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

24 sample cards from the Section 2: Scientific Knowledge and Applications — Mathematics deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

1. Give the formulas for the circumference and area of a circle of radius $r$.

   Circumference $= 2\pi r = \pi d$; Area $= \pi r^{2}$.

2. What are the arc length and sector area for an angle $\theta$ (in degrees) in a circle of radius $r$?

   Arc length $= \dfrac{\theta}{360}\times 2\pi r$; Sector area $= \dfrac{\theta}{360}\times \pi r^{2}$.

3. Give the volume formulas for a cuboid, a cylinder, and a sphere.

   Cuboid: $lwh$. Cylinder: $\pi r^{2} h$. Sphere: $\dfrac{4}{3}\pi r^{3}$.

4. Give the volume formulas for a cone and a pyramid.

   Cone: $\dfrac{1}{3}\pi r^{2} h$. Pyramid: $\dfrac{1}{3} \times \text{base area} \times h$.

5. What is the curved surface area of a cylinder, and the total surface area of a sphere?

   Cylinder curved surface area $= 2\pi r h$ (total $= 2\pi r h + 2\pi r^{2}$). Sphere surface area $= 4\pi r^{2}$.

6. What is the curved (lateral) surface area of a cone with slant height $l$?

   Curved surface area $= \pi r l$; total surface area $= \pi r l + \pi r^{2}$.

7. State Pythagoras' theorem for a right-angled triangle.

   $a^{2} + b^{2} = c^{2}$, where $c$ is the hypotenuse (the side opposite the right angle) and $a,b$ are the other two sides.

8. Define $\sin$, $\cos$, and $\tan$ for a right-angled triangle (SOHCAHTOA).

   $\sin\theta = \dfrac{\text{opposite}}{\text{hypotenuse}}$, $\cos\theta = \dfrac{\text{adjacent}}{\text{hypotenuse}}$, $\tan\theta = \dfrac{\text{opposite}}{\text{adjacent}}$.

9. Give the exact values of $\sin$, $\cos$, and $\tan$ for $30^{\circ}$, $45^{\circ}$, and $60^{\circ}$.

   $\sin30^{\circ}=\tfrac{1}{2},\,\cos30^{\circ}=\tfrac{\sqrt{3}}{2},\,\tan30^{\circ}=\tfrac{1}{\sqrt{3}}$; $\sin45^{\circ}=\cos45^{\circ}=\tfrac{1}{\sqrt{2}},\,\tan45^{\circ}=1$; $\sin60^{\circ}=\tfrac{\sqrt{3}}{2},\,\cos60^{\circ}=\tfrac{1}{2},\,\tan60^{\circ}=\sqrt{3}$.

10. State the sine rule and the cosine rule for a general triangle.

    Sine rule: $\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}$. Cosine rule: $a^{2} = b^{2} + c^{2} - 2bc\cos A$.

11. What is the area of a triangle given two sides and the included angle?

    $\text{Area} = \dfrac{1}{2}ab\sin C$, where $C$ is the angle between sides $a$ and $b$.

12. What do the interior angles of a triangle and of a quadrilateral sum to?

    Triangle: $180^{\circ}$. Quadrilateral: $360^{\circ}$. In general an $n$-sided polygon has interior angle sum $(n-2)\times 180^{\circ}$.

13. What is the size of each interior and exterior angle of a regular $n$-sided polygon?

    Each exterior angle $= \dfrac{360^{\circ}}{n}$; each interior angle $= 180^{\circ} - \dfrac{360^{\circ}}{n}$. Exterior angles always sum to $360^{\circ}$.

14. State the angle facts for parallel lines cut by a transversal.

    Corresponding angles are equal; alternate angles are equal; co-interior (allied) angles sum to $180^{\circ}$.

15. Name two key circle theorems involving the angle at the centre and the angle in a semicircle.

    The angle at the centre is twice the angle at the circumference on the same arc. The angle in a semicircle is $90^{\circ}$ (subtended by a diameter).

16. How do you calculate the mean, median, and mode of a data set?

    Mean $= \dfrac{\text{sum of values}}{\text{number of values}}$. Median = middle value when data are ordered. Mode = most frequently occurring value.

17. What is the range, and what is the interquartile range (IQR)?

    Range $= \text{highest} - \text{lowest}$. IQR $= Q_{3} - Q_{1}$ (upper quartile minus lower quartile); it measures spread of the middle $50\%$ and is resistant to outliers.

18. How do you estimate the mean from a grouped frequency table?

    Use midpoints $x$ of each class: estimated mean $= \dfrac{\sum f x}{\sum f}$, where $f$ is the frequency of each class.

19. On a box plot, what five values are shown?

    Minimum, lower quartile $Q_{1}$, median $Q_{2}$, upper quartile $Q_{3}$, and maximum. The box spans $Q_{1}$ to $Q_{3}$ with the median marked inside.

20. What does a cumulative frequency graph let you read off, and how do you find the median from it?

    It gives the running total of frequencies. The median is read at the $\dfrac{n}{2}$ value, $Q_{1}$ at $\dfrac{n}{4}$, and $Q_{3}$ at $\dfrac{3n}{4}$, read across to the curve and down to the data axis.

21. In a histogram with unequal class widths, what represents frequency?

    The area of each bar represents frequency; the vertical axis is frequency density, where $\text{frequency density} = \dfrac{\text{frequency}}{\text{class width}}$.

22. State the basic probability formula for equally likely outcomes and the range a probability can take.

    $P(\text{event}) = \dfrac{\text{number of favourable outcomes}}{\text{total number of outcomes}}$, with $0 \leq P \leq 1$. $P(\text{not } A) = 1 - P(A)$.

23. State the AND and OR rules for combining probabilities.

    For independent events: $P(A \text{ and } B) = P(A)\times P(B)$. For mutually exclusive events: $P(A \text{ or } B) = P(A) + P(B)$. Generally $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.

24. When multiplying or dividing without a calculator, how can powers of $10$ and estimation help?

    Separate significant figures from powers of ten, e.g. $0.0006 \times 4000 = (6\times10^{-4})(4\times10^{3}) = 24\times10^{-1} = 2.4$. Round to $1$ significant figure first to sense-check the magnitude of an answer.

What this deck covers

Section 2: Scientific Knowledge and Applications — Mathematics flashcards FAQ