{"id":"pert-free","timeLimitSec":420,"questions":[{"id":"pf-01","section":"math","q":"Solve for x: 3x − 7 = 2x + 5","options":["−12","2","12","−2"],"answer":2,"explain":"Subtract 2x from both sides to get x − 7 = 5, then add 7: x = 12. Check: 3(12) − 7 = 29 and 2(12) + 5 = 29."},{"id":"pf-02","section":"math","q":"Which expression is the factored form of x² − 5x − 14?","options":["(x − 7)(x + 2)","(x − 7)(x − 2)","(x + 7)(x − 2)","(x − 14)(x + 1)"],"answer":0,"explain":"Find two numbers that multiply to −14 and add to −5: −7 and +2. So x² − 5x − 14 = (x − 7)(x + 2)."},{"id":"pf-03","section":"reading","q":"Many people think of bamboo as a tree, but it is actually a grass. Some species can grow almost a meter in a single day, and a bamboo stand can be harvested every few years without replanting, because new shoots keep rising from the same roots. For these reasons, builders in several countries now use bamboo in place of slow-growing timber. Which statement best expresses the main idea of the passage?","options":["Bamboo has to be replanted after every harvest.","Bamboo's fast regrowth makes it a useful building material.","Builders should stop using timber altogether.","Bamboo grows faster than any other plant on Earth."],"answer":1,"explain":"The passage builds to its last sentence: bamboo grows fast and regrows from its roots, so builders use it instead of timber. The other choices overstate or contradict the text."},{"id":"pf-04","section":"writing","q":"Choose the sentence that is written correctly.","options":["The box of old photographs is on the top shelf.","The box of old photographs have been on the top shelf.","The box of old photographs are on the top shelf.","The box of old photographs were on the top shelf."],"answer":0,"explain":"The subject is \"box\" (singular); \"of old photographs\" is only a phrase describing it. A singular subject takes \"is\" or \"has been\"."},{"id":"pf-05","section":"writing","q":"Read the two sentences: \"The library closed early on Friday. The heating system had broken down.\" Which choice combines them most clearly?","options":["The library closed early on Friday, but the heating system had broken down.","Closing early on Friday, the heating system at the library had already broken down.","The library closed early on Friday, the heating system had broken down.","The library closed early on Friday because the heating system had broken down."],"answer":3,"explain":"The second sentence gives the reason for the first, so \"because\" shows the relationship. Joining them with only a comma is a comma splice, \"but\" signals a contrast that is not there, and the \"Closing early\" version says the heating system closed early."}]}