In a few days, Mark Bratton will start ninth grade at Yorktown High School in Arlington. He already has been assigned to a home room and to the required classes in English, mathematics, world geography and physical education. For his two elective courses, Mark chose advanced band -- he plays the trombone -- and woodworking.

Since Yorktown is a public school supported by tax revenues, Mark will be able to walk into the red brick building without paying a penny for registration or tuition. The instruction and the books that he receives there will be free.

That does not mean he will not have any school expenses.

He and the thousands of other Washington-area students now getting ready for the new school year will face a number of fees and financial payments, ranging from the $10 needed for a woodworking class project to $40 for a pair of football cleats. Actual costs will vary widely, depending on student interests and family ability to pay.

Mark estimates that his back-to-school bills will total nearly $150 in the first few weeks, with most of that going for his band activities. That does not count what the Brattons are spending on Mark's school clothes, lunches or basic pencil and paper supplies, or the estimated $20 in monthly expenses for everything from dances to soft drinks at school play intermissions during the year.

The first day of financial reckoning will come officially for Mark on Sept. 8, when students return to school in Arlington, Alexandria and the District of Columbia. It will come today in Prince George's County, Tuesday in Montgomery and Sept. 9 in Fairfax.

Although the miscellaneous school costs are optional in most cases, parents who have the means to pay them generally do so. "When parents can't, I can see where it would be traumatic for the kids," said Pat Good, whose son John attends Bethesda-Chevy Chase High School.

School officials tend to play down the expenses, emphasizing that most are optional and that fees may be waived for children whose parents cannot pay. "Anyone who qualifies for a free lunch also qualifies for a free musical instrument," said Roy Smith, the music curriculum specialist for the Alexandria schools, which normally charge $25 a year for instrument rental.

In between those who cannot afford lunch and those who can afford almost anything are the middle-income families who try to provide their youngsters with all of the essentials and enough of the extras to allow them to participate in the mainstream of the school experience. Here is a summary of some typical expenses that parents can expect in the days to come:

Elementary school: Insurance, about $4 a year; school pictures, $5 to $6, and membership in the PTA (Parent-Teacher Association), about $2.50 per person. In addition, some schools have a one-week camp for sixth-graders to give them a "hands-on environmental experience." For example, students at Cannon Road Elementary School, Silver Spring, who took part in the camp program last year paid $32 each. Other schools may have one-day field trips ranging from as little as 75 cents to as much as $10.

Intermediate school: Gym clothes, $6 to $10; towel service, from as little as $2 a year at Prince George's schools to as much as $9.50 a year at Fairfax County schools; lockers and locks, up to $3 a year at some schools. Materials for art, industrial arts, woodworking and home economics vary widely and can range up to $10, depending on school policy and student project choice; field trips may range up to $15; school dances, $1 to $2; athletic game admissions, $1 to $2; school pictures, $5 to $10; insurance, about $4 a year, and PTA, about $2.50 a person. Alexandria intermediate students also pay $6 for book rental.

High school: In addition to the expenses listed for intermediate schools, high school costs also typically include yearbooks, $15 to $20; class dues, which may be only $3 for freshmen, sophomores and juniors but perhaps as much as $60 for seniors; school dances, $3 to $5. Alexandria high school students also pay a $6 book rental charge. Juniors at area high schools may order senior rings that average $75 to $100 each but can range up to $300 for gold. And seniors can expect cap and gown rentals, about $6; senior yearbook pictures, $25 to $50, and senior prom expenses that may range into hundreds of dollars.

News of the latest school expenses often reaches families in the form of organized notices like the one that Jo-Anne Spriggs just received from Woodson High School in Northeast D.C., where she now is starting her senior year. Among other things, the notice said, "Our class fee for seniors will be somewhere between $45 and $60 and will include everything except the prom and the class ring."

The fee, Jo-Anne said, will be used to defray costs for the senior prom, class trip, graduation ceremony, senior class picnic and senior class night.

Parents often learn about school expenses informally, when students come home and announce the need for special supplies.

"Some teachers have specific things you have to buy," said John Good, who is starting his junior year at Bethesda-Chevy Chase High School. "Like last year, I had to have carbon paper for Latin class because the teacher wanted us to have one copy of our homework assignments to keep and one for her to check.

"And then I had to buy my French book -- it was about $4 -- because the teacher wanted us to write in it," John said. He also purchased a French-English dictionary and a French composition workbook.

Probably the biggest bills that students run up are for special school teams and activities, such as football, journalism and band.

"It can get expensive," said Shirley Bratton, who estimates that they probably will spend about $100 to get son Mark started in band. That includes the recommended clothing for band members, the $25 rental fee for Mark's trombone and the $5 membership in the band boosters club.

In addition, there is the maintenance of the instrument itself.

"You have to buy things like slide oil for a trombone," Mrs. Bratton said. A year's supply cost about $4. "And then, last year, he bent the slide and it cost $25 to repair it."

Besides the $100 band costs, Mark expects his school expenses to include $10 for woodworking class projects, $10 for school pictures, $10 for gym clothes, $8 for gym towel service and $3 for a gym lock. That works out to nearly $150.

Other students may spend much less than that -- or much more.

Yeva Johnson, who plays flute and piccolo in the band at Bethesda-Chevy Chase High School, attended music camp for two weeks this summer at a cost of $200. She owns her own flute, which cost $600, and rents a piccolo from a music store at an annual cost of $80. Each week she takes a music lesson from a private teacher who charges $13 an hour.

There are unpredictable band expenses, too. "Last year, I lost a band folder and the music that was in it. That was $15 to $20 that I had to pay for," Yeva said.

Journalism students can have their own brand of extra school expenses.

Jo-Anne Spriggs, who will be editor of the Woodson High student newspaper, hopes to attend a conference for student journalists here in November and another one in New York next March. The D.C. meeting probably will cost about $10 for registration, she said. The New York meeting could be as much as $120.

Another school activity with a price tag is football. Here is a rundown from Jim Crawford, the football coach at Friendly High School in Oxon Hill and the father of a senior football player, Jim Jr.:

"A football physical exam cost roughly $25. Spikes are about $40 a pair and he needs two pair each season. Socks and things are about $20 a year. And my son has been to football camp for eight straight years -- that is $150 for the week plus spending money."

Team mothers also contribute casserole dishes, drinks and desserts for dinners that are held regularly for the players, Crawford said. The cost for a host family for one team dinner can amount to as much as $200, he said. Then there is an annual banquet that costs $12.50 a person.

Players and parents obviously are willing to pay the price.

"I had 141 come out for football this year," Crawford said. That is nearly 50 percent more than the 95 he will pick for the team.