```typescript
@Entry
@Component
struct QuickTestMainPage {
  @State paperAllTime: number = 0; // Total exam duration (exam mode)
  @State remainTimeUi: string = "00:00"; // Formatted time display
  @State remainTime: number = 0; // Actual time value (countdown or stopwatch)

  private doExamTimer: number | null = null; // Timer reference

  aboutToAppear(): void { 
    this.timerInit(); // Initialize timer on component appearance
  }

  aboutToDisappear(): void {
    // Clean up timer when component disappears
    if (this.doExamTimer) {
      clearTimeout(this.doExamTimer);
      this.doExamTimer = null;
    }
  }

  // Initialize timer based on mode
  timerInit() {
    if (this.isTest) {
      // Exam mode: countdown from total time
      this.remainTime = this.paperAllTime - this.makeTime;
    } else {
      // Practice mode: stopwatch timing
      this.remainTime = this.makeTime;
    }
    this.updateTimeDisplay();
    this.startTimer();
  }

  // Update UI with formatted time
  updateTimeDisplay() {
    this.remainTimeUi = Utils.formatSeconds(this.remainTime);
  }

  // Core timer logic
  startTimer() {
    this.doExamTimer = setTimeout(() => {
      if (this.isTest) {
        // Exam countdown mode
        this.remainTime--;
        this.makeTime = this.paperAllTime - this.remainTime;

        // Stop timer when time expires
        if (this.remainTime <= 0) {
          this.handleTimeExpired();
          return;
        }
      } else {
        // Practice stopwatch mode
        this.remainTime++;
        this.makeTime = this.remainTime;
      }

      this.updateTimeDisplay();
      this.startTimer(); // Recursive call for continuous timing
    }, 1000);
  }

  // Handle exam time expiration
  handleTimeExpired() {
    // Implement exam submission logic here
    console.log("Exam time has expired!");
  }

  build() {
    Column() {
      // Timer icon
      CustomIcon({
        iconType: CustomIconType.icon_timer,
        iconSize: 19,
        iconColor: StyleRes.getStyleColor(StyleColor.textBoldColor, this.lightMode)
      })

      // Time display
      Text(this.remainTimeUi)
        .fontColor(StyleRes.getStyleColor(StyleColor.texSubColor, this.lightMode))
        .fontSize(11)
    }
  }
}
```

```typescript
class Utils {
  static formatSeconds(seconds: number): string {
    const mins = Math.floor(seconds / 60).toString().padStart(2, '0');
    const secs = (seconds % 60).toString().padStart(2, '0');
    return `${mins}:${secs}`;
  }
}
```

   this.isTest = true;
   this.paperAllTime = 3600; // 60 minutes in seconds

   this.isTest = false;
   this.makeTime = 0; // Start from zero