How to set cornerRadius for only top-left and top-right corner of a UIView?

I am not sure why your solution did not work but the following code is working for me. Create a bezier mask and apply it to your view. In my code below I was rounding the bottom corners of the _backgroundView with a radius of 3 pixels. self is a custom UITableViewCell:

UIBezierPath *maskPath = [UIBezierPath
    bezierPathWithRoundedRect:self.backgroundImageView.bounds
    byRoundingCorners:(UIRectCornerBottomLeft | UIRectCornerBottomRight)
    cornerRadii:CGSizeMake(20, 20)
];

CAShapeLayer *maskLayer = [CAShapeLayer layer];

maskLayer.frame = self.bounds;
maskLayer.path = maskPath.CGPath;

self.backgroundImageView.layer.mask = maskLayer;

Swift 2.0 version with some improvements:

let path = UIBezierPath(roundedRect:viewToRound.bounds, byRoundingCorners:[.TopRight, .BottomLeft], cornerRadii: CGSizeMake(20, 20))
let maskLayer = CAShapeLayer()

maskLayer.path = path.CGPath
viewToRound.layer.mask = maskLayer

Swift 3.0 version:

let path = UIBezierPath(roundedRect:viewToRound.bounds,
                        byRoundingCorners:[.topRight, .bottomLeft],
                        cornerRadii: CGSize(width: 20, height:  20))

let maskLayer = CAShapeLayer()

maskLayer.path = path.cgPath
viewToRound.layer.mask = maskLayer

Swift extension here

And finally… there is CACornerMask in iOS11! With CACornerMask it can be done pretty easy:

let view = UIView()
view.clipsToBounds = true
view.layer.cornerRadius = 10
view.layer.maskedCorners = [.layerMaxXMinYCorner, .layerMinXMinYCorner] // Top right corner, Top left corner respectively