KBAT Problems
SPM Mathematics KBAT / HOTS Problem Bank
Original, worked KBAT-style problems, the multi-step, real-situation questions that separate an A from an A+.
Form 4 problems
KBAT Problem: Quadratics in a Real Situation
A worked KBAT-style problem that hides a quadratic inside a real situation, the kind of multi-step question that separates an A from an A+.
KBAT Problem: Making a Decision with Statistics
A KBAT-style problem where you compare two data sets and justify a decision, testing whether you can interpret spread, not just calculate it.
KBAT Problem: Comparing Two Savings Plans
A KBAT-style consumer-maths problem where you compare two savings options and justify the better one, using only the formulae the exam provides.
KBAT Problem: Finding a Shortest Route
A KBAT-style problem using a weighted network, the kind of real-situation graph question that tests whether you can model, not just calculate.
KBAT Problem: A Number-Base Puzzle
A KBAT problem where a real counting situation is set in an unfamiliar base, testing whether you understand place value, not just conversion steps.
KBAT Problem: Classifying with Sets
A KBAT problem where a survey result must be split with a Venn diagram, the challenge is turning words into regions before any counting.
KBAT Problem: Testing an Argument
A KBAT problem where you must judge whether a conclusion really follows from given statements, logic, not calculation.
KBAT Problem: A Region from Constraints
A KBAT problem where real limits (budget, time, capacity) become linear inequalities and a feasible region, modelling before graphing.
KBAT Problem: Reading a Journey from a Graph
A KBAT problem where a speed–time graph tells a real story, you must interpret gradients and areas, not just read points.
KBAT Problem: A Two-Stage Probability
A KBAT problem where two events happen in sequence and a tree diagram organises the outcomes, the challenge is deciding whether the events are independent.
KBAT Problem: Comparing Two Discounts
A KBAT problem where two discount offers must be compared, the trap is that successive percentages do not simply add.
KBAT Problem: Gradient and Area Together
A KBAT problem that needs both the gradient and the area under a graph in one question, connecting two graph skills.
KBAT Problem: Working in Standard Form
A KBAT problem with very large or very small numbers where standard form keeps the arithmetic manageable and the answer sensible.
KBAT Problem: Best Use of a Fixed Length
A KBAT problem about fencing a maximum area with a fixed length, optimisation that leads back to a quadratic.
KBAT Problem: Repeated Growth with Indices
A KBAT problem where a quantity grows by the same factor each period, indices turn repeated multiplication into one clean expression.
KBAT Problem: Is the Answer Even Reasonable?
A KBAT problem that rewards estimation and sanity-checking, deciding whether a computed answer can possibly be right.
KBAT Problem: Working Backwards from a Percentage
A KBAT problem where you know the result after a percentage change and must find the original, the classic reverse-percentage trap.
KBAT Problem: Choosing Between Two Data Plans
An original multi-step KBAT problem that models two mobile data plans as linear cost functions, finds the break-even usage, and turns the maths into a real recommendation.
Form 5 problems
KBAT Problem: Setting Up a Variation
A KBAT-style problem where the hard part is translating a worded real situation into a correct variation relationship before any calculation.
KBAT Problem: Solving with a Matrix
A KBAT problem where two real conditions become simultaneous equations, then a matrix inverse solves them, connecting a worded situation to matrix method.
KBAT Problem: Finding a Height You Cannot Measure
A KBAT problem using angles of elevation to find a height indirectly, the classic real use of trigonometry.
KBAT Problem: A Combined Transformation
A KBAT problem where a shape is moved by two transformations in turn, order matters, and you must describe the single transformation that does the same job.
KBAT Problem: Choosing an Insurance Coverage
A KBAT consumer-maths problem comparing insurance options on cost and coverage, arithmetic plus a justified choice, not financial advice.
KBAT Problem: Working Out Income Tax
A KBAT consumer-maths problem that computes tax after reliefs, multi-step arithmetic set in a real situation, not tax advice.
KBAT Problem: Building a Model from Scratch
A KBAT mathematical-modelling problem where you turn a messy real situation into a clean equation, solve it, then check the answer makes sense.
KBAT Problem: Which Data Set Is More Consistent?
A KBAT grouped-data problem where you compute and compare spread from two frequency tables and justify a conclusion.
KBAT Problem: Scale, Ratio and a Real Map
A KBAT problem using a map scale to move between drawing distance and real distance, proportional reasoning in a real setting.
KBAT Problem: Two Unknowns in a Real Situation
A KBAT problem where a real situation gives two conditions and you solve simultaneous equations to answer it.
KBAT Problem: When One Question Hides Two Topics
A KBAT problem that deliberately combines two chapters, the difficulty is recognising both are needed and switching between them.
KBAT Problem: A Battery Batch Accept-or-Reject Decision
An original KBAT problem that reads a grouped lifespan distribution off its cumulative frequency curve to decide, with working, whether a supplier's batch should be accepted.