DP Mathematics HL Questionbank

• Syllabus

1.9

Sub sections and their related questions

Solutions of systems of linear equations (a maximum of three equations in three unknowns), including cases where there is a unique solution, an infinity of solutions or no solution.

• 12M.2.hl.TZ2.11a: Find the values of k for which the following system of equations has no solutions and the value...
• 12N.1.hl.TZ0.6a: If each of these equations defines a plane, show that, for any value of a , the planes do not...
• 12N.1.hl.TZ0.6b: Find the value of b for which the intersection of the planes is a straight line.
• 08N.2.hl.TZ0.5: (a)     Find the set of values of k for which the following system of equations has no...
• SPNone.1.hl.TZ0.7a: Show that this system does not have a unique solution for any value of \(\lambda \) .
• SPNone.1.hl.TZ0.7b: (i)     Determine the value of \(\lambda \) for which the system is consistent. (ii)     For...
• 13M.2.hl.TZ1.2: Find the value of k such that the following system of equations does not have a unique...
• 10M.2.hl.TZ1.2: The system of equations \[2x - y + 3z = 2\] \[3x + y + 2z = - 2\] \[ - x + 2y + az = b\] is...
• 10M.2.hl.TZ2.7a: Find the value of each of a, b and c.
• 10M.2.hl.TZ2.7b: The equations of three planes are      \(2x - 4y - 3z = 4\)      \( - x + 3y + 5z = - 2\)     ...
• 13M.2.hl.TZ2.2a: Express the system of equations in matrix form.
• 13M.2.hl.TZ2.2b: Find the solution to the system of equations.
• 11M.2.hl.TZ1.11a: Given that \(a = 0\) , show that the three planes intersect at a point.
• 11M.2.hl.TZ1.11b: Find the value of a such that the three planes do not meet at a point.
• 11M.2.hl.TZ1.11c: Given a such that the three planes do not meet at a point, find the value of \(k\) such that the...
• 14M.2.hl.TZ1.4: A system of equations is given below.      \(x + 2y - z = 2\)      \(2x + y + z = 1\)     ...
• 14M.1.hl.TZ2.3: (a)     Show that the following system of equations has an infinite number of solutions.     ...
• 15M.2.hl.TZ2.7a: Find conditions on \(\alpha \) and \(\beta \) for which (i)     the system has no...
• 15M.2.hl.TZ2.7b: In the case where the number of solutions is infinite, find the general solution of the system of...
• 15N.2.hl.TZ0.2: The three planes having Cartesian equations \(2x + 3y - z = 11,{\text{ }}x + 2y + z = 3\) and...
• 16M.1.hl.TZ2.1: The following system of equations represents three planes in space. \[x + 3y + z =  -...
• 17N.2.hl.TZ0.1: Boxes of mixed fruit are on sale at a local supermarket. Box A contains 2 bananas, 3 kiwifruit...