The Complete NBT Mathematics Practice Book
935 questions with full worked solutions, covering every topic the National Benchmark Test draws on — from factorising to differentiation.
No email address, no sign-up, no watermark.
Wrong answers taken apart
Most books tell you the right answer. This one takes the wrong options apart and shows you the specific mistake that produces each — so you recognise the trap before you fall into it. Every one of the 935 questions has a worked solution, and every one of them explains all three wrong options individually — the three mock exams included.
Written in plain language
No assumed knowledge and no showing off. Each solution leads with the idea, walks the steps, and ends with a transferable takeaway you can use on the next question.
Checked by machine, not just proofread
Every one of the 935 questions carries a specification that a computer runs on every build: it re-derives the answer, or checks the facts the answer rests on, and confirms the result is the option marked correct. It also checks the printed options against it, that no two are the same value, and that every wrong option comes from a named mistake — 2 805 accounted for, 1 571 reproduced by machine. The two editions are compared question by question as well.
Chapters
-
00
Study Guide and Formula Sheet
Every formula the test draws on, what you may take in, and a study plan guide -
01
Algebraic Processes
Factorising, equations, inequalities, exponents, surds, logarithms 101 Q -
02
Number Sense
Fractions, percentages, ratio, parity, scientific notation, speed 90 Q -
03
Functions and Graphs
Lines, parabolas, hyperbolas, exponentials, absolute-value graphs 102 Q -
04
Trigonometry
Ratios, special angles, identities, equations, sine and cosine rules 94 Q -
05
Geometry
Angles, triangles, circles, similarity, mensuration, coordinates 93 Q -
06
Data Handling and Probability
Averages, spread, counting, compound probability 65 Q -
07
Financial Mathematics
Interest, depreciation, annuities, hire purchase, exchange rates 65 Q -
08
Sequences and Series
Arithmetic, geometric, sigma notation, sums to infinity 68 Q -
09
Three Full Mock Examinations
Three complete 60-question papers, fully solved 180 Q -
10
Differential Calculus
First principles, rules, tangents, stationary points, optimisation 57 Q -
11
The Challenge Set
Twenty questions harder than the test will ask 20 Q
What the NBT Mathematics test actually is
The National Benchmark Tests are written by prospective university students in South Africa. The Mathematics (MAT) paper is a three-hour, 60-question multiple-choice paper, and you may not use a calculator. Universities use the result for admission and for placement — whether you start in a mainstream course or an extended one.
Two things follow from that format, and this book is built around both. First, since there is no calculator, arithmetic fluency is worth real marks; the mental arithmetic trainer exists for exactly that. Second, because it is multiple choice, the wrong options are designed around specific, predictable mistakes — which is why the chapter solutions dissect all three of them.
What the NBT is, and how it is scored — the longer answer: both tests and the shape of the test day, what you may and may not take in, what the Mathematics paper examines, how your result is reported, and what the national figures look like.
Confirm current dates, fees and arrangements with the official NBT administration before you register. This site is independent and cannot do that for you.
Sharing this book
Please do — with classmates, a study group, a whole school. Teachers are welcome to print it and use it in class. The only things asked are that you pass it on complete and unaltered, and that you link to this page rather than re-uploading the file, so readers always get the corrected version.
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