KEY TO ENJOY LEARNING MATHS

🌟 TACHS Mathematics Studio

Test for Admission into Catholic High Schools • Complete Math revision • Topic practice • 50-question TACHS-style mock • scoring • diagnosis • worked solutions • printable teacher records

Important: Official 2026 TACHS materials publish the Mathematics content areas and four-choice format, but do not publish an exact Mathematics question count or topic weighting. This page therefore uses an original 50-question TACHS-style practice simulation for training, not an official TACHS paper.

📘 Complete TACHS Mathematics Study Map

Official domains: Number Sense & Operations • Algebraic Patterns & Connections • Data Analysis / Probability / Statistics • Geometry • Measurement

1. Number Sense & Operations

Whole numbersIntegersFractionsDecimalsPercentsRatioRatesFactorsMultiplesExponentsOrder of operationsEstimation

Percent = part ÷ whole × 100

2. Algebraic Patterns & Connections

ExpressionsSubstitutionEquationsPatternsSequencesCoordinate relationshipsWord problems

Perform the same operation on both sides of an equation.

3. Data / Probability / Statistics

TablesGraphsMeanMedianModeRangeProbability

Probability = favorable outcomes ÷ total equally likely outcomes

4. Geometry

AnglesTrianglesQuadrilateralsPolygonsCirclesCoordinatesSymmetry

Triangle angle sum = 180° • Quadrilateral angle sum = 360°

5. Measurement

LengthPerimeterAreaVolumeTimeMoneyConversionsScale

Rectangle A = l × w • Triangle A = ½bh • Prism V = lwh

Fast-Test Skills

Estimate firstEliminate choicesCheck unitsBack-substituteUse benchmarksAnswer every item

TACHS guidance says wrong answers are not penalized, so an educated guess is better than leaving an item unanswered.

Practice blueprint: 50 original questions per mock across all five official domains. The distribution is for balanced teaching practice and is not an official TACHS weighting.

Suggested Final-Week Plan

Day	Focus	Target
1	Number sense, fractions, decimals, percent, ratio	25–30 questions + error review
2	Algebra, patterns, equations, word problems	25–30 questions + speed
3	Geometry, measurement, statistics, probability	25–30 questions
4	Full 50-question TACHS-style mock	Complete + diagnose weak topics
5	Weak-topic repair + light revision	Accuracy before speed

✏️ Topic Practice Generator

TopicDifficultyQuestions

⏱️ Full TACHS-Style Mathematics Mock

Practice simulation: 50 questions • 4 choices each • Suggested 40-minute training timer. This timer and question count are practice settings, not official 2026 TACHS published limits.

40:00

⚡ Final Revision Sheet

Fraction Benchmarks

½ = 0.5 = 50%

¼ = 0.25 = 25%

¾ = 0.75 = 75%

⅕ = 0.2 = 20%

⅛ = 0.125 = 12.5%

Fast Percent Methods

10%: divide by 10

5%: half of 10%

25%: divide by 4

50%: divide by 2

75%: take ¾

Geometry

P rectangle = 2(l + w)

A rectangle = lw

A triangle = ½bh

C circle = 2πr

A circle = πr²

Statistics

Mean = total ÷ count

Median = middle after ordering

Mode = most frequent

Range = greatest − least

Algebra

Distribute.

Combine like terms.

Undo operations in reverse order.

Check by substitution.

Exam Strategy

Read exactly what is asked.

Estimate before calculating.

Eliminate impossible choices.

Watch units.

Answer every item.

🏆 Score & Diagnostic Report

Complete a full mock to create a topic-by-topic diagnostic report.

Original educational practice material • Not affiliated with or endorsed by TACHS • keytoenjoylearningmaths.blogspot.com

🌈⚡Key To Enjoy Learning Maths☘🌈