Study Skills

Convert among inches, feet, yards, and miles using proportional reasoning.

Convert a metric linear measurement to imperial units using a conversion factor.

Convert an imperial linear measurement to metric units using a conversion factor.

Solve a chained linear conversion that requires more than one conversion factor.

Distinguish an exact conversion from an approximate conversion.

Round a converted measurement to an appropriate degree of precision.

Solve an applied linear measurement problem that mixes metric and imperial units.

Detect and correct an unreasonable unit-conversion result using estimation and unit size.

Use the Pythagorean theorem to calculate a slant height required in a surface-area problem.

Calculate the surface area of a right prism or right cylinder.

Calculate the surface area of a right pyramid or right cone.

Calculate the surface area of a sphere.

Calculate the volume of a right prism or right cylinder.

Calculate the volume of a right pyramid or right cone.

Calculate the volume of a sphere.

Convert between square or cubic units using the appropriate area or volume scale factor.

Calculate the exposed surface area of a composite three-dimensional object.

Calculate the volume of a composite three-dimensional object.

Determine a missing dimension from the surface area of a three-dimensional object.

Determine a missing dimension from the volume of a three-dimensional object.

Predict how a scale factor changes the surface area and volume of a three-dimensional object.

Solve a three-dimensional measurement problem that combines metric and imperial units.

Explain why sine, cosine, and tangent are constant for similar right triangles with the same acute angle.

Identify the hypotenuse, opposite side, and adjacent side relative to a specified acute angle.

Calculate sine, cosine, and tangent ratios from the side lengths of a right triangle.

Select the appropriate primary trigonometric ratio from the known and unknown parts of a right triangle.

Calculate a missing side length using a primary trigonometric ratio.

Calculate an acute angle using an inverse trigonometric ratio.

Solve a right triangle using trigonometry and the Pythagorean theorem.

Check whether a calculated side or angle is reasonable for the given right triangle.

Determine unknown angles using relationships formed by parallel lines and a transversal.

Use slopes or angle relationships to determine whether two lines are parallel or perpendicular.

Translate an applied trigonometry problem into a labelled right-triangle diagram.

Solve a problem involving an angle of elevation.

Solve a problem involving an angle of depression.

Solve mixed Math 10C measurement and trigonometry exam-style problems.

Convert measurements among common SI units and prefixes used in physics.

Convert speeds between kilometres per hour and metres per second.

Distinguish scalar quantities from vector quantities in simple motion situations.

Distinguish distance from displacement for motion along a straight path.

Calculate average speed from distance and elapsed time.

Calculate average velocity from displacement and elapsed time.

Interpret the slope and shape of a position–time graph.

Calculate average acceleration from a change in velocity and elapsed time.

Interpret the direction and shape of a velocity–time graph.

Identify contact and non-contact forces acting on an object in a familiar situation.

Calculate an object’s weight from its mass and gravitational field strength.

Draw a free-body diagram for an object acted on by horizontal and vertical forces.

Calculate the net force on an object when forces act along one line.

Use Newton’s first law to predict motion when forces are balanced or unbalanced.

Use Newton’s second law to solve one-step problems involving force, mass, and acceleration.

Identify action–reaction force pairs using Newton’s third law.

Identify kinetic, gravitational potential, elastic, thermal, chemical, electrical, and radiant energy in everyday systems.

Trace a sequence of energy transformations in a device or physical process.

Apply conservation of energy to account for useful and dissipated energy.

Calculate mechanical work when a constant force acts along the direction of motion.

Calculate an object’s kinetic energy from its mass and speed.

Calculate gravitational potential energy from mass, gravitational field strength, and height.

Calculate power from work or energy transferred over time.

Calculate the efficiency of an energy transformation as a percentage.

Distinguish thermal energy from temperature.

Explain conduction using particle collisions in solids.

Explain convection using density changes in fluids.

Explain thermal radiation as energy transfer by electromagnetic waves.

Compare conduction, convection, and radiation in a familiar technology.

Represent the energy inputs, useful outputs, and waste outputs of a technological system.

Compare renewable and non-renewable energy sources using efficiency, reliability, and environmental evidence.

Select the appropriate motion, force, work, energy, power, or efficiency relationship from the information in a problem.

Solve a two-step physics problem while showing substitutions, units, and a reasonable final answer.

Interpret a table or graph to identify a relationship between two physical variables.

Identify independent, dependent, and controlled variables in a physics investigation.

Identify a likely source of experimental error and explain how it could affect a result.

Apply matter, motion, force, and energy concepts to mixed exam-style questions.