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A Level Further Maths Core Pure
Exam Questions and Answers A+
Graded (2025)
Form of complex numbers - CORRECT ANSWER-a + bi
Real and imaginary parts of z = a + bi - CORRECT ANSWER-Re(z) = a, Im(z) = b
When two complex numbers are equal, what is true - CORRECT ANSWER-Their
real parts are equal and their imaginary parts are equal
i² - CORRECT ANSWER--1
i³ - CORRECT ANSWER--i
i⁴ - CORRECT ANSWER-1
Determinant for two real roots (distinct roots) - CORRECT ANSWER-b² - 4ac > 0
Determinant for one real root (repeated roots) - CORRECT ANSWER-b² - 4ac = 0
Determinant for no real roots (two distinct complex roots) - CORRECT ANSWER-
b² - 4ac < 0
Complex conjugate for z = a + bi - CORRECT ANSWER-z* = a - bi
Product zz* is always - CORRECT ANSWER-Real
Expansion of (z - α)(z - β) = 0 - CORRECT ANSWER-z² - (α + β)z + αβ = 0
Possible Roots in a Cubic Equation - CORRECT ANSWER-Three real roots or one
real root and a complex conjugate pair of roots
Possible Roots in a Quartic Equation - CORRECT ANSWER-Four real roots or two
real roots and a complex conjugate pair of roots or two sets of conjugate pairs
A Level Further Maths Core Pure
Exam Questions and Answers A+
Graded (2025)
Form of complex numbers - CORRECT ANSWER-a + bi
Real and imaginary parts of z = a + bi - CORRECT ANSWER-Re(z) = a, Im(z) = b
When two complex numbers are equal, what is true - CORRECT ANSWER-Their
real parts are equal and their imaginary parts are equal
i² - CORRECT ANSWER--1
i³ - CORRECT ANSWER--i
i⁴ - CORRECT ANSWER-1
Determinant for two real roots (distinct roots) - CORRECT ANSWER-b² - 4ac > 0
Determinant for one real root (repeated roots) - CORRECT ANSWER-b² - 4ac = 0
Determinant for no real roots (two distinct complex roots) - CORRECT ANSWER-
b² - 4ac < 0
Complex conjugate for z = a + bi - CORRECT ANSWER-z* = a - bi
Product zz* is always - CORRECT ANSWER-Real
Expansion of (z - α)(z - β) = 0 - CORRECT ANSWER-z² - (α + β)z + αβ = 0
Possible Roots in a Cubic Equation - CORRECT ANSWER-Three real roots or one
real root and a complex conjugate pair of roots
Possible Roots in a Quartic Equation - CORRECT ANSWER-Four real roots or two
real roots and a complex conjugate pair of roots or two sets of conjugate pairs
