The teacher reviewed the use of the past participle (haber + past participle). Then, the teacher explained the conjugation of haber and reviewed the rules for forming past participles with both regular and irregular verbs. At the end of the lesson, the student practiced by writing 10 original sentences using the present perfect tense and completed an additional exercise in which they conjugated the verbs in parentheses.

We worked on forming past participles by adding -ado to -ar verb stems and -ido to -er/-ir verb stems. We learned that they function as adjectives and must match gender/number or would be used with haber for perfect tenses. Then we went over some of the key irregular verbs.

redox tutoring

We reviewed and practiced solving quadratic equations by factoring, the quadratic equation, and completing the square. We determined the domain and range of square root functions. We solved word problems involving quadratic equations in standard form. Then we mapped a 1 to 1 function to determine the cost of a ticket based on the age of the recipient.

We learned that algebraic manipulation comes into play when solving logarithmic equations or simplifying expressions. We worked on a practice test to solve logarithmic exponents.

We reviewed for the final exam in geometry.
10-6 Secants, Tangents, and Angle Measures – We reviewed formulas for calculating angles where secants and tangents meet outside of a circle. Then we derived the equation of a circle with a given center and radius using the Pythagorean theorem. We used the equation of a circle to graph it on a coordinate plane.

13-3 Geometric Probability – We learned to analyze areas with geometric probability. We calculated the probability that a point chosen at random lies in a certain region. Then we learned that two events are independent if the probability of occurring together is the product of their probabilities. Events are dependent if the probability of one occurring in some way changes the probability of the other.

We reviewed for the final exam in geometry.
10-6 Secants, Tangents, and Angle Measures – We constructed tangent lines from points outside of a circle. We learned to use the Segments of Chords Theorem to find the lengths of chords in circles. We used the quadratic function when the equations could not be factored.

12.2 Surface Areas of Prisms and Cylinders – We understand that cylinders have congruent bases. We applied geometric methods to solve problems. We could design an object or structure to satisfy physical constraints or minimize cost.
12-3 Surface Areas of Pyramids and Cones – We understand the difference between the slant height and height of the pyramid. The slant height is the height of the lateral face, while the height is the altitude of the pyramid. We learned to use trigonometric ratios to find the length of the apothem and the area of the base. We understand that in an oblique cone the axis is not the altitude.

12.2 Surface Areas of Prisms and Cylinders – We learned to apply geometric methods to solve problems. These methods can be used to design an object or structure to satisfy physical constraints or minimize cost. We understand how to work with typographic grid systems based on ratios.
12-3 Surface Areas of Pyramids and Cones – We practiced finding lateral areas and surface areas of pyramids and cones. We learned to use geometric shapes, their measures, and their properties to describe objects.

11.5 Areas of Similar Figures – We practiced finding areas of similar figures by using scale factors. Then we found the scale factors or missing measures given the areas of similar figures. We learned that architecture firms often hire model makers to make scale models and projects that are used to sell their designs. Since the base of a model is geometrically similar to the base of the actual building it represents, their areas are related.
12-2 Surface Areas of Prisms and Cylinders – We practiced finding the lateral areas and surface areas of prisms.