What courses must be taught to homeschoolers? How many hours a day are required?

Since homeschools in California operate under the private school regulations in the Education Code, we need to follow the Code guidelines for courses to be taught.

Course Requirements
Private schools are required to “offer instruction in the several branches of study [i.e., subjects] required to be taught in public schools,” that is, English, arithmetic, social studies, science, fine arts, health and physical education (plus driver training for high school). No specific number of minutes per course are assigned in the Ed Code, but the presumption is that enough time will be spent to accomplish each grade level’s goals.
Content Guidelines - Elementary
There is flexibility in the resources each family chooses and the amount of content to be covered each year. The teaching methods may be chosen to best fit the learning style of each student, or to allow for development of a student’s giftedness.
Content Guidelines - High School
Although the flexibility and personalization aspects of home study continue into high school, by 9th grade courses should be challenging and preparing a student for adulthood, whether that is matriculating to college/university or moving into a trade, apprenticeship, or marriage and family. Some families who have used unit studies in younger grades, find ways to continue that into high school courses. However more frequently, homeschooled high school students use traditional resources for their core classes, typically covering at least 80% of the curriculum (College Prep or Honors courses may require more). This usually requires about 170-180 days of instruction per school year, which is similar to a public school year. Whether pursuing general education or college preparatory goals, coursework should be planned with objectives that can be quantitatively measured. Testing should be timed and writing should include critical thinking and literary analysis.
Typical Course of Study
For a general guideline to what is commonly taught in each grade, Pre-K through 12th, open this listing from World Book. If you choose to use a published curriculum that covers major topics (such as BJU Press or A Beka Book), they will likely have their own Scope and Sequence that their curriculum supports.