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Skills available for Texas Precalculus standards

Standards are in black and IXL math skills are in dark green. Hold your mouse over the name of a skill to view a sample question. Click on the name of a skill to practice that skill.

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1 The student uses mathematical processes to acquire and demonstrate mathematical understanding.

2 The student applies mathematical processes to apply understandings about statistical studies, surveys, and experiments to design and conduct a study and use graphical, numerical, and analytical techniques to communicate the results of the study.

  • A compare and contrast the benefits of different sampling techniques, including random sampling and convenience sampling methods;

  • B distinguish among observational studies, surveys, and experiments;

  • C analyze generalizations made from observational studies, surveys, and experiments;

  • D distinguish between sample statistics and population parameters;

  • E formulate a meaningful question, determine the data needed to answer the question, gather the appropriate data, analyze the data, and draw reasonable conclusions;

  • F communicate methods used, analyses conducted, and conclusions drawn for a data-analysis project through the use of one or more of the following: a written report, a visual display, an oral report, or a multi-media presentation; and

  • G critically analyze published findings for appropriateness of study design implemented, sampling methods used, or the statistics applied.

3 The student applies the mathematical process standards when describing and modeling variability.

  • A distinguish between mathematical models and statistical models;

  • B construct a statistical model to describe variability around the structure of a mathematical model for a given situation;

  • C distinguish among different sources of variability, including measurement, natural, induced, and sampling variability; and

  • D describe and model variability using population and sampling distributions.

4 The student applies the mathematical process standards to represent and analyze both categorical and quantitative data.

5 The student applies the mathematical process standards to connect probability and statistics.

6 The student applies the mathematical process standards to make inferences and justify conclusions from statistical studies.

  • A explain how a sample statistic and a confidence level are used in the construction of a confidence interval;

  • B explain how changes in the sample size, confidence level, and standard deviation affect the margin of error of a confidence interval;

  • C calculate a confidence interval for the mean of a normally distributed population with a known standard deviation;

  • D calculate a confidence interval for a population proportion;

  • E interpret confidence intervals for a population parameter, including confidence intervals from media or statistical reports;

  • F explain how a sample statistic provides evidence against a claim about a population parameter when using a hypothesis test;

  • G construct null and alternative hypothesis statements about a population parameter;

  • H explain the meaning of the p-value in relation to the significance level in providing evidence to reject or fail to reject the null hypothesis in the context of the situation;

  • I interpret the results of a hypothesis test using technology-generated results such as large sample tests for proportion, mean, difference between two proportions, and difference between two independent means; and

  • J describe the potential impact of Type I and Type II Errors.

7 The student applies the mathematical process standards to analyze relationships among bivariate quantitative data.