Quadratic
What is the highest power of the variable in a quadratic equation?
2
What digits are used in base 2?
0 and 1
State whether this statement is true or false: All prime numbers are odd numbers.
False
What is a vertex in graph theory?
A point or node in a graph.
Determine the value of x if x² − 9 = 0.
x = 3 or x = −3
Convert 1011₂ into base 10.
11₁₀
Identify the quantifier in the statement: All squares have four equal sides.
All
What is an edge in a graph?
A connection between two vertices.
Factorise x² − 7x + 12 completely.
(x − 3)(x − 4)
Convert 45₁₀ into base 5.
140₅
Write the converse of: If a number is divisible by 4, then it is even.
If a number is even, then it is divisible by 4.
A graph has vertices A, B, C and D, with edges AB, AC, BC and CD. Find the degree of vertex C.
3
Find the axis of symmetry of f(x) = x² − 6x + 5.
3
Calculate 1011₂ + 1101₂. Give your answer in base 2.
11000₂
Premise 1: If p, then q. Premise 2: p is true. What is the conclusion?
q is true
A graph has 5 vertices with degrees 2, 3, 3, 4 and 4. How many edges does the graph have?
8 edges
The function f(x) = x² − 8x + k has a minimum value of −7. Find k.
k = 9
Given 234₅ = N₈, determine N.
101₈
Determine whether the argument is valid: If a number is divisible by 6, then it is divisible by 3. 12 is divisible by 3. Therefore, 12 is divisible by 6.
Invalid
A connected graph has exactly two vertices of odd degree. Can an Euler trail exist that uses every edge exactly once?
Yes