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Partnership for Assessment of Readiness for College and Careers (PARCC) Mathematics: High School Geometry, Statistics, and Modeling Syllabus

The Mathematics: High School Geometry, Statistics, and Modeling syllabus for Partnership for Assessment of Readiness for College and Careers (PARCC) in full: 5 chapters, 15 topics and 31 sub-topics, every one listed below, plus 51 Mathematics: High School Geometry, Statistics, and Modeling flashcards with answers.

5Chapters
15Topics
31Sub-topics
51Flashcards

Mathematics: High School Geometry, Statistics, and Modeling syllabus: all 5 chapters

Expand any chapter to see its topics and sub-topics.

  1. Congruence and Similarity

     3 topics
    • Rigid Motions and Congruence
      • Transformations in the plane
      • Triangle congruence criteria and proofs
    • Similarity and Dilations
      • Properties of dilations
      • Similarity proofs and applications
    • Geometric Constructions
      • Compass and straightedge constructions
      • Constructing inscribed and circumscribed figures

  2. Right Triangles and Trigonometry

     3 topics
    • Pythagorean Relationships
      • Proofs and converse applications
      • Distance in the coordinate plane
    • Trigonometric Ratios
      • Sine, cosine, and tangent in right triangles
      • Solving real-world right-triangle problems
    • Laws of Sines and Cosines
      • Non-right triangle applications
      • Area of a triangle using trigonometry

  3. Circles and Coordinate Geometry

     3 topics
    • Circle Theorems
      • Arcs, chords, and inscribed angles
      • Tangent and secant relationships
    • Equations of Conics
      • Deriving the equation of a circle
      • Parabola from focus and directrix
    • Geometry on the Coordinate Plane
      • Slope criteria for parallel and perpendicular lines
      • Partitioning segments and polygon properties

  4. Geometric Measurement and Dimension

     3 topics
    • Volume and Surface Area Formulas
      • Prisms, cylinders, cones, and spheres
      • Cavalieri's principle
    • Two- and Three-Dimensional Relationships
      • Cross-sections of solids
      • Solids of rotation
    • Modeling with Geometry
      • Density and design problems
      • Geometric shapes in real-world contexts

  5. Statistics and Probability in High School

     3 topics
    • Interpreting Categorical and Quantitative Data
      • Distributions and outliers
      • Two-way frequency tables
      • Linear regression and correlation
    • Making Inferences and Justifying Conclusions
      • Sampling and experimental design
      • Drawing conclusions from data
    • Conditional Probability and Rules of Probability
      • Independence and conditional probability
      • Addition and multiplication rules

Partnership for Assessment of Readiness for College and Careers (PARCC) Mathematics: High School Geometry, Statistics, and Modeling flashcards — 51 questions with answers

  1. What is a rigid motion (isometry), and which properties does it preserve?

    A transformation that preserves distance and angle measure. The three rigid motions are translations, rotations, and reflections; they preserve length, angle measure, parallelism, and betweenness, so the image is congruent to the original.

  2. What does it mean for two figures to be congruent in terms of transformations?

    Two figures are congruent if and only if one can be mapped onto the other by a sequence of rigid motions (translations, rotations, and/or reflections).

  3. State the SAS, ASA, SSS, and AAS triangle congruence criteria.

    SAS: two sides and the included angle. ASA: two angles and the included side. SSS: all three sides. AAS: two angles and a non-included side. Each guarantees triangle congruence.

  4. What is a dilation, and how does it affect lengths and angles?

    A dilation is a transformation with a center and scale factor k that stretches or shrinks a figure. It multiplies all lengths by |k|, preserves angle measures, and maps a line not through the center to a parallel line.

  5. What is the definition of similar figures, and what do AA, SAS, and SSS similarity require?

    Similar figures have equal corresponding angles and proportional corresponding sides (related by a similarity transformation). AA: two pairs of equal angles. SAS similarity: two proportional sides with equal included angle. SSS similarity: all three pairs of sides proportional.

  6. For similar figures with linear scale factor k, how do perimeter, area, and volume scale?

    Perimeter (and any length) scales by k, area scales by k², and volume scales by k³.

  7. How do you construct the perpendicular bisector of a segment with compass and straightedge?

    Place the compass at each endpoint and draw arcs (radius more than half the segment) above and below; the two arc intersections define a line that is the perpendicular bisector.

  8. How do you bisect an angle with compass and straightedge?

    From the vertex draw an arc crossing both sides; from those two intersection points draw equal arcs that cross inside the angle; the ray from the vertex through that crossing bisects the angle.

  9. State the Pythagorean Theorem and its converse.

    For a right triangle with legs a, b and hypotenuse c: a² + b² = c². Converse: if a² + b² = c² in a triangle, then the triangle is right-angled (with the right angle opposite c).

  10. What are the side ratios in 45-45-90 and 30-60-90 special right triangles?

    45-45-90: legs equal, hypotenuse = leg·√2, ratio 1 : 1 : √2. 30-60-90: sides opposite 30°, 60°, 90° are in ratio 1 : √3 : 2.

  11. Define the sine, cosine, and tangent ratios for an acute angle in a right triangle.

    sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent (SOH-CAH-TOA).

  12. What is the relationship between the sine and cosine of complementary angles?

    The sine of an angle equals the cosine of its complement: sin(θ) = cos(90° − θ), and cos(θ) = sin(90° − θ).

  13. State the Law of Sines.

    In any triangle, a/sin A = b/sin B = c/sin C, where each side is opposite its corresponding angle.

  14. State the Law of Cosines.

    c² = a² + b² − 2ab·cos C (and cyclic forms). It generalizes the Pythagorean Theorem and is used when you know two sides and the included angle, or all three sides.

  15. When do you use the Law of Sines versus the Law of Cosines?

    Use the Law of Sines for ASA, AAS, or SSA cases. Use the Law of Cosines for SAS (find third side) or SSS (find an angle).

  16. What is the formula for the area of a triangle using two sides and the included angle?

    Area = ½·a·b·sin C, where a and b are two sides and C is the included angle.

  17. What is the relationship between an inscribed angle and the central angle subtending the same arc?

    The inscribed angle is half the central angle that subtends the same arc (Inscribed Angle Theorem).

  18. What is the measure of an inscribed angle that subtends a semicircle (diameter)?

    It is a right angle, 90° (Thales' Theorem). Any angle inscribed in a semicircle is a right angle.

  19. What is the relationship between a tangent line to a circle and the radius at the point of tangency?

    A tangent line is perpendicular to the radius drawn to the point of tangency.

  20. State the formulas for arc length and area of a sector with central angle θ (in radians) and radius r.

    Arc length = rθ; sector area = ½r²θ. In degrees: arc length = (θ/360)·2πr, sector area = (θ/360)·πr².

Show the other 31 Mathematics: High School Geometry, Statistics, and Modeling flashcards

  1. What is the standard equation of a circle with center (h, k) and radius r?

    (x − h)² + (y − k)² = r².

  2. What is the standard equation of a parabola with vertex (h, k) opening vertically, and what is p?

    (x − h)² = 4p(y − k), where p is the directed distance from the vertex to the focus (and to the directrix). It opens up if p > 0, down if p < 0.

  3. What is the defining focus-directrix property of a parabola?

    A parabola is the set of all points equidistant from a fixed point (the focus) and a fixed line (the directrix).

  4. What is the distance formula between points (x₁, y₁) and (x₂, y₂)?

    d = √[(x₂ − x₁)² + (y₂ − y₁)²].

  5. What is the midpoint formula for a segment with endpoints (x₁, y₁) and (x₂, y₂)?

    Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2).

  6. What is the relationship between the slopes of parallel lines and of perpendicular lines?

    Parallel lines have equal slopes (m₁ = m₂). Perpendicular lines have slopes that are negative reciprocals (m₁·m₂ = −1).

  7. How do you find a point that partitions a segment from (x₁, y₁) to (x₂, y₂) in the ratio m:n?

    Point = (x₁ + (m/(m+n))(x₂ − x₁), y₁ + (m/(m+n))(y₂ − y₁)), i.e., move the fraction m/(m+n) of the way from the first endpoint to the second.

  8. What are the volume formulas for a prism/cylinder and for a pyramid/cone?

    Prism/cylinder: V = B·h (base area times height). Pyramid/cone: V = ⅓·B·h. For a cylinder V = πr²h; for a cone V = ⅓πr²h.

  9. What are the volume and surface area formulas for a sphere?

    Volume = (4/3)πr³; surface area = 4πr².

  10. What is the surface area formula for a cylinder?

    Surface area = 2πr² + 2πrh (two circular bases plus the lateral rectangle of height h and width 2πr).

  11. What is Cavalieri's Principle?

    If two solids have the same height and equal cross-sectional areas at every level, then they have the same volume.

  12. What two-dimensional shapes result from cross-sections of a cylinder cut parallel versus perpendicular to its base?

    A cut parallel to the base yields a circle (congruent to the base); a cut perpendicular to the base (through the axis) yields a rectangle.

  13. What solid is generated by rotating a right triangle about one of its legs, and a rectangle about one of its sides?

    Rotating a right triangle about a leg generates a cone; rotating a rectangle about a side generates a cylinder.

  14. What is population density, and how is it modeled with geometry?

    Population density = number of people / area (or per unit volume). It is a ratio used to model and compare how concentrated a quantity is over a region, e.g., people per square mile.

  15. In a frequency distribution, what does the shape (skew) tell you about mean vs. median?

    In a right-skewed (positive) distribution the mean is greater than the median; in a left-skewed (negative) distribution the mean is less than the median; in a symmetric distribution mean ≈ median.

  16. When should you use the mean and standard deviation versus the median and IQR to summarize data?

    Use mean and standard deviation for roughly symmetric data with no outliers; use median and interquartile range (IQR) for skewed data or data with outliers, since they are resistant to extreme values.

  17. How is the interquartile range (IQR) computed, and what is the 1.5·IQR outlier rule?

    IQR = Q3 − Q1. A value is an outlier if it is below Q1 − 1.5·IQR or above Q3 + 1.5·IQR.

  18. In a two-way frequency table, what is the difference between a joint, marginal, and conditional relative frequency?

    Joint: a cell count relative to the grand total. Marginal: a row or column total relative to the grand total. Conditional: a cell relative to its own row or column total (probability given a category).

  19. What does the correlation coefficient r measure, and what is its range?

    r measures the strength and direction of a linear relationship between two quantitative variables; it ranges from −1 to +1, where ±1 is a perfect linear relationship and 0 is no linear relationship.

  20. What is the key distinction between correlation and causation?

    Correlation indicates that two variables are associated, but it does not establish that one causes the other; causation can only be inferred from a well-designed randomized experiment, not from observational correlation.

  21. In the empirical (68-95-99.7) rule for a normal distribution, what percent of data falls within 1, 2, and 3 standard deviations of the mean?

    About 68% within 1 SD, about 95% within 2 SD, and about 99.7% within 3 SD of the mean.

  22. What is the difference between a sample survey, an experiment, and an observational study?

    A sample survey estimates a population characteristic from a sample; an experiment imposes a treatment to test cause and effect; an observational study records data without imposing treatments and cannot establish causation.

  23. Why is random assignment important in an experiment, and random selection in a survey?

    Random assignment balances confounding variables across treatment groups so differences can be attributed to the treatment (causation). Random selection makes a sample representative so results generalize to the population.

  24. What is the purpose of using simulation to evaluate whether a result is statistically significant?

    Simulation generates the distribution of outcomes expected by chance under a model; if the observed result is rare (in the tails) of that simulated distribution, it is statistically significant and unlikely due to chance alone.

  25. What is the addition rule for the probability of A or B?

    P(A or B) = P(A) + P(B) − P(A and B). If A and B are mutually exclusive, P(A and B) = 0, so P(A or B) = P(A) + P(B).

  26. What is the formula for conditional probability P(A | B)?

    P(A | B) = P(A and B) / P(B), provided P(B) > 0. It is the probability of A given that B has occurred.

  27. What is the multiplication rule for P(A and B), and how does it simplify for independent events?

    P(A and B) = P(A)·P(B | A). If A and B are independent, P(B | A) = P(B), so P(A and B) = P(A)·P(B).

  28. What condition defines two events A and B as independent?

    A and B are independent if P(A | B) = P(A) (equivalently P(B | A) = P(B), or P(A and B) = P(A)·P(B)). Knowing one occurred does not change the other's probability.

  29. What is the complement rule in probability?

    P(not A) = 1 − P(A). The probability that an event does not occur is one minus the probability that it does.

  30. What does it mean for two events to be mutually exclusive (disjoint)?

    They cannot occur at the same time, so P(A and B) = 0. Mutually exclusive events with nonzero probability are necessarily dependent.

  31. How can a two-way table be used to determine whether two categorical variables are independent?

    Compare conditional relative frequencies: if the conditional distribution of one variable is the same across all categories of the other (e.g., P(A|B) = P(A|not B) = P(A)), the variables are independent; if they differ, the variables are associated.

Partnership for Assessment of Readiness for College and Careers (PARCC) Mathematics: High School Geometry, Statistics, and Modeling FAQ

What is in the Partnership for Assessment of Readiness for College and Careers (PARCC) Mathematics: High School Geometry, Statistics, and Modeling syllabus?

Partnership for Assessment of Readiness for College and Careers (PARCC) Mathematics: High School Geometry, Statistics, and Modeling is split into 5 chapters: Congruence and Similarity, Right Triangles and Trigonometry, Circles and Coordinate Geometry, Geometric Measurement and Dimension and Statistics and Probability in High School. Together they contain 15 topics and 31 sub-topics.

How many chapters are in Partnership for Assessment of Readiness for College and Careers (PARCC) Mathematics: High School Geometry, Statistics, and Modeling?

5 chapters, containing 15 topics and 31 sub-topics. The largest chapter is Congruence and Similarity, with 3 topics.

Are there flashcards for Partnership for Assessment of Readiness for College and Careers (PARCC) Mathematics: High School Geometry, Statistics, and Modeling?

Yes — a 51-card Mathematics: High School Geometry, Statistics, and Modeling deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.