Oo Flashcards
What are upper and lower bounds?
Upper: just below the next value. Lower: the truncated value. E.g., 5.2 (1 d.p.) → Lower: 5.2, Upper: 5.299…
Upper and lower bounds are used in measurements to indicate the range of possible values for a given number.
What are compound measures?
Measures like speed (distance/time) or density (mass/volume).
Compound measures combine two different physical quantities.
How do you construct an angle bisector?
Use a compass to measure the vertex, draw arcs inside the angle, then connect the vertex to where the arcs intersect.
This method ensures that the angle is divided into two equal parts.
What is a locus?
A set of points following a rule, e.g., points equidistant from a fixed point form a circle.
Loci can represent various geometric shapes based on different conditions.
How do you find the nth term of a linear sequence?
Find the difference between terms (d), then use: nth term = dn + (first term - d).
Linear sequences have a constant difference between consecutive terms.
What is a quadratic sequence?
A sequence where the second differences are constant, e.g., 1, 4, 9, 16 (squares).
Quadratic sequences can be identified by their parabolic relationships.
How do you solve a quadratic by factorising?
Set to 0, factorise into two brackets, solve each bracket = 0. E.g., x² + 5x + 6 = 0 → (x+2)(x+3) = 0 → x = -2, -3.
Factorising is a method to find the roots of a quadratic equation.
How do you solve simultaneous equations graphically?
Plot both equations; the intersection point is the solution.
Graphical solutions provide a visual representation of the solutions to the equations.
What does y = mx + c represent?
A linear equation where m is the gradient, c is the y-intercept.
This formula describes a straight line on a Cartesian plane.
How do you interpret curved graphs?
Look at the shape; e.g., a quadratic graph (parabola) shows a squared term.
Curved graphs can indicate non-linear relationships between variables.
How do you convert between area units?
1 m² = 10,000 cm²; 1 cm² = 100 mm².
Understanding area unit conversions is essential for solving geometry problems.
How do you find the surface area of a cylinder?
Use 2πr² (bases) + 2πrh (curved surface).
Surface area calculations are crucial in various applications, including packaging and design.
What is the AND rule in probability?
P(A and B) = P(A) × P(B) if independent.
This rule helps in calculating the probability of two independent events occurring simultaneously.
What is the OR rule in probability?
P(A or B) = P(A) + P(B) - P(A and B).
This rule accounts for the overlap between two events in probability calculations.
What is relative frequency?
Frequency of an event ÷ total trials.
Relative frequency provides an empirical way to estimate probabilities based on experimental data.
How do you use Venn diagrams?
Show overlapping sets; intersection is shared, union is all elements.
Venn diagrams visualize relationships between different sets in statistics and probability.
What is a bearing?
Angle measured clockwise from North (0° to 360°).
Bearings are used in navigation and mapping to indicate direction.
How do you produce scale drawings?
Use a scale, e.g., 1 cm = 2 km, to represent distances proportionally.
Scale drawings are essential in architecture and engineering.
How do you construct triangles?
Use a ruler and compass to draw sides and angles accurately.
Precise construction methods are crucial in geometric drawings.
What are plans and elevations?
2D views of a 3D shape: front, side, and top views.
These views help visualize three-dimensional objects in two dimensions.
How do you plot a time series graph?
Plot data points over time on a graph, connect with a line.
Time series graphs are used to analyze trends over intervals.
What are sampling methods?
Random, stratified, or systematic sampling to represent a population.
Different sampling methods can affect the accuracy and reliability of statistical conclusions.
How do you calculate with powers?
Multiply powers: a^m × a^n = a^(m+n); divide: a^m ÷ a^n = a^(m-n).
Understanding powers is fundamental in algebra and higher mathematics.
What is standard form?
A × 10^n, where 1 ≤ A < 10, e.g., 4500 = 4.5 × 10^3.
Standard form simplifies the representation of large and small numbers.
