Geometry and algebra
Review the permitted syllabus objectives and practice reviewed questions for this CSCA topic.
What to study
- equations and properties of lines, circles, ellipses, hyperbolas and parabolas
- vector operations
- basic arithmetic with complex numbers
- three-dimensional Cartesian coordinates and properties of simple solids
The scope shown here follows the syllabus-derived guardrails used by the CSCAPrep question factory. Related advanced material is not added unless it appears in the defined scope.
Practice this topic
Easy · Geometry and algebraWhat is the product (2 + 3i)(1 - i)?Standard · Geometry and algebraWhat is the center of the circle given by x^2 + y^2 - 4x + 6y - 3 = 0?Easy · Geometry and algebraGiven vectors u = (3, -2) and v = (1, 4), what is 2u - v?Easy · Geometry and algebraA rectangular box has vertices at (0,0,0), (4,0,0), (0,3,0), and (0,0,12). What is the length of the space diagonal of this box?Standard · Geometry and algebraWhat is the value of (3 + 2i) / (1 - i)?Easy · Geometry and algebraA cube has vertices at (0,0,0), (2,0,0), (0,2,0), and (0,0,2). What is the distance from the origin to the center of the…Easy · Geometry and algebraAn ellipse has its center at the origin, a focus at (3, 0), and a vertex at (5, 0). What is the…Easy · Geometry and algebraGiven vectors u = (2, -3) and v = (-1, 4), what is the vector 3u - 2v?Hard · Geometry and algebraWhat is the center of the ellipse given by the equation 9x^2 + 25y^2 - 18x + 100y - 116 = 0?Easy · Geometry and algebraA rectangular box has dimensions 3, 4, and 12. What is the length of the space diagonal of the box?