The Complete NBT Mathematics Practice Book
915 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.
Every wrong answer explained
Most books tell you the right answer. This one takes each of the three wrong options apart and shows you the specific mistake that produces it — so you recognise the trap before you fall into it.
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 computation
Every numeric claim in the book was verified by computer algebra before it was published — including the distractors, so the explanation of a wrong option is never hand-waved.
Chapters
-
00
Study Guide
Every formula, rule and method, with 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
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 every solution here dissects all three of them.
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