Specialist Mathematics flashcards

85 QCE Specialist Mathematics cards across 2 modules (3 definitions, 40 key facts, 7 fill-the-gap, 35 formulas). Each session gives you 20 cards, due cards first. Swipe right for easy, left for hard, down for again. Keyboard: Space to flip, 1 to 4 to rate.

Loading flashcards…

What this deck covers

Unit 3: Mathematical induction, and further vectors, matrices and complex numbers (44 cards, 10 dot points)
Unit 4: Further calculus, and statistical inference (41 cards, 10 dot points)

Sample cards from this deck

Definition
Mathematical induction (QCE Specialist Mathematics Unit 3)
Define Base step
Show $P(1)$ is true by direct substitution. State both sides and confirm they are equal.
Fill the gap
Confidence intervals for a population mean (QCE Specialist Mathematics Unit 4)
The quantity $z^{*}\dfrac{\sigma}{\sqrt{n}}$ is the ___, the half-width of the interval.
The quantity $z^{*}\dfrac{\sigma}{\sqrt{n}}$ is the margin of error, the half-width of the interval.
Definition
Systems of linear equations and larger matrices in QCE Specialist Mathematics Unit 3
Define No solution
No solution ( $\det A = 0$ , system inconsistent): the planes have no common point, for example two are parallel, or they form a triangular prism arrangement.
Fill the gap
Distribution of the sample mean and the central limit theorem (QCE Specialist Mathematics Unit 4)
Its distribution is called the ___, and it has its own mean and standard deviation.
Its distribution is called the sampling distribution of the mean, and it has its own mean and standard deviation.
Fill the gap
Vector and Cartesian equations of planes in QCE Specialist Mathematics Unit 3
A plane is determined by a point $A$ with position vector $\mathbf{a}$ and a ___ vector $\mathbf{n}$ perpendicular to the plane.
A plane is determined by a point $A$ with position vector $\mathbf{a}$ and a normal vector $\mathbf{n}$ perpendicular to the plane.
Fill the gap
Simpson's rule for numerical integration in QCE Specialist Mathematics Unit 4
Divide $[a, b]$ into $n$ equal subintervals, where $n$ must be ___.
Divide $[a, b]$ into $n$ equal subintervals, where $n$ must be even.
Fill the gap
Factorising polynomials over the complex field in QCE Specialist Mathematics Unit 3
If a polynomial has ___ coefficients and $z = \alpha + i\beta$ is a root, then its conjugate $\bar z = \alpha - i\beta$ is also a root.
If a polynomial has real coefficients and $z = \alpha + i\beta$ is a root, then its conjugate $\bar z = \alpha - i\beta$ is also a root.
Key fact
Areas between curves and volumes of revolution in QCE Specialist Mathematics Unit 4
Tell me about Area between two curves
Find the intersection points to fix the limits $a$ and $b$ . If the curves cross within the interval, split the integral at each crossing and integrate the positive difference on each piece.
Fill the gap
Matrices and linear transformations of the plane (QCE Specialist Mathematics Unit 3)
Matrix multiplication is associative but ___ commutative, so $MN \neq NM$ in general.
Matrix multiplication is associative but not commutative, so $MN \neq NM$ in general.
Key fact
First-order differential equations and separation of variables (QCE Specialist Mathematics Unit 4)
Tell me about Separation of variables
Treating $\dfrac{dy}{dx}$ as a ratio of differentials is a valid shortcut for this technique. Include a single constant of integration, then solve algebraically for $y$ where possible.