GBML Conventions + Arithmetic
Can you put a "?" next to any of your answers?
No.
How do you find the determinant of this 2x2 matrix?
[ a b ]
[ c d ]
ad-bc
What is a centroid and what is the Centroid Theorem?
1. The point where all the medians of a triangle intersect
2.The centroid splits all medians in the ratio of 2:1.
Name and describe the 3 forms of a quadratic equation
Standard: y = ax2 + bx + c
Factored: y = a(x-r1)(x-r2)
Vertex: y = a(x-h)2 + k
Name all of the trig functions and their right triangle definitions.
Sin = opposite/hypotenuse
Cos = adjacent/hypotenuse
Tan = opp/adj
Cot = adj/opp
Sec = hyp/adj
Csc = hyp/opp
The solutions to x2 + 2x = 0 are x=0 and x=2. How do you write this as your answer?
x=0, x=2
How do you multiply these 2x2 matrices?
[ a b ] [ e f ]
[ c d ] [ g h ]
[ ae+bg af+bh ]
[ ce+dg cf+dh ]
How many degrees are in each angle of a polygon with n sides?
180(n-2)/n
What are Vieta's Formulas?
In quadratic equation ax2 + bx +c = 0, the sum of the roots is -b/a, and the product of the roots is c/a.
sin2x + cos2x = ?
1
Consider the infinite set of integers {2 * 3 * 4 * 5, 3 * 4 * 5* 6, 4 * 5 * 6 * 7, ..., n * (n+1) * (n+2) * (n+3)}. Compute the greatest common factor for this set of integers.
24
George's age is three times the age of his daughter Marah. In five years, the ratio of their ages will be 5:2. Compute Marah's current age.
15
The supplement of the complement of ∠ABC measures 152°. Compute m∠ABC in degrees.
62
For some integer b, one factor of 5x2 + bx - 80 is x + 8. Compute b.
30
Name 3 different ways to define cos(2x)
2cos2x - 1
cos2x - sin2x
1 - 2sin2x
Let A, B, and C be three numbers such that A = 2√38, B = (√1351)/3, and C = √486 - √96. Arrange the three numbers from least to greatest.
C < B < A
1234x + 923y = 301
784x + 1095y = 1717
Find x.
-2
In Triangle △QUA, D is the midpoint of QA. Given that QA = 18, DU = 9, and QU = 10, compute AU.
4√14
Suppose that i = √-1. Given that -3 + i is a root of x3 + cx - 90 = 0 for some integer c, compute c.
-26
Solve on the interval 0 ≤ x < 360°: sin2x + 3cos2x = 1
x = 90°, x = 270°
Compute the least positive integer N such that √(6! * 7! * N) is a perfect square.
8575
Find A-1 (the inverse of this matrix) if A =
[ a b ]
[ c d ]
[Show on board]
Point C is the centroid of equilateral triangle PQR. Compute the perimeter of △PQR, if the perimeter and area of △CQR are numerically equal.
12(2+√3)
A 30-inch piece of wirer is cut into two pieces. One piece is bent to form a square and the other piece is bent to form an isosceles right triangle. Given that the area of the square is equal to the area of the isosceles right triangle, compute the length of a leg of the isosceles right triangle in the form (a√2 - b)/c, where a, b, and c are positive, relatively prime integers.
(45√2 - 30)/7
Given that 1/(1-cos2x) = 2022, compute cos(2x).
1010/1011