WASHINGTON — The Supreme Court is beginning a new term with controversial issues that offer the court’s conservative majority the chance to move aggressively to undo limits on campaign contributions, undermine claims of discrimination in housing and mortgage lending, and allow for more government-sanctioned prayer.

Assuming the government shutdown doesn’t get in their way, the justices also will deal with a case that goes to the heart of the partisan impasse in Washington: whether and when the president may use recess appointments to fill key positions without Senate confirmation.

The court was unaffected for the first few days of the government shutdown and there was no expectation that arguments set for October would have to be rescheduled.

The new term that starts Monday may be short on the sort of high-profile battles over health care and gay marriage that marked the past two years. But several cases ask the court to overrule previous decisions – bold action in an institution that relies on the power of precedent.

“There are an unusual number of cases going right to hot-button cultural issues and aggressive briefing on the conservative side asking precedents to be overruled,” said Georgetown University law professor Pamela Harris, who served in President Obama’s Justice Department.

There is a familiar ring to several cases the justices will take up.

Campaign finance, affirmative action, legislative prayer and abortion clinic protests all are on the court’s calendar. The justices also will hear for the second time the case of Carol Anne Bond, a woman who was convicted under an anti-terrorism law for spreading deadly chemicals around the home of her husband’s mistress.

The justices probably will decide in the fall whether to resolve competing lower court decisions about the new health care law’s requirement that employer-sponsored health plans include coverage of contraceptives.

An issue with a good chance to be heard involves the authority of police to search the contents of a cellphone found on someone they arrest. Justice Ruth Bader Ginsburg said over the summer that the right to privacy in the digital age “is bound to come up in many forms” in the years ahead.

The court may hear its first abortion case since 2007, a review of an Oklahoma law that would restrict the use of certain abortion-inducing drugs such as RU-486.

The campaign finance argument on Tuesday is the first major case on the calendar. The 5-4 decision in the Citizens United case in 2010 allowed corporations and labor unions to spend unlimited sums in support of or opposition to candidates, as long as the spending is independent of the candidates.

The new case, McCutcheon v. Federal Election Commission, is a challenge to the overall limits on what an individual may give to candidates, political parties and political action committees in a two-year federal election cycle, currently $48,600 to candidates and $123,600 in total. The $2,600 limit on contributions to a candidate is not at issue.

Among other top cases already set for review:

• Greece, N.Y., a suburb of Rochester, is asking the court to uphold its practice of opening town council meetings with a prayer, despite an appeals court ruling that found the invocations a violation of the First Amendment because they almost always were Christian prayers.

• Massachusetts is defending a law that creates a 35-foot buffer zone at abortion clinics to limit protesters’ ability to interact with patients.