BioMedical Admissions Test (BMAT) Section 2: Scientific Knowledge and Applications — Mathematics Syllabus

Section 2: Scientific Knowledge and Applications — Mathematics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Section 2: Scientific Knowledge and Applications — Mathematics in BioMedical Admissions Test (BMAT), not a summary of it.

1. 1

   Number and Algebra

   3 topics

   • Core number skills
     • Fractions, decimals and percentages
     • Ratio and proportion
     • Indices and standard form
   • Algebraic manipulation
     • Expanding and factorising
     • Solving linear and quadratic equations
     • Simultaneous equations
   • Sequences and formulae
     • Substitution and rearrangement
     • Arithmetic sequences
2. 2

   Geometry and Measures

   3 topics

   • Area, surface area and volume
     • Standard 2D and 3D shapes
   • Pythagoras and trigonometry
     • Right-angled triangle problems
     • Sine, cosine and tangent ratios
   • Angles and shape properties
     • Angle rules and polygons
3. 3

   Statistics and Probability

   3 topics

   • Averages and spread
     • Mean, median, mode and range
   • Data representation
     • Frequency tables and charts
   • Probability
     • Single and combined events
     • Tree diagrams and expected outcomes
4. 4

   Speed and Accuracy under Exam Conditions

   3 topics

   • Mental and rapid calculation
     • Estimation and approximation
   • Non-calculator technique
     • Efficient working without a calculator
   • Applying maths to science questions
     • Cross-section calculations in biology, chemistry and physics

Section 2: Scientific Knowledge and Applications — Mathematics flashcards for BioMedical Admissions Test (BMAT)

23 of 50 cards from the Section 2: Scientific Knowledge and Applications — Mathematics deck — real questions with worked answers.

1. State the standard order of operations (BIDMAS/BODMAS).

   Brackets, Indices (powers/roots), Division and Multiplication (left to right), then Addition and Subtraction (left to right). Evaluate $6 + 2 \times 3^{2}$ as $6 + 2 \times 9 = 24$.

2. What is the product rule for indices, and give an example?

   $a^{m} \times a^{n} = a^{m+n}$. Example: $2^{3} \times 2^{4} = 2^{7} = 128$.

3. What is the quotient rule for indices?

   $\dfrac{a^{m}}{a^{n}} = a^{m-n}$. Example: $\dfrac{5^{6}}{5^{2}} = 5^{4}$.

4. What is the power-of-a-power rule for indices?

   $(a^{m})^{n} = a^{mn}$. Example: $(3^{2})^{4} = 3^{8}$.

5. Express a negative index and a fractional index in terms of roots/reciprocals.

   $a^{-n} = \dfrac{1}{a^{n}}$ and $a^{\frac{m}{n}} = \sqrt[n]{a^{m}} = \left(\sqrt[n]{a}\right)^{m}$. Also $a^{0} = 1$ for $a \neq 0$.

6. How do you convert a recurring decimal such as $0.\overline{36}$ to a fraction?

   Let $x = 0.363636\dots$, so $100x = 36.3636\dots$. Subtract: $99x = 36$, giving $x = \dfrac{36}{99} = \dfrac{4}{11}$.

7. Define a prime number and give the prime factorisation of $84$.

   A prime has exactly two distinct positive factors: $1$ and itself. $84 = 2^{2} \times 3 \times 7$.

8. How do you find the HCF and LCM from prime factorisations?

   HCF: multiply the lowest power of each shared prime. LCM: multiply the highest power of every prime appearing. For $12 = 2^{2}\times3$ and $18 = 2\times3^{2}$: $\text{HCF}=2\times3=6$, $\text{LCM}=2^{2}\times3^{2}=36$.

9. What is standard form (scientific notation) and write $0.00042$ in it?

   A number written as $a \times 10^{n}$ where $1 \leq a < 10$ and $n$ is an integer. $0.00042 = 4.2 \times 10^{-4}$.

10. How do you find a percentage change?

    $\text{Percentage change} = \dfrac{\text{new} - \text{original}}{\text{original}} \times 100\%$. A rise from $40$ to $50$ is $\dfrac{10}{40}\times100 = 25\%$.

11. What is the multiplier for compound interest, and the formula for the final amount?

    For rate $r\%$ per period over $n$ periods: amount $= P\left(1 + \dfrac{r}{100}\right)^{n}$. To reverse, divide by the multiplier.

12. Expand $(a + b)(c + d)$ and state the rule used.

    $(a+b)(c+d) = ac + ad + bc + bd$ (expand each term in the first bracket across the second; FOIL for two binomials).

13. State the three key algebraic identities (perfect squares and difference of two squares).

    $(a+b)^{2} = a^{2} + 2ab + b^{2}$; $\;(a-b)^{2} = a^{2} - 2ab + b^{2}$; $\;a^{2} - b^{2} = (a+b)(a-b)$.

14. Factorise $x^{2} - 7x + 12$.

    Find two numbers multiplying to $+12$ and adding to $-7$: $-3$ and $-4$. So $x^{2} - 7x + 12 = (x-3)(x-4)$.

15. State the quadratic formula for $ax^{2} + bx + c = 0$.

    $x = \dfrac{-b \pm \sqrt{b^{2} - 4ac}}{2a}$.

16. What does the discriminant tell you about the roots of a quadratic?

    Discriminant $\Delta = b^{2} - 4ac$. If $\Delta > 0$: two distinct real roots; $\Delta = 0$: one repeated real root; $\Delta < 0$: no real roots.

17. How do you add two algebraic fractions such as $\dfrac{1}{x} + \dfrac{1}{y}$?

    Use a common denominator: $\dfrac{1}{x} + \dfrac{1}{y} = \dfrac{y + x}{xy}$.

18. Make $r$ the subject of $V = \dfrac{4}{3}\pi r^{3}$.

    $r^{3} = \dfrac{3V}{4\pi}$, so $r = \sqrt[3]{\dfrac{3V}{4\pi}}$.

19. How do you solve a pair of simultaneous linear equations by elimination?

    Scale equations so one variable has equal coefficients, add or subtract to eliminate it, solve for the remaining variable, then back-substitute. E.g. from $2x+y=7$ and $x+y=4$, subtract to get $x=3$, then $y=1$.

20. Simplify $\sqrt{50}$ (surd manipulation).

    $\sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}$.

21. How do you rationalise the denominator of $\dfrac{1}{\sqrt{3}}$?

    Multiply top and bottom by $\sqrt{3}$: $\dfrac{1}{\sqrt{3}} \times \dfrac{\sqrt{3}}{\sqrt{3}} = \dfrac{\sqrt{3}}{3}$.

22. What is the formula for the $n$th term of an arithmetic sequence?

    $a_{n} = a + (n-1)d$, where $a$ is the first term and $d$ is the common difference.

23. What is the formula for the $n$th term of a geometric sequence?

    $a_{n} = a r^{\,n-1}$, where $a$ is the first term and $r$ is the common ratio.

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