Math Help Website Needs New Design

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This customer received 31 web designs from 12 designers. They chose this web design from tanya as the winning design.
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Web Design Brief
Looking to refresh the design of my existing site (freemathhelp.com) to be easier on the eyes. I am fully capable of doing the HTML coding and have for years, but I don't have the eye for good design, colors, layout, and fonts. This is where I need help!
I need both a new design scheme and a new logo that matches. The overall functionality will be the same as the existing site, and should not be unrecognizable.
Target Market(s)
It should appeal to students (age 13-22) and their parents, so it should NOT be childish in appearance, nor should it be corporate.
Look and feel
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Upmarket
Requirements
Must have
- Should be simple, easy-to-navigate, and neither childish nor corporate. I am looking for a design for both the homepage and a similar "content" page. Simple, bold colors are preferred. A logo should be prominent at the top, with a search bar nearby. Below that I need a similar navigational area like I already have. Then, I need about 200px wide ad space on the left of the main body area.