SHSAT Drills has two halves. The first is 25 timed practice tests— 19 full-length and 6 shorter mixed reviews — that mirror the real exam's structure and pacing. The second is a Practice section built for targeted repetition: 89 concept-subtopic drills, one per skill, plus 37 technique drills that train specific speed skills and the classic traps that cost points.
Coverage spans all seven SHSAT-8 math reporting categories. We built the list of subtopics by auditing publicly-released NYC DOE SHSAT practice forms (2018–2024) question-by-question, cross-checked against community-maintained topic lists (see Sources). Every subtopic below has real, released-exam questions behind its inclusion in the taxonomy.
All questions on this site are original — written or generated in the style of the SHSAT, not copied from any real or released exam. What we borrowed from the released forms is the shapeof what's tested, not the questions themselves.
The SHSAT is now a computer-based exam, and not every question is multiple choice. About a quarter of the real math section is made up of technology-enhanced items: mostly type-in questions (you enter a number or fraction) and multi-selectquestions (choose more than one answer), plus a smaller number of drag-and-drop and plot-a-point interactions. Our practice includes type-in and multi-select questions so those formats feel familiar. For the drag-and-drop and plotting tools — and the exact on-screen interface — use the NYC DOE's own free SHSAT practice portal and its Student Readiness Tool, which run the real test software.
Writing & simplifying ratios · Equivalent ratios & ratio tables · Solving proportions · Unit rates · Constant of proportionality · Proportional relationships & graphs · Scale drawings, maps & models · Dividing a quantity in a ratio · Combining ratios via a shared quantity · Ratios as fractions of a whole · Unit conversion by proportion · Comparing ratios & rates
Integer operations · Fraction & mixed-number arithmetic · Decimal arithmetic & place value · Fraction/decimal/percent equivalence & ordering · Number line representation · Order of operations · Exponents & powers · Square & cube roots, radicals · Scientific notation · Absolute value · Reciprocal & unit-fraction reasoning · Primes & prime factorization · GCF & LCM · Divisibility, factors & multiples · Number properties & even/odd rules · Rounding & estimation
Evaluating expressions · Simplifying expressions · Translating words to expressions · One-variable linear equations · Multi-step equations · Literal equations & rearranging formulas · Linear inequalities · Systems of equations · Slope · Graphing lines & slope-intercept form · Proportional vs. linear relationships · Patterns & sequences · Consecutive-integer setups
Perimeter & circumference · Area of 2D shapes · Volume of 3D solids · Surface area & nets · Cross-sections & slicing · Angle relationships · Parallel lines & transversals · Angles in triangles & polygons · Pythagorean theorem & right triangles · Similar figures · Congruent figures · Transformations · Coordinate geometry · Segment lengths & midpoints · Composite & shaded regions · Triangle Inequality
Measures of center & spread · Weighted & combined averages · Reading data displays · Stem-and-leaf & box plots · Outliers & their effect · Two-way tables · Set logic, Venn & inclusion-exclusion · Simple probability · Compound probability · Fundamental counting principle · Permutations & combinations · Sampling & inference
Percent of a number · Percent/fraction/decimal conversion · Finding the whole · Percent increase & decrease · Discount & markup · Tax & tip · Simple interest · Percent comparison · Successive percent changes · Multi-step percent problems
Distance, rate & time · Unit pricing & best buy · Average rate · Work-rate problems · Mixture problems · Multi-step arithmetic word problems · Age problems · Money & cost problems · Proportional word problems · Rate conversion
Alongside the 89 concept subtopics, 37 technique drills target two things that are easy to overlook when you only study concepts: fluency (computations you need to do fast and correctly under time pressure) and error patterns(the specific mistakes a question is designed to bait — the kind that's obvious in hindsight but easy to fall for live).
SHSAT Drills is not affiliated with or endorsed by the NYC Department of Education or any specialized high school. See our Sources page for exactly what we used to build this coverage map.