AMAYTYC Student Math League Test Questions and Solutions Arranged by Topic

AMAYTYC Student Math League Test Questions and Solutions Arranged by Topic

By Kevin Mirus, Madison Area Technical College

I. Analytic Geometry

October-November-December 2000 Test

Long (Analytic) Solution

Quick (Calculator) Solution

1). Graph the point (-3, -2)
2). Note that the steepest line not passing through quadrant II goes through the origin.
3). Find the slope between these two points:
/ 1). The equation of a line with slope m through a point (x0, y0) is:
y – y0 = m(x – x0)
è y = m(x – x0) + y0
2). Enter these equations into your TI graphing calculator:

3). Pick the correct graph:

(Choice C; you’d have to keep track of which line corresponds to which answer as the calculator graphs)

October-November-December 2000 Test

Long (Analytic) Solution

Quick (Calculator) Solution

1) Graph the points:

2) Calculate the lengths of the three sides:

3) Plug into Heron’s formula for the area of a triangle:

Note:

/ 1). The equation of a line with slope m through a point (x0, y0) is:
y – y0 = m(x – x0)
è y = m(x – x0) + y0
2). Use this to enter the equations for the lines between the points into your TI graphing calculator:

3). Plot the graph to verify your equations:

4). Use the fnInt function to find the area between the lines…

Test

Long (Analytic) Solution

Quick (Calculator) Solution

Test

Long (Analytic) Solution

Quick (Calculator) Solution

Test

Long (Analytic) Solution

Quick (Calculator) Solution

Test

Long (Analytic) Solution

Quick (Calculator) Solution

Test

Long (Analytic) Solution

Quick (Calculator) Solution

Test

Long (Analytic) Solution

Quick (Calculator) Solution

II. Geometry

October-November-December 2000 Test

Long (Analytic) Solution

Quick (Calculator) Solution

Test

Long (Analytic) Solution

Quick (Calculator) Solution

Test

Long (Analytic) Solution

Quick (Calculator) Solution

Test

Long (Analytic) Solution

Quick (Calculator) Solution

Test

Long (Analytic) Solution

Quick (Calculator) Solution

Test

Long (Analytic) Solution

Quick (Calculator) Solution

Test

Long (Analytic) Solution

Quick (Calculator) Solution

Test

Long (Analytic) Solution

Quick (Calculator) Solution

III. Trigonometry

October-November-December 2000 Test

Long (Analytic) Solution

Quick (Calculator) Solution

Test

Long (Analytic) Solution

Quick (Calculator) Solution

Test

Long (Analytic) Solution

Quick (Calculator) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

IV. Word Problems

October-November-December 2000 Test

Long (Analytic) Solution

Quick (Calculator) Solution

1) Let d = the number of diners

2) Therefore, 369 diners maximum / 366 ¸ 12 = 30 r. 6 è 31 servers needed
366 + 31 = 397
367 ¸ 12 = 30 r. 7 è 31 servers needed
367 + 31 = 398
368 ¸ 12 = 30 r. 8 è 31 servers needed
368 + 31 = 399
369 ¸ 12 = 30 r. 9 è 31 servers needed
369 + 31 = 400

October-November-December 2000 Test

Long (Analytic) Solution

Quick (Calculator) Solution

In ascending order, the letters would be
C, T, A, A, Y, M
BUT, no adjacent identical letters means:
C, T, A, Y, A, M
è Y is the fourth letter.

October-November-December 2000 Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

V. Complex Numbers

October-November-December 2000 Test

Long (Analytic) Solution

Quick (Calculator) Solution

/ 1). Make sure your TI graphing calculator is in complex (a + bi) mode:

2). Then punch it in:

Long (Analytic) Solution

Quick (Calculator) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

VI. Polynomial and Rational Functions

October-November-December 2000 Test

Long (Analytic) Solution

Quick (Calculator) Solution

Test

Long (Analytic) Solution

Quick (Calculator) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

VII. Probability/Combinatorics

October-November-December 2000 Test

Long (Analytic) Solution

Quick (Calculator) Solution

Test

Long (Analytic) Solution

Quick (Calculator) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

VIII. Logic

October-November-December 2000 Test

Long (Analytic) Solution

Quick (Calculator) Solution

Test

Long (Analytic) Solution

Quick (Calculator) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

IX. Exponents, Exponentials, and Logarithms

October-November-December 2000 Test

Long (Analytic) Solution

Quick (Calculator) Solution

Test

Long (Analytic) Solution

Quick (Calculator) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

X. Number Theory

October-November-December 2000 Test

Long (Analytic) Solution

Quick (Calculator) Solution

Test

Long (Analytic) Solution

Quick (Calculator) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

XI. Properties of Functions

October-November-December 2000 Test

Long (Analytic) Solution

Quick (Calculator) Solution

Test

Long (Analytic) Solution

Quick (Calculator) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

XII. Algebra

October-November-December 2000 Test

Long (Analytic) Solution

Quick (Calculator) Solution

|2x – 1| = 7
2x – 1 = ±7
2x = 1 ± 7
2x = 8 or –6
x = 4 or –3
4 + (-3) = 1 / 1) Graph the equations y = |2x – 1| and y = 7

2) Use the CALC button to access the menu to find the intersection points

3) Sum the intersection points: 4 + (-3) = 1

Test

Long (Analytic) Solution

Quick (Calculator) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

Test

Long (Analytic) Solution

XIII. gf

XIV. fg

XV. er

XVI. xx