Heather Morris and co. demonstrating why girls “Run the World.” (Fox)

Harry Shum Jr. proved he can both sing and dance. Amber Riley matched Jennifer Hudson note for note. And as plucky school presidential candidate Brittany S. Pierce, Heather Morris demonstrated that girls really can run the world ... as long as they remember their leather mini-skirts and thigh-high boots.

Indeed, the musical-number-per-minute ratio in this week’s episode of “Glee” — title: “Asian F” — bumped up from last week, yielding six total, or roughly one per 10 minutes of air time (commercials included). Tuesday’s latest peek inside William McKinley High also stands as the best episode of Season 3 so far, and perhaps a sign that the showrunners weren’t kidding when they promised “Glee” would get back to basics after its semi-bumpy second year.

Naturally, “Asian F” prompted contemplation of various questions: Does Principal Figgins really still think Tina is a vampire? Why was Mike allowed to incorporate half the football team into his “West Side Story” audition for the part of Riff? And hey, wasn’t it good to see Ralph Malph, a.k.a. Don Most, on TV again in the role of Emma’s “ginger supremacist” father?

But let’s turn our attention to assessing those musical performances.

Jennifer Hudson’s “Spotlight” sung by Mercedes

Mercedes is supposedly shining with new confidence. Personally, I thought she always projected a certain sense of pride that masked any private insecurities she may have had. But that’s me. According to the narrative arc of “Asian F” — in which her uber-supportive boyfriend, Shane (“Friday Night Lights’s” Lamarcus Tinker) persuades her to go full-on diva — Mercedes decides it’s time to start going for the starring roles, a new attitude demonstrated by Mercedes’s performance of Hudson’s “Spotlight.” Grade: B+ (which, according to this episode, is the equivalent of an Asian F-, I guess?)

Beyonce’s “Run the World (Girls)” sung by Brittany and co.

Is there anything more exciting than an all company, pro-girl power musical number that also doubles as a political rally? Don’t think so. As always, Morris showed off her amazing dance skills, which was great to see even if this bump-and-grind attempt at female empowerment suggested that girls are more likely to run a stripper-pole aerobics class than any higher branches of government. Grade: A-.

“Cool” from “West Side Story” sung by Mike Chang

Chang, as played by Harry Shum Jr., has phenomenal moves. We know this. But in his try-out for the role of Riff in “West Side Story” — part of the longest, highest-production-value audition process in high school musical history — Mike proved he can sing, too. Also, that he’s adept at recruiting members of the football team to participate in his audition and teaching them elaborate choreography seemingly overnight. (Did anyone else completely forget Mike was on the football team? Good. Not just me.) Grade: A for execution, C for believability.

“It’s All Over” from “Dreamgirls,” sung by Mercedes and co.

This was the best number of the night. The transition from tension-filled Booty Camp rehearsal — in which Mercedes totally lost it on Mr. Schue (Matthew Morrison) — to this song from “Dreamgirls,” featuring lyrics adapted with a McKinley High spin, was seamless. It highlighted an existing storyline in a way that made sense and even gave us some impressive high notes from both Mercedes and Kurt (Chris Colfer), This is how it’s done, “Glee.” Grade: A. (Text updated and video updated at 10:37 a.m.)

“Out Here on My Own” from “Fame,” as performed by Rachel and Mercedes

The showdown for the female lead in “West Side Story” came down to this Maria-off, in which Rachel (Lea Michele) and Mercedes had to out-vocalize each other during callbacks while their fellow New Directions members frothed at the mouth in showtune anticipation. Both ladies delivered, a fact that led to double casting the part and Mercedes’s defection to McKinley’s rival (and totally unnecessary-except-from-a-plot-perspective) glee club. Grade: A-

“Fix You” by Coldplay, by Will Schuester and full cast

Okay, this was an admittedly sappy closer of the episode. But it mostly worked, especially when the song was paired with that the image of Emma (Jayma Mays) and Mr. Schue praying and that wonderful montage of the Gleeks checking the “West Side” cast list. When everyone gathered onstage in white shirts and suddenly appeared to be doing a choral number in a Gap commercial, the emotional impact lost some of its wallop. Grade: A-.