Algebra Content Analysis 5 KEY
Evaluate r ÷ 2 – s2 when
r = 20 and s = 4
Page 1
Evaluate the expression:
This graph shows the solution for
which inequality?
(– 9)2
Substitutes values for variables
20 ÷ 2 – 42
20 ÷ 2 – 16
20 ÷ – 14
Applies the exponent
– 81
-8 -6 -4 -2 0 2 4 6 8
x>4
Further reduces elements in the
expression
Shows evidence of understanding
simplifying of inequalities by
dividing answer options to isolate
variables
10 – 16
a)
b)
c)
d)
a) – 18
38
16
–2
–6
Simplify:
4u – 6 + 5u2 – 3 + 2u
Combines any 2 like terms (i.e.,
u, constants)
6u OR – 9
Combines both like terms, but
makes an error in computation or
manipulation of integers

c) –
d) 81
Determines correct slope
OR applies slope formula
5  3 or 3  5 or m = 1


2
4 8
8 4
Uses correct slope and one other
aspect of point-slope formula,
EX: 
y – 5 = 1 ( x – )
2

16u – 9
5u2 + 6u – 9
5u2 + 2u – 3
11u2 + 3u
1
81
1
18
Write the equation of a line through
(– 8, 3) (– 4, 5). Use point-slope form.
EX: 5u2 + 6u – 3
a)
b)
c)
d)
b) –
1
(
2
1
=
2
= 1
2
y–3=
x – )
y–
(x + 4)
y–
a)
b)
c)
d)
x<4
2x > 8
– 4x > 3
4x  8
Solve:
6c – 8 = 28
c=
Isolates variables by adding 8 to each
side
6c = 36
Isolates variable and divides by
6 to solve for c
(x + 8)
a)

b) 7
c) 6
d) 42
(x – 5)
c) y – 3 = 2(x + 8)
1
d) y – 5 = (x + 4)
2


1
2
Solves correctly for 1 variable using
either method OR follows steps to
solve, but makes computational
errors OR plugs in solution for 1
variable if using substitution
a)
b)
c)
d)
(4, – 1)
(10, 2)
(– 4, – 5)
(2, 5)
Evaluate 4f – 3g2 when
f = 5 and g = 2
Substitutes values for variables
4 (5) – 3 • 22
20 – 3 • 4
Further reduces elements in the
expression
20 – 12
a) y + 8 = 2(x – 3)
b) y =
Solve the linear system:
2x – 4y = 12
6x + 2y = 22
Chooses a correct multiplier for
combination (i.e., divides 1st
equation by 2 or multiplies 2nd by 2)
OR Isolates one variable (x = , y =) for
substitution
3
4
6
a)
b)
c)
– 16
10
14
d)
8
© 2009, Project AAIMS, Iowa State University
OSEP Award# H324C030060

Algebra Content Analysis 5 KEY
Page 2
Write the equation in slope-intercept
Simplify:
9(2p – 1) – 6(p – 2)
2
form if m = and b = – 5
3
Distributes either term so that
response includes
18p – 9
OR
– 6p + 12
OR
12p
Distributes both terms correctly
18p – 9 – 6p + 12
OR Distributes either term
correctly and includes 12p or + 3
in response
a)
b)
c)
d)
3p – 3
24p – 21
12p – 3
12p + 3
Finds slope, but makes an error
in computation
c)
1
2
2
x – 5 (but no ‘y = ‘)
3
2
a) y = x – 5
3
2
b) y = x + 5
3
2
c) y = – 5x +
3
Simplify the expression:
3
b)
2
d)
–
Multiplies across to combine
terms OR simplifies by reducing
either the f or g terms
3
3 3
EX: f g or f  g
OSEP Award# H324C030060
g
f
Simplifies both the f and g terms,
but expression is not fully

reduced.
a)
1
2
2
f g
g

2
g
fg
g3 f

a) – 2
2
x
3
d) y = – 5x + 2
Find the slope of a line through
(2, 3), (8, – 9)
Draws a graph to determine slope
OR uses slope formula

93
3 9
or
82
28

y = mx + b
OR an expression that includes
f 3g 2
fg 3
2 2
EX: f g2
g
f
b) g

c) f 2
d)
f3
fg
Solve:
7x – 3 = – 2x + 6
x=
Isolates variables on 1 side (+ 2x
or – 7x to both sides)
OR Isolates constants on 1 side
(– 6 or + 3 to both sides)
Which line on the graph is
y + 2x = – 3?
y = – 2x – 3
B
A
C
D
Isolates constants and variables
OR Isolates variables or constants
and divides to solve for x
a)
3
5
c) 1
b) – 1
d)
9
2
Simplify:
4(3 – f) + 2(3f + 4)
Distributes either term so that
response includes
12 – 4f
OR
6f + 8
OR
2f
Distributes both terms correctly
12 – 4f + 6f + 8
OR Distributes either term
correctly and includes 2f or + 20
in response
a) 10f + 20
b) 2f +7
c) 8f + 16
d) 2f + 20
a)
b)
c)
d)
Line A
Line B
Line C
Line D
Solve the linear system:
2x + y = 11
x–y= 4
Combines equations or chooses a
correct multiplier for combination
(i.e., multiplies 2nd equation by – 2)
OR Isolates one variable (x = , y =) for
substitution
Solves correctly for 1 variable using
either method OR follows steps to
solve, but makes computational
errors OR plugs in solution for 1
variable if using substitution
a)
b)
c)
d)
(7, – 3)
(5, 1)
(7, 3)
(3, 5)
© 2009, Project AAIMS, Iowa State University