This math test contains 4 questions covering various topics: 1) Coordinate geometry involving graphing a trapezoid and finding lengths of sides and diagonals. 2) Solving and graphing a linear equation algebraically and graphically. 3) Writing and using a linear equation to model the depreciation of equipment over time. 4) Completing a scatter plot table with fertilizer amount and corn yield data and using it to determine the line of best fit and predict future yield.

1. Math 4R Test1A Name:
For each question: Show all work. Justify each answer in the space provided. Circle final answers.
(1) Coordinate Geometry
Graph the trapezoid ABCD: A(0,0), B(b,0), C(b-a,h), D(a,h) where 2a<b
and a, b and h are all positive constants.
(1a) Find the length of diagonal AC .
(1b) Find the length of diagonal BD .
(1c) Find the length of side AD .
(1d) Find the length of side BC .
(1e) What have you demonstrated?
a:TEST1A.4Rt

2. Math 4R Test1A Name:
For each question: Show all work. Justify each answer in the space provided. Circle final answers.
(2) Solving Equations and Graphing
Given the equation: 15 – 2x = x
(2a) Solve for x algebraically.
(2b) Check by solving for x graphically.
a:TEST1A.4Rt

3. Math 4R Test1A Name:
For each question: Show all work. Justify each answer in the space provided. Circle final answers.
(3) Linear Models
A small business purchases a piece of equipment for $875. 5 years
later, the equipment is outdated and has no value!
(3a) Write a linear equation giving the value V of the equipment in terms of
time t in years, 0 ≤ t ≤ 5.
(3b) Use your linear equation to interpolate V(2).
(3c) Solve for t: V(t) = $200.
a:TEST1A.4Rt

4. Math 4R Test1A Name:
For each question: Show all work. Justify each answer in the space provided. Circle final answers.
(4) Scatter Plots: Solve Numerically
Complete the following table. X represents the number of pounds of
fertilizer used on a corn farm. Y represents the yield in bushels of corn.
x y xy x2
0 58
1 60
2 59
3 61
4 63
5 66
6 65
7 67
8 70
(5a) Find ∑x
(5b) Find ∑y
(5c) Find ∑xy
(5d) Find ∑x2
n∑xy – ∑x∑y
(5d) Find m =
n∑x2 – (∑x)2
∑y – m∑x
(5e) Find b = n
(5f) State y = mx + b exactly.
(5g) Find y(10).
a:TEST1A.4Rt