10 Questions
Match the following methods of proof with their descriptions:
Proof by exhaustion = trying all the options Disproof by counter example = showing that a statement is untrue Factor Theorem = using the equation of a circle in the form (x − a)2 + (y − b)2 = r2 Remainder Theorem = proceeding from given assumptions through a series of logical steps
Match the following algebraic concepts with their definitions:
Quotient = the result of dividing one polynomial by another Remainder = the amount left over when one polynomial is divided by another Factor = a polynomial multiplied by another to get a product Divisor = a polynomial that divides another polynomial
Match the following circle properties with their descriptions:
The angle in a semicircle is a right angle = a characteristic of a circle's centre The perpendicular from the centre to a chord bisects the chord = a property of a circle's radius The perpendicularity of radius and tangent = a characteristic of a circle's circumference The equation of a circle in the form (x − a)2 + (y − b)2 = r2 = a property of a circle's diameter
Match the following mathematical concepts with their applications:
Coordinate geometry = proving that a statement is untrue Algebraic division = finding the equation of a circle Factor Theorem = dividing a polynomial by (ax + b) Remainder Theorem = determining the remainder of a polynomial division
Match the following mathematical concepts with their examples:
Cubic expressions = x3 + 3x2 − 4 and 6x3 + 11x2 − x − 6 Linear equations = x + 2 = 5 Quadratic equations = x2 + 4x + 4 = 0 Polynomial long division = dividing a polynomial by (ax + b)
Match the following mathematical concepts with their corresponding areas of mathematics:
Arithmetic sequences and series = Sequences and series Laws of logarithms = Exponentials and logarithms Binomial expansion = Algebra Trigonometric equations = Trigonometry
Match the following mathematical formulas with their corresponding applications:
tanθ = sinθ/cosθ = Trigonometry Σ notation = Sequences and series $a^x$ = Exponentials and logarithms $n!$ = Binomial expansion
Match the following mathematical equations with their corresponding solution methods:
2sin(x) + 3 = 4 = Trigonometric equations $ax = b$ = Exponentials and logarithms $x^n + 1 = f(x^{n-1})$ = Sequences and series $y = ax$ = Exponentials and logarithms
Match the following mathematical concepts with their corresponding theorems or formulas:
Sum of a finite arithmetic series = Formula for the nth term Sum to infinity of a convergent geometric series = Formula for the sum of a finite geometric series Binomial expansion of (a + bx)^n = n! and nCr notation Laws of logarithms = Logarithmic identities
Match the following mathematical concepts with their corresponding graphical representations:
y = ax = Exponential graph sin^2(x) + cos^2(x) = 1 = Trigonometric graph Arithmetic sequence = Linear graph Geometric sequence = Exponential graph
Understand the structure of mathematical proof and apply methods such as proof by exhaustion and disproof by counter example. Practice proving statements about integers and algebra, including showing that certain statements are untrue.
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