WASHINGTON — After a storm of complaints, the Obama administration on Tuesday unveiled simplified forms to apply for insurance under the president’s new health care law. You won’t have to lay bare your medical history but you will have to detail your finances.

An earlier version of the forms had provoked widespread griping that they were as bad as tax forms and might overwhelm uninsured people, causing them to give up in frustration.

The biggest change: a five-page short form that single people can fill out. That form includes a cover page with instructions and another page if you want to designate someone to help you through the process.

But the abridged application form for families still runs to 12 pages, even if most households will not have to fill out every page. Most people are expected to take another option, applying online.

Americans remain confused about what the health law will mean for them. A Kaiser Family Foundation poll released Tuesday found that 4 in 10 are unaware it’s the law of the land. Some think it’s been repealed by Congress.

At his news conference Tuesday, President Barack Obama hailed the simplified forms as an example of how his team listened to criticism from consumer groups and made a fix. The law’s full benefits will be available to all next year, he emphasized, even if Republicans in Congress still insist on repeal and many GOP governors won’t help put it into place.

When the first draft of the application turned out to be a clunker, “immediately, everybody sat around the table and said, ‘Well, this is too long, especially...in this age of the Internet,”’ Obama recounted. “‘People aren’t going to have the patience to sit there for hours on end. Let’s streamline this thing.”’

The flap over the application forms was a “first test” of the administration’s ability to confront problems as they emerge, said Sam Karp, vice president of programs at the California HealthCare Foundation.

The applications will start becoming familiar to consumers less than six months from now, on Oct. 1, when new insurance markets open for enrollment in every state. They are not for people already signed up in their employer’s plan, only the uninsured. Filling out the application is just the first part of the process, which lets you know if you qualify for financial help. The government asks to see what you’re making because Obama’s Affordable Care Act is means-tested, with lower-income people getting the most generous help to pay premiums. Consumers who aren’t applying for financial help still have to fill out a five-page form.