How to Prepare for AST Math A (分科測驗數學甲): A 12-Week Study Plan

In July 2026, half of the candidates on the Advanced Subjects Test Math A paper scored 25 levels or less out of 60. With that year's level width, 25 levels meant a raw score of at most 38.63 out of 100. The middle of the field, in other words, lost more than 60 of the 100 points, and the maximum of 60 levels went to anything above 91.17.

That is Taiwan's Advanced Subjects Test (分科測驗, often called AST) Mathematics A (數學甲), the university entrance paper run every July by the College Entrance Examination Center (大學入學考試中心, CEEC). It has the widest syllabus of any 大考 mathematics paper, calculus included, and its scores feed placement admission (分發入學). This guide covers the format, how raw points become levels, what grade 12 adds to the GSAT material, and a 12-week plan for the weeks before July 10, 2027.

One Paper, 80 Minutes, No Calculator

The 2027 exam regulations set the AST for July 10 and 11, 2027. Math A is on Saturday, July 10, from 14:00 to 15:20; Math B is on Sunday, July 11, at the same time. Every AST subject lasts 80 minutes and is marked out of 100. Registration runs from June 3 to June 15, 2027, test rooms are published on July 6, and score notices go out on July 29.

No calculator is allowed: devices with a calculating function are on CEEC's list of items you may not bring to your seat. A ruler, set square, protractor and compass are allowed, and the paper ends with a page of reference formulas and values. In 2026 it held series sums, the cosine rule, standard deviation and the regression line, √2, √3, π, the common logarithms of 2, 3, 5 and 7, and the mean and variance of the binomial and geometric distributions. Bringing smart glasses to your seat voids that session's score, whether you use them or not.

CEEC's exam description for the mathematics papers, in force since the 2025 sitting, fixes only the proportions: Part I (single-choice, multiple-select and fill-in) carries about 70 to 76% of the points, and Part II (mixed and written question sets) about 24 to 30%. This is how the July 2026 Math A paper was built:

In 2026, one Part II set defined a polynomial through an integral and ended with a 6-point maximum and minimum question; the other used two planes in space and ended with a proof that a triangle is equilateral. Written answers without the calculation or reasoning lose marks.

From Raw Points to the 60-Level Scale

AST results are reported in levels from 0 to 60. CEEC averages the raw scores of the top 1% of candidates in the subject and divides by 60 to get the level width (級距), and each level is one width of raw score. In 2026 the Math A width was 1.54517, and CEEC's 2026 statistics give these five standards (五標) for the 20,785 candidates who sat it:

Only 114 candidates, 0.55%, reached 60 levels. The raw ranges come from the published level table and move every July with the top 1%.

The useful part is the exchange rate. At a width of about 1.5, one 6-point item is worth almost 4 levels and one 8-point multiple-select item more than 5. Two extra multiple-select items move a candidate about 10 levels, from the average standard to just below the front standard. Reliable routine items matter far more than the last item of Part II.

Scoring Rules That Change How You Answer

Multiple-select: every option is an answer. Each option is judged on its own, marked or not. With n options and k of them wrong, you keep (n − 2k)/n of the item, never below zero. On a five-option, 8-point item, one wrong option leaves 4.8 points, two leave 1.6, three leave nothing, and so does a blank item. Decide true or false for all five options every time.

Fill-in: every blank or nothing. The answer format is printed, and you mark it digit by digit, sign included. It scores only if every blank is right, but a wrong answer carries no deduction, so never leave one empty. If your fraction does not fit the printed boxes, recheck the working.

Part II: the working is graded. CEEC publishes the marking principles for the written items (非選擇題評分原則) next to each paper in its past-paper archive. Read them for two or three recent papers to see which steps earn credit.

What Math A Adds to the GSAT Core

Math A tests the grade 10 required course, the grade 11 A-track course and the grade 12 elective Math A (數學甲). The first two are the GSAT Math A material, covered in the GSAT guide, and the 2026 space-planes set shows they still earn points in July. This table maps the grade 12 items in the exam description to what to drill, with the limits CEEC writes down:

The calculus is deliberately polynomial, so the difficulty comes from combining ideas, as in the 2026 integral-defined polynomial, not from hard antiderivatives. The reference page already gives the binomial and geometric means and variances; spend the time on setting the variable up. The derivatives guide and the integrals guide build both ideas from rates and accumulation, and complex numbers in polar form covers De Moivre's theorem.

Math A or Math B: Let Departments Decide

Since 2025 the AST has offered two mathematics subjects. Math B (數學乙) covers grade 10, the grade 11 content shared by the A and B tracks, and the grade 12 Math B elective with a lighter calculus unit (polynomial derivatives, integrals of linear and quadratic functions). Candidates choose their subjects freely, and each department decides which ones it counts in placement admission. Check what your realistic departments count and sit that; the papers fall on different days in 2027, so you can sit both.

The 12-Week Plan

The plan covers the 12 weeks from Saturday, April 17, to July 10, 2027. Before week 1, sit one Math A paper from 2022 or later cold: 80 minutes, no calculator, marked strictly with the official key and marking principles. Sort every lost point into concept gaps, method gaps, arithmetic slips, reading and time problems, or format errors, and weight the blocks toward the bins that cost most. Keep every session calculator-free and end it with ten minutes of mixed items from earlier blocks; spaced repetition explains why.

Weeks 1 and 2: limits, series and functions. Sequence limits, the squeeze theorem, infinite geometric series, then function limits, continuity, the intermediate value theorem, and composite, inverse, odd and even functions. Start with the limits guide.

Weeks 3 and 4: differentiation. The limit definition, tangent lines, the product, quotient and chain rules, higher derivatives, monotonicity, concavity, inflection points, linear approximation and optimization, with cubics as the main case. Practise on the derivatives topic page.

Weeks 5 and 6: integration. Riemann sums, polynomial antiderivatives, the fundamental theorem, area, displacement and total change, average value, slicing and solids of revolution. Practise on the integrals topic page.

Weeks 7 and 8: complex numbers and conics. Polar form, De Moivre's theorem, n-th roots, conjugate imaginary roots, then the three conics in standard form and the parametric ellipse.

Weeks 9 and 10: probability and grade 11 refresh. Discrete random variables, the binomial and geometric distributions, then conditional probability, space vectors, planes and lines in space, and matrices. From week 3 on, practise the format habits daily: all five options judged, a format check on each fill-in, a full line of reasoning for each written step.

Weeks 11 and 12: full papers. Sit complete Math A papers from 2022 onward at 14:00 if you can, mark them with the official key and marking principles, and redo every lost item from a blank page the next day. In the last days, add nothing new.

Where Math Zen Fits, and What It Does Not Cover

Math Zen has an AST Math A (分科測驗) path that groups its general problem templates by the syllabus areas above, from polynomials, vectors and matrices to limits, complex numbers, conics, derivatives, integrals and the binomial distribution. Difficulty adapts as you answer, which suits the short calculator-free sessions the plan asks for.

Its limits matter. The path has no templates in the AST's own style, and every item takes a single answer, so it cannot rehearse multiple-select marking, the fill-in format or written proofs. Riemann sums, linear approximation, volume by slicing, average value, imaginary roots of polynomials, foci and eccentricity of conics, and the geometric distribution beyond simple cases have little or no practice there yet. Some derivative and integral drills use exponential and trigonometric functions, beyond the polynomial calculus Math A asks for; treat those as extra. Official papers remain the core of the plan. For the January papers, see the GSAT (學測) path.

Exam-Day Pacing for 80 Minutes

A suggested budget, not a CEEC rule; test it on practice papers.

• Minute 1: read both Part II setups.
• About 42 minutes for Part I: 11 items, roughly 4 minutes each, less on single-choice, more on multiple-select.
• About 28 minutes for Part II, written working included.
• The last 9 minutes: marked items, a format check on every fill-in, and any blank still on the answer sheet.

When an item has taken twice its share, mark it and move on.

The Bottom Line

AST Math A is one 80-minute, calculator-free paper from grade 10 to the grade 12 Math A elective, on a 60-level scale where one Part I item is worth four or five levels. The calculus is polynomial and conceptual, the multiple-select and fill-in rules punish carelessness, and Part II pays for written reasoning. Choose Math A or Math B from what your departments count, start with a diagnostic paper, and finish with full official papers at exam time.