Almost half — 47% — of Americans surveyed in 2010 agreed that "human beings, as we know them today, developed from earlier species of animals," and 38% agreed that "the universe began with a huge explosion."
Those results are reported in Science and Engineering Indicators 2012 (PDF), a biennial report from the National Science Board. The figures are basically unchanged through the years for which data is provided (PDF), from 1985 for evolution and from 1988 for the Big Bang. The report also contains a brief discussion of the public controversies over evolution education.
Science Engineering Indicators 2010 deleted a section similarly describing the survey results about the American public's beliefs about evolution and the Big Bang, a decision which drew criticism at the time, including from veteran science literacy researcher Jon Miller, who originally devised the question about evolution, and from NCSE's Joshua Rosenau, who told Science (April 9, 2010; subscription required), "Discussing American science literacy without mentioning evolution is intellectual malpractice ... It downplays the controversy."
The National Science Board later acknowledged to Science (July 22, 2011; subscription required) that deleting the text was a mistake. But although the new report discusses the survey data, those questions are excluded from its measure of science literacy. Eleven factual questions, covering a variety of topics in addition to evolution and the Big Bang, were used to assess science literacy in previous versions of Science Engineering Indicators; nine questions, excluding evolution and the Big Bang, are used in the 2010 and 2012 versions.
In 2010, the then chair of the Science and Engineering Indicators committee told Science that the questions were excluded as "flawed indicators because the responses conflated knowledge and beliefs." The 2012 report, however, argues that they were excluded as unnecessary: "the social science foundation for using either 11 items or 9 items together in one scale is well-supported," adding, "Whether or not these two questions are included in a scale of factual science knowledge has little bearing on the summary portrait of Americans' knowledge that the scale portrays."