United States
Hong KongA worked Mathematics question
Three worked items, all ours. Each one shows where its wrong options come from: stopping a step short, using the neighboring formula, and slipping a decimal place. Every distractor on this subtest is a real calculation, which is why finding your answer in the list is not confirmation.
All three questions below were written by us against the Mathematics competencies in Section 82, which Rule 6A-4.0021 incorporates. None is an FTCE question and we have not seen one, because the official samples are in the vendor's Test Information Guides and those block automated access.
- Subtest
- Mathematics (828)
- Items
- 35 in 100 minutes
- Per item (ours)
- 2.86 minutes, the loosest clock on the test
- Cut
- At most 63% correct, so at most 22 of 35
- Competencies
- 4, covering 21 skills
- Supplied
- An on-screen calculator and a reference sheet
Question one: the one-step-short trap
If 3x + 7 = 22, what is the value of 2x?
- 5
- 10
- 15
- 30
Nothing about choosing option A feels like a mistake. The working was right, the number is clean, and there it is in the list. That is precisely why it is the largest single family of wrong answers on this subtest.
The defense costs three seconds. After you compute, look back at the last clause of the stem and check that the quantity you found is the quantity it named. Not the topic. The quantity.
Question two: the neighboring formula
A square classroom rug measures 10 feet on each side. A school orders binding tape to run around the rug's edge, plus 5 extra feet for the corners and overlap. How many feet of tape are needed?
- 20 feet
- 40 feet
- 45 feet
- 100 square feet
Option D is worth more attention than it looks. Mixed units in an option list are the cheapest elimination available on this subtest and most candidates never glance at them. If three options are lengths and one is an area, the area is gone before you compute anything.
The wider pattern is the neighboring formula: area offered for perimeter, circumference for area, mean for median. Both formulas sit side by side on any reference sheet, which is why the supplied sheet does not help here. The item is about selection, not recall.
Question three: place value
A candidate answers 21 of the 30 questions on a subtest correctly. What percentage of the questions did the candidate answer correctly?
- 7%
- 9%
- 30%
- 70%
Estimating first kills options A and B instantly. Twenty-one out of thirty is clearly most of the questions, so any answer under half is wrong before you calculate. That habit is worth more on this subtest than any formula, and it costs about two seconds.
70% is what FLDOE publishes as the maximum percentage of correct answers needed to reach a scaled 200 on the Reading subtest, which is 21 of its 30 items on our arithmetic. It is the highest cut of the three multiple-choice subtests. The published figures are maximums, so a harder version can pass on fewer.
What the three have in common
Every wrong option above is a real calculation. Somebody's working produces each one, and in most cases that working was mostly correct. There are no silly options, because a silly option only helps candidates who do not know the material.
So the rule follows directly: your answer appearing in the list is not evidence. It tells you that your result was one an item writer anticipated, which is as consistent with a known mistake as with a correct method.
Use the clock you actually have
Mathematics allows 2.86 minutes an item on our arithmetic, against 1.33 in English Language Skills. More than twice as long. Candidates who fear this subtest tend to rush it, which is the wrong instinct on the one subtest with room to spare, and rushing is exactly what produces all three errors above.
Estimate before computing. Check the quantity after. Look at the units in the options. None of that is mathematics and all of it is marks.
Common questions
Are these real FTCE math questions?
No. All three were written for this site against the published Mathematics competencies. Official sample items sit in the vendor's Test Information Guides, which block automated access, so nothing here reproduces or paraphrases an FTCE question.
Why is my wrong answer always one of the choices?
Because distractors are built from real calculations. Each wrong option is what a specific common mistake produces, most often stopping one step short of what the question asked for. Finding your answer in the list confirms nothing.
What is the most common error on FTCE Mathematics?
Solving for the wrong quantity: finding x when the stem asked for 2x, or a radius when it asked for a diameter. The arithmetic is correct and the result is in the option list, so nothing about the experience signals a mistake.
How can units help me eliminate options?
An option carrying different units cannot answer the question. If a stem asks how many feet of tape and one option is in square feet, that option is an area and it is gone without any calculation. It is the cheapest elimination on the subtest.
How many Mathematics questions do I need right to pass?
At most 22 of 35, on our arithmetic from FLDOE's published maximum of 63% correct. That leaves room for 13 misses. Because the published percentage is a maximum rather than a fixed threshold, a harder version may pass on slightly fewer.