WASHINGTON — The Supreme Court heads into the last two weeks of its annual term Monday seemingly poised to hand down a series of decisions that will come as defeats to President Obama and victories for foes of abortion.

Already this year, the court has bolstered the rights of big campaign donors and upheld Christian prayers at public meetings.

The themes of free speech and religious freedom are likely to be heard, and two other cases involve adapting the law to fast-developing technology. Another case could deal a major blow to public employees unions.

The justices try to finish their work by the end of June. The annual rush this time of year means many of their hardest cases are decided in the last two weeks of the month – often by 5-4 splits. Currently, 16 cases remain unresolved. Here are highlights:

• Contraceptives and religious liberty: Do the owners of private companies, citing their religious faith, have a right to refuse to provide their workers with the full range of contraceptives promised under President Obama’s health insurance law?

A ruling for the business owners, which seems likely, could open the door for new claims of legal exemptions based on religion. (Sebelius v. Hobby Lobby Stores)

• Abortion and free speech: Can Massachusetts enforce a 35-foot quiet zone near the doors of abortion clinics, or does that violate the First Amendment rights of “sidewalk counselors” who hope to persuade patients not to end their pregnancies?

The justices could rule that the quiet zone law was too broad, but they might go further and outlaw any buffer zone that covers public sidewalks. (McCullen v. Coakley)

• Unions and free speech: Did Illinois violate the rights of home health care workers when it authorized them to be unionized and allowed their union to require workers to either join or pay a fee to cover the cost of collective bargaining? The court could rule narrowly in this case, but anti-union advocates hope the justices will strike down forced fees for public-sector workers, which would significantly weaken unions. (Harris v. Quinn)

• Smartphones and police searches: Can police who make an arrest examine a suspect’s smartphone, or does such a search without a warrant violate the Fourth Amendment? During oral arguments, the justices seemed to be looking for a way to permit such searches, but only in cases involving serious crimes. (Riley v. California)

• Congress and presidential power: Did Obama exceed his power when he bypassed the Senate and filled three seats on the National Labor Relations Board using a recess appointment? Since World War II, presidents have regularly made such appointments during Senate breaks, but the court is likely to rule Obama went too far. The effect of the case will depend on how much the court reins in the presidential authority. (NLRB v. Noel Canning)

• Greenhouse gases and power plants: Did Obama’s environmental regulators stretch the law by requiring that permits for new power plants include measures to reduce carbon emissions? Industry groups are likely to win this case, but a key issue will be whether the ruling sweeps broadly enough to affect the Environmental Protection Agency’s recently announced climate change rules for existing power plants. (Utility Air Regulatory Group v. EPA)