UPCAT & Civil Service (Philippines) · Mathematics & Science Proficiency

Algebra and Coordinate Geometry

6 practice questions, each with the answer and an explanation.

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All 6 questions

Find the roots of the quadratic equation $3 x^{2} - 10 x + 8 = 0$ .
What is the equation of the line passing through $(- 3, 5)$ and perpendicular to the line $2 x - 4 y + 7 = 0$ ?
If $lo g_{10} (x) + lo g_{10} (x - 3) = 1$ , what is the value of $x$ ?
Simplify the algebraic expression: $\frac{x ^{3} - 27}{x ^{2} - 9} \times \frac{x + 3}{x ^{2} + 3 x + 9}$ .
What is the distance between the center of the circle $x^{2} + y^{2} - 4 x + 6 y - 12 = 0$ and the origin $(0, 0)$ ?
If the sum of an infinite geometric series is 12 and the common ratio is $\frac{1}{4}$ , what is the first term $a_{1}$ ?

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