NCEA L1 Maths flashcards
NCEA L1 Maths · Build recall with a focused review session.
32 cards. Read the term and the definition here. The deck at the top of this page is optional.
- Quadratic formula
- For ax² + bx + c = 0, x = [-b ± √(b² - 4ac)] / (2a). The discriminant b² - 4ac tells how many real solutions exist.
- Discriminant
- The expression b² - 4ac in the quadratic formula. If positive, there are two real roots; if zero, one repeated root; if negative, no real roots.
- Sine rule
- In any triangle, a/sin A = b/sin B = c/sin C, where side a is opposite angle A. Useful when two angles and any side are known.
- Cosine rule
- a² = b² + c² - 2bc cos A. Use it to find a side when two sides and the included angle are known, or to find an angle when all three sides are known.
- Triangle area formula
- Area = ½ab sin C, where a and b are two sides and C is the angle between them. Requires the included angle, not just any angle.
- Gradient of a line
- m = (y₂ - y₁)/(x₂ - x₁) for two points on the line. It measures the vertical change per unit horizontal change; parallel lines have equal gradients.
- Point-slope equation
- y - y₁ = m(x - x₁) gives the equation of a line with gradient m passing through (x₁, y₁). Rearrange to y = mx + c if needed.
- Exponential growth formula
- A = A₀(1 + r)^t models growth, where A₀ is the initial amount, r is the decimal rate per period, and t is the number of periods.
- Exponential decay
- A = A₀(1 - r)^t models decay, where r is the decimal decrease per period. The value approaches zero but never becomes negative.
- Independent events
- Events are independent if the occurrence of one does not change the probability of the other. Then P(A and B) = P(A) × P(B).
- Addition rule
- For any two events, P(A or B) = P(A) + P(B) - P(A and B). Subtract the overlap so outcomes counted twice are only counted once.
- Mean
- The sum of all data values divided by the number of values. It is affected by extreme values, unlike the median.
- Median
- The middle value when data are ordered from smallest to largest. If there is an even number of values, average the two middle values.
- Mode
- The value that appears most often in a data set. A data set can have one mode, several modes, or no mode if all values occur equally often.
- Standard deviation
- A measure of how spread out values are around the mean. A larger standard deviation means values are more dispersed.
- Census
- A survey that collects data from every member of a population. It avoids sampling error but can be costly and time-consuming.
- Sample
- A subset of a population selected for measurement. Conclusions about the population are inferred from sample statistics.
- Simple random sample
- A sampling method in which every member of the population has an equal chance of being selected, and every possible sample is equally likely.
- Stratified sampling
- The population is divided into subgroups (strata) and random samples are taken from each stratum, ensuring all subgroups are represented.
- Sampling bias
- A systematic error that makes a sample unrepresentative of the population. Increasing sample size reduces variability but does not fix bias.
- Normal distribution
- A symmetric bell-shaped distribution. About 68% of values lie within one standard deviation of the mean, 95% within two, and 99.7% within three.
- z-score
- z = (x - μ)/σ measures how many standard deviations a value x lies from the mean μ. A positive z-score means above the mean.
- Box plot
- A graph showing median, lower quartile Q1, upper quartile Q3, and extremes. The box represents the middle 50% of the data.
- Interquartile range
- IQR = Q3 - Q1, the range of the middle 50% of data. It is resistant to outliers, unlike the full range.
- Outlier rule
- A value is often considered an outlier if it lies below Q1 - 1.5×IQR or above Q3 + 1.5×IQR.
- Correlation
- A measure of the strength and direction of a linear relationship between two variables, often given by the correlation coefficient r between -1 and 1.
- Causation
- A relationship where one variable directly causes a change in another. Correlation alone does not prove causation; a lurking variable may explain both.
- Line of best fit
- A straight line that best represents the trend in bivariate data, often found by least-squares regression. It can be used to make predictions.
- Explanatory variable
- The variable that is used to predict or explain changes in another variable. It is plotted on the horizontal axis of a scatter plot.
- Response variable
- The variable that is measured or predicted in a relationship. It is plotted on the vertical axis of a scatter plot.
- Probability scale
- Probabilities range from 0 (impossible) to 1 (certain). The sum of probabilities of all mutually exclusive outcomes is 1.
- Relative frequency
- The number of times an event occurs divided by the total number of trials. It estimates probability and tends to stabilise as trials increase.