writes d/dx sin(3x²) = cos(3x²), omitting the inner derivative.
The candidate pattern-matches the outer function and does not inspect the argument as a separate function.
What to do instead
Name the outer and inner functions first: outer = sin u, inner = u = 3x². Apply the chain rule as outer′(u) · u′, then simplify.
Produces an intermediate value as the final answer, such as giving the area of a rectangle when the question asks for the cost of fencing the perimeter.
Time pressure and strong habitual calculation lead the candidate to stop as soon as a number is obtained rather than rereading the target quantity.
What to do instead
Underline the requested quantity before starting and write it at the top of the working. After calculating, check units, reasonableness, and whether the final line answers the underlined question.
Diagnoses a student's wrong answer as carelessness without identifying the underlying misconception, then reteaches the same procedure unchanged.
The candidate focuses on the incorrect result rather than on the pattern of reasoning that produced it.
What to do instead
Analyse the student's steps, ask the student to explain the rule being used, and compare it with a correct representation. Choose a targeted task that confronts the specific misconception.
Converts area or volume units using the linear factor, e.g. states that 1 m² = 100 cm² or that 1 m³ = 100 cm³.
The candidate applies the familiar linear conversion factor to squared or cubed units without accounting for both or three dimensions.
What to do instead
Convert each dimension separately, or raise the linear factor to the appropriate power: 1 m² = (100 cm)² = 10 000 cm² and 1 m³ = (100 cm)³ = 1 000 000 cm³.
Treats f(x + 1) as f(x) + 1, or interprets the slope and intercept of a linear model without relating them to the context.
Function notation is read as ordinary algebraic distribution, and symbolic parameters are manipulated without checking their meaning.
What to do instead
Substitute the whole expression x + 1 into the function rule, then simplify. For a linear model, state what the slope and intercept mean in context and test with a sample input.