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Below are the final questions from SAT Practice Test — September 2026 Asia Form A — Math Module 2, one of the real timed practice exams in our question bank, with full explanations.
\(x^2-14x+y^2+22y=26\) In the xy-plane, the graph of the given equation is a circle. What is the length of the circle's diameter?
Explanation: Completing the square gives \((x-7)^2+(y+11)^2=196\). The radius is 14, so the diameter is 28.
\(f(x)=5x^2+90x+406\) The function \(g\) is defined by \(g(x)=f(x+8)\). What is the minimum value of \(g(x)\)?
Explanation: \(f(x)=5(x+9)^2+1\), so its minimum is 1. A horizontal shift in \(g(x)=f(x+8)\) does not change that minimum.
The function \(f(n)=7(20.52)^{n/4}\) gives each term of a sequence as a function of the term's position, \(n\), in the sequence, where \(n\) is a whole number. The value of the term in position 14 is \(p\)% more than the value of the term in position 10. What is the value of \(p\)?
Explanation: \(f(14)/f(10)=(20.52)^{(14-10)/4}=20.52\). The percent increase is \((20.52-1)100=1{,}952\%\).
In isosceles triangle \(ABC\), sides \(AB\) and \(AC\) are congruent. Point \(D\) divides side \(BC\) such that the length of segment \(BD\) is \(\frac{3}{4}\) of the length of segment \(BC\). Point \(E\) lies on side \(AB\) and point \(F\) lies on side \(AC\) such that when segments \(DE\) and \(DF\) are drawn, angle \(BED\) is congruent to angle \(CFD\). If the length of segment \(BE\) is 12, what is the length of segment \(CF\)?
Explanation: Since \(BD=(3/4)BC\), \(BD/DC=3\). The angle condition yields corresponding similar triangles, so \(CF=BE/3=4\).
Which expression is a factor of \(y^2(x-8)-9(x-8)^3\)?
Explanation: Factor to get \((x-8)[y^2-9(x-8)^2]=(x-8)(y-3x+24)(y+3x-24)\).