Exams

What we do

Lessons follow the school's own syllabus. We take the current topic apart, rebuild it from whatever the student already understands, and work examples until the method is theirs rather than copied.

Why it matters

Most difficulty at this age is not the current topic — it is a gap one or two years further back that never got closed. Working alongside the class makes that gap visible early, while it is still small enough to fix quickly.

Topics

• Place value & operations
• Fractions & decimals
• Ratios & percentages
• Expressions & equations
• Geometry & measurement
• Word problems

What we do

The student works, I watch where the reasoning stalls, and we fix that point. Homework gets finished, but the objective is that the next set is easier without me.

Why it matters

Homework is where confidence is won or lost. A student who dreads it stops attempting anything unfamiliar, and that habit costs far more over a year than the individual assignments do.

Topics

• Reading the question properly
• Choosing a method
• Showing working clearly
• Checking an answer
• Recovering from a wrong start

What we do

Given each spring across grades 3 to 8, split over two sessions, mixing multiple-choice with constructed-response questions where the student has to show their work.

Why it matters

Scores feed into middle school placement and accelerated program eligibility, and in some districts into high school admissions. It is also the first exam where gaps in arithmetic and fractions surface plainly.

Topics

• Operations & algebraic thinking
• Fractions & decimals
• Ratios & proportional relationships
• Expressions & equations
• Geometry & measurement
• Statistics & probability

What we do

Taken in 8th grade, three hours split evenly between English and Math. The math half has 57 questions — 52 multiple-choice and 5 grid-in — with no calculator allowed.

Why it matters

The SHSAT is the only criterion for Stuyvesant, Bronx Science, Brooklyn Tech and the rest; grades and recommendations play no part. Competition is severe, so the gap between a strong score and a qualifying one usually comes down to speed and accuracy under time pressure.

Topics

• Number theory & operations
• Ratios, rates & percentages
• Algebra & word problems
• Geometry & coordinate geometry
• Probability & statistics
• Pacing without a calculator

What we do

A computer-adaptive test paired with a performance task. Questions adjust to the student's answers, and the performance task asks for a sustained, written mathematical argument.

Why it matters

Because it adapts, pacing and confidence matter as much as content — an early run of wrong answers steers the whole test easier and caps the achievable score. The performance task also rewards explanation, which is rarely practised in class.

Topics

• Concepts & procedures
• Problem solving
• Communicating reasoning
• Modelling & data analysis
• Adaptive-test pacing

What we do

Progress monitoring administered in autumn, winter and spring, so the same student sits it repeatedly and the results are read as a trajectory rather than a single mark.

Why it matters

Because it runs three times a year, an autumn result is an early warning with two full terms left to act on it. Families who treat the first sitting as information rather than a verdict tend to see the largest movement by spring.

Topics

• Number sense & operations
• Algebraic reasoning
• Geometric reasoning
• Data analysis & probability
• Fractions & proportional reasoning

What we do

Given each spring in grades 3 to 8 and again for high school courses, aligned to the Texas TEKS standards and delivered online with a mix of question formats.

Why it matters

STAAR results carry real weight in Texas — they inform promotion decisions in some grades and follow the student's record. The test also leans on multi-step problems in context, which is a different skill from the drill work most classes practise.

Topics

• Numerical representations
• Computations & algebraic relationships
• Geometry & measurement
• Data analysis & personal financial literacy
• Multi-step problems in context

What we do

Linear and quadratic equations, systems, functions and their graphs, exponential relationships, and the statistics strand that accompanies them.

Why it matters

A shaky Algebra I is the single most common reason students struggle in Geometry and Algebra II two years on. Those concepts are not retaught later — they are assumed.

Topics

• Linear equations & inequalities
• Systems of equations
• Quadratics & factoring
• Exponential functions
• Function notation & transformations
• Statistics & data modelling

What we do

Congruence and similarity, formal proof, circles, right-triangle trigonometry, coordinate geometry and solid geometry.

Why it matters

Geometry asks for deductive reasoning rather than computation, which is a genuinely different skill. It also builds the proof-writing and spatial habits that later calculus quietly relies on.

Topics

• Congruence & similarity
• Formal proofs
• Circles, arcs & angles
• Right triangle trigonometry
• Coordinate geometry
• Volume & solids

What we do

Polynomial, rational, exponential and logarithmic functions, trigonometry and the unit circle, sequences and series, complex numbers, and statistical inference.

Why it matters

This is the course that decides whether a STEM track stays open. It is also required for an Advanced Regents diploma, which competitive colleges look for.

Topics

• Polynomial & rational functions
• Exponential & logarithmic functions
• Trigonometry & the unit circle
• Sequences & series
• Complex numbers
• Statistical inference

What we do

Function families and their behaviour, a full treatment of trigonometry and identities, polar and parametric representations, vectors, and an introduction to limits.

Why it matters

Students rarely struggle in Calculus because of calculus — they struggle because their algebra and trigonometry are not automatic. Precalculus is where that gets fixed, or does not.

Topics

• Function families & transformations
• Trigonometric identities
• Polar & parametric forms
• Vectors
• Sequences & series
• Introduction to limits

What we do

AB covers limits, differentiation and integration with their applications. BC adds integration by parts and partial fractions, improper integrals, parametric and polar calculus, and infinite sequences and series.

Why it matters

A 4 or 5 earns college credit at most universities — real money and a full semester saved. BC reports an AB subscore alongside it, so a student is never penalised for attempting the harder paper.

Topics

• Limits & continuity
• Differentiation & its applications
• Related rates & optimisation
• Definite & indefinite integrals
• Fundamental Theorem of Calculus
• Series & Taylor expansions (BC)

What we do

Three hours: 40 multiple-choice questions and 6 free-response, one an extended investigative task. Answers must be justified in context, not merely computed.

Why it matters

Students lose most of their marks here not to arithmetic but to incomplete written justification — which is very coachable, and rarely drilled in class.

Topics

• Exploring & describing data
• Sampling & experimental design
• Probability & random variables
• Sampling distributions
• Confidence intervals
• Hypothesis testing

What we do

Rather than a year of algebra then a year of geometry, each year blends all three strands. Common in California and a growing number of districts.

Why it matters

Students moving between an integrated district and a traditional one arrive with the same total knowledge in a different order, and can look badly behind when they are not. Mapping what they have against what the new course assumes clears that up quickly.

Topics

• Linear & exponential relationships
• Geometric congruence & similarity
• Quadratic functions
• Trigonometric ratios
• Probability & statistics
• Modelling across strands

What we do

Three hours each, with multiple-choice and constructed-response sections where partial credit depends entirely on showing clear, correct work.

Why it matters

Passing the Algebra I Regents is a graduation requirement in New York, and all three together are needed for an Advanced Regents diploma. Marks are also lost to presentation as often as to method, which is fixable.

Topics

• Exam-specific question formats
• Showing work for partial credit
• Reference-table fluency
• Timing across sections
• Past-paper practice

What we do

Adaptive across two modules — performance on the first sets the difficulty of the second — running 70 minutes over 44 questions, calculator permitted throughout with Desmos built in.

Why it matters

Math is half the total score and the half that responds quickest to preparation, because the content is narrow and the same question archetypes recur year after year. For scholarship thresholds, a 100-point gain is often entirely achievable.

Topics

• Algebra & linear relationships
• Advanced math: nonlinear functions
• Problem solving & data analysis
• Geometry & trigonometry
• Desmos strategy
• Adaptive-module pacing

What we do

Covers a wider content range than the SAT, including matrices, logarithms and more trigonometry. No adaptive element; difficulty climbs steadily from the first question to the last.

Why it matters

Every U.S. college accepts either test, and most students score meaningfully better on one. The ACT rewards speed and breadth, the SAT care and depth — working out which suits a student is worth more than months of generic prep.

Topics

• Pre-algebra & elementary algebra
• Intermediate algebra
• Coordinate geometry
• Plane geometry
• Trigonometry
• One-minute-per-question pacing

What we do

Functions and their graphs, polynomial and rational expressions, radicals, exponentials and logarithms, systems of equations and matrices.

Why it matters

College Algebra has one of the highest failure rates of any freshman course, and failing it can delay graduation by a year where prerequisites chain. Students who struggle are rarely short of ability — they are short three or four specific high school topics.

Topics

• Functions & their graphs
• Polynomial & rational expressions
• Exponential & logarithmic equations
• Systems & matrices
• Inequalities
• Modelling with functions

What we do

Descriptive statistics, probability, sampling distributions, confidence intervals, hypothesis testing and regression — usually alongside software such as Excel, SPSS or R.

Why it matters

It is required by far more majors than calculus, and it trips up students who are comfortable with arithmetic but new to reasoning under uncertainty. Most of the marks are in interpreting a result, not in producing the number.

Topics

• Descriptive statistics
• Probability distributions
• Sampling & the Central Limit Theorem
• Confidence intervals
• Hypothesis testing
• Correlation & regression

What we do

Limits and continuity, the definition of the derivative, differentiation rules, curve sketching, optimisation, related rates, and an introduction to integration.

Why it matters

The pace jumps sharply from high school, and students who fall behind in the first three weeks — usually on limits — rarely recover unaided, because everything afterward is built on that footing.

Topics

• Limits & continuity
• Definition of the derivative
• Product, quotient & chain rules
• Implicit differentiation
• Related rates & optimisation
• Introduction to integration

What we do

Advanced integration techniques, applications to volume, arc length and work, improper integrals, differential equations, parametric and polar calculus, and infinite sequences and series.

Why it matters

Unlike Calculus I there is no single algorithm that solves everything — the student has to recognise which of a dozen techniques applies. It is the most commonly repeated course in a STEM degree, and the one where tutoring makes the largest difference.

Topics

• Integration by parts & trig substitution
• Partial fractions
• Volume, arc length & work
• Improper integrals & convergence
• Series convergence tests
• Taylor & Maclaurin series

What we do

Unit conversion, dimensional analysis, oral and injectable dosages, IV flow rates and drip factors, weight-based paediatric dosing, and titration.

Why it matters

Most nursing programmes require a very high pass mark and allow only a limited number of attempts, because an arithmetic slip here is a patient-safety issue. The maths itself is not advanced — what it demands is a reliable method and zero careless error.

Topics

• Unit conversion
• Dimensional analysis
• Oral & injectable dosages
• IV flow rates & drip factors
• Weight-based paediatric dosing
• Titration & infusion rates

What we do

Quantitative Reasoning is 21 problem-solving questions in 45 minutes with no calculator. Data Insights adds data sufficiency, table analysis, graphics interpretation and multi-source reasoning, and counts toward the total score on the Focus Edition.

Why it matters

Top programmes publish median scores, and the quant sections are read as a proxy for analytical rigour. The underlying maths is material most applicants already learned — what they need is to relearn it in the specific, trap-laden way the GMAT asks it.

Topics

• Arithmetic & number properties
• Algebra & word problems
• Rates, work & mixtures
• Data sufficiency logic
• Table & graphics interpretation
• Mental math without a calculator