Class x
mandatory maths
A. Algebra review
- Ratios and proportions
- Scale drawings: word problems
- Number sequences
- Shape patterns
- Properties of exponents
- Simplify radical expressions
- Write variable expressions
- Solve linear equations
- Solve linear inequalities
- Solve systems of linear equations
- Solve a quadratic equation by factoring
- Solve a quadratic equation using the quadratic formula
B. Points, lines, line segments, and planes
- Lines, line segments, and rays
- Properties of planes, lines, and points
- Describe intersections in a plane
- Lengths of segments on number lines
- Additive property of length
- Midpoints
- Congruent line segments
- Construct a congruent segment
- Perpendicular Bisector Theorem
- Midpoint formula: find the midpoint
- Partition a line segment in a given ratio
- Midpoint formula: find the endpoint
- Distance formula
- Distance to the origin in three dimensions
- Construct the midpoint or perpendicular bisector of a segment
Checkpoint skill Checkpoint: Partition a line segment
C. Angles
- Angle vocabulary
- Angle measures
- Identify complementary, supplementary, vertical, adjacent, and congruent angles
- Find measures of complementary, supplementary, vertical, and adjacent angles
- Angle diagrams: solve for the variable
- Angle bisectors
- Construct an angle bisector
- Construct a congruent angle
- Proofs involving angles
D. Parallel and perpendicular lines
- Identify parallel, intersecting, and skew lines and planes
- Construct a perpendicular line
- Transversals: name angle pairs
- Transversals of parallel lines: find angle measures
- Transversals of parallel lines: solve for x
- Construct parallel lines
- Proofs involving parallel lines I
- Proofs involving parallel lines II
Checkpoint skill Checkpoint: Definitions of geometric objects
Checkpoint skill Checkpoint: Line and angle theorems
E. Lines in the coordinate plan
- Coordinate plane review
- Slopes of lines
- Graph a linear equation
- Equations of lines
- Slopes of parallel and perpendicular lines
- Equations of parallel and perpendicular lines
- Find the distance between a point and a line
- Find the distance between two parallel lines
Checkpoint skill Checkpoint: Coordinate proofs
Checkpoint skill Checkpoint: Parallel and perpendicular lines
F. Introduction to triangles
- Classify triangles
- Triangle Angle-Sum Theorem
- Exterior Angle Theorem
- Exterior Angle Inequality
G. Two-dimensional figures
- Polygon vocabulary
- Interior angles of polygons
- Exterior angles of polygons
- Review: interior and exterior angles of polygons
- Construct an equilateral triangle or regular hexagon
- Construct a square
H. Three-dimensional figures
- Parts of three-dimensional figures
- Three-dimensional figure vocabulary
- Nets and drawings of three-dimensional figures
- Cross sections of three-dimensional figures
- Solids of revolution
Checkpoint skill Checkpoint: Cross sections and solids of revolution
I. Logic
- Identify hypotheses and conclusions
- Counterexamples
- Conditionals
- Negations
- Converses, inverses, and contrapositives
- Biconditionals
- Truth tables
- Truth values
J. Introduction to congruent figures
- Congruence statements and corresponding parts
- Solve problems involving corresponding parts
- Identify congruent figures
K. Congruent triangles
- SSS and SAS Theorems
- Proving triangles congruent by SSS and SAS
- ASA and AAS Theorems
- Proving triangles congruent by ASA and AAS
- SSS, SAS, ASA, and AAS Theorems
- SSS Theorem in the coordinate plane
- Proving triangles congruent by SSS, SAS, ASA, and AAS
- Proofs involving corresponding parts of congruent triangles
- Congruency in isosceles and equilateral triangles
- Proofs involving isosceles triangles
- Hypotenuse-Leg Theorem
L. Transformations
- Classify congruence transformations
- Translations: graph the image
- Translations: find the coordinates
- Translations: write the rule
- Reflections: graph the image
- Reflections: find the coordinates
- Rotate polygons about a point
- Rotations: graph the image
- Rotations: find the coordinates
• New! Reflections and rotations: write the rule - Glide reflections: graph the image
- Sequences of congruence transformations: graph the image
- Sequences of congruence transformations: find the rules
- Transformations that carry a polygon onto itself
- Congruence transformations: mixed review
- Dilations: graph the image
- Dilations: find the coordinates
- Dilations: find length, perimeter, and area
- Dilations: find the scale factor
- Dilations: find the scale factor and center of the dilation
- Dilations and parallel lines
Checkpoint skill Checkpoint: Transformations in the plane
Checkpoint skill Checkpoint: Transformations of geometric figures
Checkpoint skill Checkpoint: Rigid motion and congruence
Checkpoint skill Checkpoint: Dilations
M. Triangles
- Midsegments of triangles
- Triangles and bisectors
- Identify medians, altitudes, angle bisectors, and perpendicular bisectors
- Angle-side relationships in triangles
- Triangle Inequality Theorem
- Construct the circumcenter or incenter of a triangle
- Construct the centroid or orthocenter of a triangle
- Find the centroid of a triangle
- Proofs involving triangles I
- Proofs involving triangles II
Checkpoint skill Checkpoint: Triangle theorems
N. Quadrilaterals
- Identify trapezoids
- Classify quadrilaterals I
- Classify quadrilaterals II
- Find missing angles in quadrilaterals
- Graph quadrilaterals
- Properties of parallelograms
- Proving a quadrilateral is a parallelogram
- Properties of rhombuses
- Properties of squares and rectangles
- Properties of trapezoids
- Properties of kites
- Review: properties of quadrilaterals
- Classify shapes on the coordinate plane: justify your answer
- Proofs involving triangles and quadrilaterals
- Proofs involving quadrilaterals
Checkpoint skill Checkpoint: Parallelogram theorems
O. Symmetry
- Line symmetry
- Rotational symmetry
- Draw lines of symmetry
- Count lines of symmetry
S. Area and perimeter
- Similarity ratios
- Similarity statements
- Identify similar figures
- Side lengths and angle measures in similar figures
- Similar triangles and indirect measurement
- Perimeters of similar figures
- Angle-angle criterion for similar triangles
- Similarity rules for triangles
- Similar triangles and similarity transformations
- Similarity of circles
- Triangle Proportionality Theorem
- Similarity and altitudes in right triangles
- Areas of similar figures
- Prove similarity statements
- Prove proportions or angle congruences using similarity
- Proofs involving similarity in right triangles
Checkpoint skill Checkpoint: Similarity transformations
Checkpoint skill Checkpoint: Triangle similarity and congruence
Checkpoint skill Checkpoint: Prove circles are similar
Q. Pythagorean theorem
- Pythagorean theorem
- Prove the Pythagorean theorem
- Converse of the Pythagorean theorem
- Pythagorean Inequality Theorems
R. Trigonometry
- Trigonometric ratios: sin, cos, and tan
- Trigonometric ratios: csc, sec, and cot
- Trigonometric ratios in similar right triangles
- Special right triangles
- Find trigonometric functions of special angles
- Solve a special right triangle
- Find trigonometric functions using a calculator
- Sine and cosine of complementary angles
- Inverses of trigonometric functions
- Trigonometric ratios: find a side length
- Trigonometric ratios: find an angle measure
- Solve a right triangle
- Law of Sines
- Law of Cosines
- Solve a triangle
- Area of a triangle: sine formula
- Area of a triangle: Law of Sines
Checkpoint skill Checkpoint: Right triangle trigonometry
Checkpoint skill Checkpoint: Laws of Sines and Cosines
S. Area and perimeter
- Perimeter
- Area of rectangles and squares
- Area of parallelograms and triangles
- Area of trapezoids
- Area of rhombuses
• New! Area of regular polygons - Area and perimeter in the coordinate plane I
- Area and perimeter in the coordinate plane II
- Area and circumference of circles
- Area of compound figures
- Area between two shapes
- Area and perimeter of similar figures
- Perimeter and area: changes in scale
- Heron’s formula
- Area and perimeter mixed review
Checkpoint skill Checkpoint: Area and perimeter in the coordinate plane
T. Surface area and volume
- Surface area and volume of rectangular prisms
- Surface area of prisms and cylinders
- Surface area of pyramids and cones
- Surface area of spheres
- Volume of prisms and cylinders
- Volume of pyramids and cones
- Volume of spheres
- Volume of compound figures
- Similar solids: find the missing length
- Surface area and volume of similar solids
- Surface area and volume: changes in scale
- Perimeter, area, and volume: changes in scale
- Surface area and volume review
Checkpoint skill Checkpoint: Volume
U. Circles
- Parts of a circle
- Central angles and arc measures
- Understand arc length and sector area of a circle
- Arc length
- Convert between radians and degrees
- Radians and arc length
- Area of sectors
- Circle measurements: mixed review
- Arcs and chords
- Tangent lines
- Perimeter of polygons with an inscribed circle
- Inscribed angles
- Angles in inscribed right triangles
- Angles in inscribed quadrilaterals I
- Angles in inscribed quadrilaterals II
- Angles formed by chords, secants, and tangents
- Segments formed by chords, secants, and tangents
- Construct a tangent line to a circle
- Construct an equilateral triangle inscribed in a circle
- Construct a square inscribed in a circle
- Construct a regular hexagon inscribed in a circle
- Construct the inscribed or circumscribed circle of a triangle
Checkpoint skill Checkpoint: Angles and lines in circles
Checkpoint skill Checkpoint: Inscribed and circumscribed circles
Checkpoint skill Checkpoint: Arc length and area of sectors
Checkpoint skill Checkpoint: Geometric constructions
V. Circles and parabolas in the coordinate plane
- Find the center of a circle
- Find the radius or diameter of a circle
- Determine if a point lies on a circle
- Write equations of circles in standard form from graphs
- Write equations of circles in standard form using properties
- Convert equations of circles from general to standard form
- Find properties of circles from equations in general form
- Graph circles from equations in standard form
- Graph circles from equations in general form
- Find the vertex of a parabola
- Find the focus or directrix of a parabola
- Find the axis of symmetry of a parabola
- Write equations of parabolas in vertex form from graphs
- Write equations of parabolas in vertex form using the focus and directrix
- Write equations of parabolas in vertex form using properties
- Convert equations of parabolas from general to vertex form
- Find properties of a parabola from equations in general form
- Graph parabolas
Checkpoint skill Checkpoint: Equations of circles
Checkpoint skill Checkpoint: Equations of parabolas
W. Measurement
- Convert rates and measurements: customary units
- Convert rates and measurements: metric units
- Convert square and cubic units of length
- Precision
- Greatest possible error
- Minimum and maximum area and volume
- Percent error
- Percent error: area and volume
- Calculate density, mass, and volume
Checkpoint skill Checkpoint: Geometric modeling and design
Checkpoint skill Checkpoint: Density
X. Probability
- Theoretical and experimental probability
- Outcomes of compound events
- Identify independent and dependent events
- Probability of independent and dependent events
- Counting principle
- Permutations
- Permutation and combination notation
- Find probabilities using combinations and permutations
- Find probabilities using two-way frequency tables
- Identify independent events
- Find conditional probabilities
- Independence and conditional probability
- Find conditional probabilities using two-way frequency tables
- Geometric probability
- Find probabilities using the addition rule
Checkpoint skill Checkpoint: Understand independence and conditional probability
Checkpoint skill Checkpoint: Probabilities of compound events
Y. Vectors
- Compass directions and vectors
- Find the magnitude of a vector
- Find the component form of a vector
- Find the component form of a vector given its magnitude and direction angle
- Graph a resultant vector using the triangle method
- Graph a resultant vector using the parallelogram method
- Add vectors
- Subtract vectors
