Download 1.0 Knowledge of Algebra, Patterns, and Functions – Students will

Grade 8 Voluntary State Curriculum
Knowledge of Algebra, Patterns, and Functions – Students will algebraically represent, model, analyze, or solve mathematical
or real-world problems involving patterns or functional relationships.
1.0
A. Patterns and Functions
1.
Item Example
Answer
Identify, describe, extend, and create
linear patterns and functions and
sequences
a)

Determine the recursive relationship
of arithmetic sequences represented
in words, in a table or in a graph
Assessment limit: Provide the nth
term no more than 10 terms beyond
the last given term using common
differences no more than 10 with
integers (-100 to 5000)
Find the 9th term in the sequence: 5, 11, 17, 23, …
53
2.
Select the answer that represents the 7th term in the sequence.
–30, –22, –14, –6, …
A. –2
B. 2
C. 18
D. 26
C
3.
Find the missing term in the table.
17
39
1.
x
2
4
6
8
10
4.
Grade 8 VSC 1.0
y
5
8
11
14
?
Select the answer that represents the 12th term in the sequence.
0.30, 0.34, 0.38, 0.42, …
A. 0.66
B. 0.70
C. 0.74
D. 0.76
C
Grade 8 Voluntary State Curriculum
BCR (3 points)
Kathy took a taxi to travel around the city. The charge for the
taxi was a flat fee of $2.00 plus $0.75 for each mile. The table
below shows the charges. Let m represent the number of miles
and C equal the total cost of the taxi.
m
C
1
$2.75
2
$3.50
3
$4.25
4
$5.00
Step A
Use the pattern in the table above to determine the total cost for
the taxi if Kathy were to travel 13 miles.
Step B
Use what you know about patterns to justify why your answer in
Step A is correct. Use words, numbers and/or symbols in your
justification.
$11.75
Since patterns repeat
themselves, I looked to
see whether there was a
constant rate of change. I
found that as the number
of miles, m, increased by
1, the cost of the taxi
increased by $0.75. I
solved this by repeating
the pattern 9 more times
and got my answer of
$11.75. Or I could have
used the equation
C  2  0.75x and
substituted m  13 .
40
b) Determine the recursive relationship
of geometric sequences represented
in words, in a table, or in a graph
 Assessment limit: Provide the nth
term no more than 5 terms beyond
the last given term using the
recursive relationship of geometric
sequences with whole numbers and
a common ratio of no more than 5:1
(0 -10,000)
Grade 8 VSC 1.0
1.
Determine the 8th term in the sequence below.
4, 12, 36, 108, …
A. 324
B. 972
C. 2,916
D. 8,748
D
2.
Determine the 6th term in the sequence below.
3, 15, 75, 375, …
A. 1,125
B. 1,875
C. 3,375
D. 9,375
D
Grade 8 Voluntary State Curriculum
3.
Determine the next term in the sequence below.
59049, 6561, 729, 81, …
9
4.
Determine the 6th term in the sequence below.
3
48, 12, 3, , …
4
3
64
BCR (3 points)
486
Study the geometric sequence below.
96, 144, 216, 324
The sequence is a
geometric sequence
because the ratio between
the terms is the same. The
3
144
ratio is
or . You
96
2
multiply each term by the
common ratio.
3
96   144 ,
2
3
144   216 ,
2
3
216   324 ,
2
3
324   486 .
2
Step A
Find the 5th term.
41
Step B
Use what you know about geometric sequences to justify why
your answer is correct. Use words, numbers, and/or symbols in
your justification.
Grade 8 VSC 1.0
Grade 8 Voluntary State Curriculum
c)

Determine whether relationships are
linear or nonlinear when represented
in words, in a table or in a graph
Assessment limit: Use a graph to
determine if a relationship is linear
or nonlinear
1.
2.
42
d) Determine whether relationships are
linear or nonlinear when represented
symbolically
Grade 8 VSC 1.0
Identify the graph that depicts a linear relationship.
A.
B.
C.
D.
Identify the graph that shows a non-linear relationship.
A.
B.
C.
D.
C
D
Grade 8 Voluntary State Curriculum
B. Expressions, Equations and Inequalities
1.
Write, simplify, and evaluate
expressions
a)

Write an algebraic expression to
represent unknown quantities
Assessment limit: Use one
unknown and no more than 3
operations and rational numbers
(-1000 to 1000)
1.
Jamar saved $3 less than half of what his sister Tanya saved. If x
represents the amount Tanya saved, which expression represents
the amount saved by Jamar?
1
x
2
1
B. 3  x
2
1
x3
C.
2
1
x3
D.
2
A. 3 
2.
43
Which of the following expressions represent the phrase 8 times
n, plus 4?
A.
B.
C.
D.
3.
C
8( n  4 )
4  8n
8n  4
8(n  4)
Which of the following expressions represent the phrase (-7)
times the sum of 5 and p?
A. 7( p  5)
B. 7  5  p
C. 7  5  p
D. p(7  5)
Grade 8 VSC 1.0
D
A
Grade 8 Voluntary State Curriculum
4.
A family of 2 adults and 3 children are going to a movie. The
price of an adult ticket is $6.25 and the price of a child’s ticket is
represented by v. Which expression represents the total cost of
the family’s movie tickets?
A.
B.
C.
D.
5.
D
2(6.25  v)
6.25  v
6.25  2v
2(6.25)  3v
Which of the following expressions is a correct translation of
three times the difference between 2 and a number m?
A
A. 3(2  m)
B. (3  2)  m
C. 3(m  2)
D. 3  2m
6.
44
Jamie bought two CD’s for x dollars each. If tax was $1.28,
which expression represents the total cost of the CD’s?
C
A. 2( x  1.28)
B. 2 x  2(1.28)
C. 2 x  1.28
D. x  1.28
7.
A person earns twice as much as she did three years ago. If the
person’s salary three years ago was r, which expression would
represent her current salary?
A. 2  r
B. 2r
r
C.
2
D. 2  r
Grade 8 VSC 1.0
B
Grade 8 Voluntary State Curriculum
8.
Billy’s test scores were 82, 96, 95, and 87. He took a test on
Friday and received a score of w. Which expression represents
Billy’s average test score?
C
82  96  95  87
4
B. 82  96  95  87  w
82  96  95  87  w
C.
5
82  96  95  87  w
D.
4
A.
ECR (4 points)
Jake is saving money to purchase a digital camera. He presently
has $23 and will save $6 from his allowance each week. He will
also save $8 each week from his paycheck.
45
Step A
Write the expression that represents the amount of money that
Jake has after w weeks.
Step B
 Use what you know about writing algebraic expressions to
explain how you arrived at your answer in Step A. Use
words, numbers, and/or symbols in your explanation.
 After 7 weeks, determine the amount of money Jake will
have saved. Use what you know about evaluating algebraic
expressions to justify why your answer is correct. Use
words, numbers, and/or symbols in your justification.
Grade 8 VSC 1.0
23  6w  8w or
23  14 w
I found the sum of 8
dollars and 6 dollars,
because these amounts are
saved. The total is
multiplied by the number
of weeks, or w. This is
represented as 14w. The
amount saved is added to
the amount Jake already
has, or 23  14 w .
To find the amount Jake
saved after 7 weeks,
substitute the 7 for w
in 23  14 w .
23  14  7  $121 . Jake
will have saved $121 after
7 weeks.
Grade 8 Voluntary State Curriculum
b) Evaluate an algebraic expressions
 Assessment limit: Use one or two
unknowns and up to three
operations and rational numbers
(-100 to 100)
1.
Evaluate the expression: 5x  ( y  4) when x  3 and y  6 .
A.
B.
C.
D.
2.
3.
5
13
43
51
Evaluate the algebraic expression 12 n  20 when n  3 .
A.
B.
C.
D.
A
–100
52
15
–20
46
4.
Evaluate the expression:
5( 4a  3c )
if a  6 and c  5 .
c2
15
5.
Evaluate the expression:
4 x  18 y
1
if x  9 and y  .
3
7
6
6.
Evaluate the expression:
y( z  x  y)
if y  5 , x  9.05 and
y
15.35
z  1.3 .
Grade 8 VSC 1.0
B
103
16
–4
–11
Evaluate the expression: 5(n  8) when n  12 .
A.
B.
C.
D.
A
Grade 8 Voluntary State Curriculum
7.
Evaluate the expression:
A.
B.
C.
D.
2 x3  3 y
when x  2 and y  4 .
y
B
13
1
–13
19
8.
The equation W  1.2 L represents the wingspan W , of a Boeing
747 jet aircraft in relationship to its length L . Find the wingspan,
in feet, if the length of the jet is 231 feet.
9.
Evaluate the following expression:
1
( x  y ) 2 if x  3 and
3
277.2
D
y  6 .
47
A.
B.
C.
D.
c)
Evaluate numeric expressions using
order of operations
Assessment limit: Use no more
than 5 operations including
exponents of no more than 3 and
2 sets of parentheses, brackets, a
division bar, or absolute value with
rational numbers (-100 to 100)
1.
Evaluate the expression.
3  23  94  79
3
2.
Evaluate the expression.
4(16  28)
2
A.
B.
C.
D.
Grade 8 VSC 1.0
–27
–3
3
27
18
66
–4
–24
13
D
Grade 8 Voluntary State Curriculum
3.
Evaluate the expression.
29.8  56  14.3
11.9
4.
Evaluate the expression.
5  2  3  7  2
C
A.
B.
C.
D.
48
5.
Evaluate the expression.
6.7  44 .4  6  144
2.1
6.
Evaluate the expression.
3  28 26  32 9
B
A.
B.
C.
D.
Grade 8 VSC 1.0
18
14
4
–4
–316
–186
25
774
Grade 8 Voluntary State Curriculum
2
ECR (4 points)
Given the following expression:
 3  7 2  13  5
 4 2  18 
Step A
Evaluate the numeric expression
16  18 
Step B
 Use words, numbers, and/or symbols to explain how you
found your answer.
 Determine how replacing the absolute value symbol with
parentheses would change the value of the expression. Use
what you know about numeric expressions to justify why
your answer is correct. Use words, numbers, and/or symbols
in your justification.
49
BCR (3 points)
2
 3  7 2   13  5  
 4 2   18  
16  18 
34
We would have subtracted
–18 instead of 18.
3


Given the expression: 6  2 32  4  7
Step A
Evaluate the expression.
Step B
Study the problem below and locate the error. Use what you
know about order of operations to justify your response. Use
words, numbers, and/or words in your justification.
6  2( 32  4 )  7
6  2( 5 )  7
45  7
20  7
27
Grade 8 VSC 1.0
 3  7 2  13  5 
6  2 9  4  7 
6  10  7 
3
The mistake is found in
the third line, subtracting
6 minus 2 and getting 4.
In the order of operations,
2 should be multiplied by
5 first, then subtracted
from 6.
Grade 8 Voluntary State Curriculum
d) Simplify algebraic expressions by
combining like terms
 Assessment limit: Use no more
than 3 variables with integers
(-50 to 50), or proper fractions
with denominators as factors of 20
(-20 to 20)
1.
Simplify the expression 33x  2 y  x  28y by combining like
terms.
A.
A
32x  30 y
B. 33x 2  30 y 2
C. 35xy  28xy
D. 34x  26 y
2.
Simplify the expression
3
1
4
1
x  x  y  y by combining like
5
5
5
5
C
4
1
3
3
x  y  x  y by combining
5
10
10
5
A
terms.
A.
B.
C.
50
D.
3.
4
3
x y
10
0
20x  15 y
4
3
x y
5
5
7
xy
20
Simplify the expression
like terms.
A.
B.
C.
D.
Grade 8 VSC 1.0
1
1
x y
2
2
10
xy
40
11
7
x
y
10
10
7
9
x
y
10
10
Grade 8 Voluntary State Curriculum
4.
Simplify the expression 6 x  2( x  4 y)  3x  5 y .
A.
B.
C.
D.
5.
B
7x  9 y
7x  3y
3x  3 y  4
9x  10xy  5 y
Simplify the expression c  5(4b  6c) by combining like terms.
C
A. 20b  31c
B. 9b  12 c
C. 20 b  29 c
D. 9b  5c
6.
1
3
Simplify the expression 8( d  3e)  15 d  10 (4 f  e) .
4
5
B
A. 17 d  30 e  40 f
B. 17 d  30 e  40 f
51
C. 17 d  30 e  40 f
D. 17d  9e  40 f
7.
The sum of the three angles of any triangle is 180°. Angle A of
ABC is half the size of angle B. If x represents the measure of
angle B, write an expression, in simplest form, that will give the
measure of angle C.
A. 180 
3
x
2
1
x)
2
1
C. 180  x  x  x
2
3
D. 180  x
2
B. 180  ( x 
Grade 8 VSC 1.0
D
Grade 8 Voluntary State Curriculum
BCR (3 points)
Andy ran 3 laps around the track. His time for the second lap was
3.9 seconds more than for the first lap. His time for the third lap
was 1.6 second less than the first lap.
Step A
If x represents Andy’s time for the first lap, write an expression
that represents Andy’s average time in simplest terms.
Step B
Use what you know about simplifying expressions to explain your
answer. Use words, numbers and/or symbols in your explanation.
e)
52
2.
x  x  3.9  x  1.6
3
3 x  2.3

3
To find the average, add
the three expressions
representing the number
of laps and divide by 3
since there are three laps.
Then, to combine like
terms, add the variable
terms together and the
constants together.
Describe a real-world situation
represented by an algebraic
expression
Identify, write, solve, and apply
equations and inequalities
ECR (4 points)
(addresses 1.B.2.a and 1.B.2.b)
2  1.50 x  16
Frontier Town charges $2.00 a day to get into the park and $1.50
for each round of miniature golf. Sam has $16 to spend that day.
2  1.50 x  16
Step A
Write the inequality that describes the maximum number of
rounds of miniature golf, x, that Sam can play.
Step B
Determine the maximum number of rounds of golf, x, that Sam
can play that day at Frontier Town. Use what you know about
solving inequalities to justify why your answer is correct. Use
words, numbers and/or symbols in your justification.
Grade 8 VSC 1.0
1.50 x  14
x  9.3333
so Sam can play at most 9
rounds of golf. He doesn’t
have enough money for 10
rounds since it would cost
2  1.5 10  2  15  17
and he only has $16.
Grade 8 Voluntary State Curriculum
BCR (3 points)
360   120   3 x  2 x  x
The sum of the interior angles of a quadrilateral equals 360˚.
360  120 
Step A
The measures of the angles in a given quadrilateral are 120˚, 3x,
2x and x. Write an equation to represent the sum of the angles in
this quadrilateral.
Step B
Determine the measure of each angle. Use what you know about
solving equations to justify why your answer is correct. Use
words, numbers and/or symbols in your justification.
a)

53
Write equations and inequalities to
represent relationships
Assessment limit: Use a variable,
the appropriate relational symbols
(>, >, <, <, =), and no more than 3
operational symbols (+, -, , ) on
either side and rational numbers
(-1000 to 1000)
1.
Write an equation to represent the sentence, the sum of three
hundred twenty-six and forty-nine equals the difference between a
number and five hundred ninety.
A.
B.
C.
D.
2.
Grade 8 VSC 1.0
240  6 x
240 6 x

6
6
x4
The angle measures are
120, 120, 80, and 40 in
this quadrilateral.
120  120  80  40  360 .
D
326  49  590  n
326 .49  509 n
300 .26  49  n  500 .90
326  49  n  590
Write an inequality for the sentence, the difference between one
hundred sixty-seven and the product of 5 and a number is greater
than ninety-six increased by eighty-eight minus seventy-two.
A.
B.
C.
D.
120  120  3 x  2 x  x
167  5n  96  88  72
167  5  n  96  88  72
5  n  167  90.6  80.8  70.2
167  5n  96  88  72
A
Grade 8 Voluntary State Curriculum
3.
Write an inequality for the sentence, twice a number decreased by
the quotient of that number and 4 is greater than or equal to 14.
A.
B.
C.
D.
4.
54
5.
n
 14
4
n
2n   14
4
2(n 
D
200  9c  680
200( 0.09 )c  680
200  9c  680
200   0.09c   680
According to a survey in the middle school, 657 students can
speak Spanish. This is 240 fewer than 3 times the number of
students that cannot speak Spanish. Which equation represents
this situation if n represents the number of students who cannot
speak Spanish?
A.
B.
C.
D.
Grade 8 VSC 1.0
2n
 14
n4
2n  (n  4)  14
Amy earns $200 per week, plus a 9% commission on the cost, c,
of the cars she sells. Amy has a weekly goal of earning at least
$680. Which inequality could be used to find the cost of the cars
she must sell to reach her goal?
A.
B.
C.
D.
D
657
657
657
657
 3n  240
 3n  240
 240  3n
 240  3n
A
Grade 8 Voluntary State Curriculum
6.
John earns $8.50 per hour for the first 7 hours and 1.5 times his
hourly rate for any additional hours. John works 10 hours. What
expression would represent the amount of money, a, John earned
that day?
B
A. 10 (8.50 )  a
B. 7(8.50 )  3(12 .75)  a
C.
D.
7.
7(8.50)  3(17.00)  a
7(8.50)  3(13.00)  a
Bill has $150.00 to take his friends and himself to a restaurant.
Each meal, m, will cost $12.99 and he wants to leave a $20.00 tip.
Which inequality represents the number of meals Bill can buy?
A.
B.
C.
D.
A
$12 .99 m  20  $150 .00
$12 .99 m  20  $150 .00
$12 .99 m  20  $150 .00
$12 .99 m  20  $150 .00
55
b) Solve for the unknown in a linear
equation
 Assessment limit: Use one
unknown no more than 3 times on
one side and up to three operations
(same or different but only one
division) and rational numbers
(-2000 to 2000)
1.
Solve for x :
A.
B.
C.
D.
2.
Grade 8 VSC 1.0
C
3
x  5  17
4
D
93.3
7
70
840
Solve for x :
A.
B.
C.
D.
3x  x  280
–16
–9
9
16
Grade 8 Voluntary State Curriculum
3.
Solve for d :
A.
B.
C.
D.
4.
56
5.
c)

Solve for the unknown in an
inequality
Assessment limit: Use a one- or
two-operation inequality with one
variable on one side no more than 3
times whose result after combining
coefficients is a positive whole
number coefficient with integers
(-100 to 100)
Grade 8 VSC 1.0
1.
A
m9
3
4
C
7w  23  100
C
–6
12
3
–12
Solve for w :
A.
B.
C.
D.
1
(6  2 x )  4
3
–3
3
–1
1
Solve for m :
A.
B.
C.
D.
D
14
13
–14
10
Solve for x :
A.
B.
C.
D.
2d  3  5d  36
w  11
w  18
w  11
w  18
Grade 8 Voluntary State Curriculum
2.
Solve for z :
A.
B.
C.
D.
29  5z  16
D
z  13
z  2.6
z7
z9
3.
Solve for n :
156 n  14  137 n  166
8
4.
Solve for c :
78  2c  8
A
2b  37  55
D
57
A. 47  c
B. 31  c
C. 43  c
D. 35  c
5.
Solve for b :
A.
B.
C.
D.
Grade 8 VSC 1.0
b  46
b  92
b9
b  9
Grade 8 Voluntary State Curriculum
d) Identify or graph solutions of
inequalities on a number line
 Assessment limit: Use one variable
once with a positive whole number
coefficient and integers (-100 to
100)
1.
Which of the inequalities is represented on the number line?
–10 –8 –6 –4 –2 0 2
A.
B.
C.
D.
2.
4 6
D
8 10
8 y 19  29
8 y 19  29
8 y 19  29
8 y 19  29
Which graph represents the inequality:
9 x  2  70 ?
C
A.
–10 –8 –6 –4 –2 0 2
4 6
8 10
–10 –8 –6 –4 –2 0 2 4 6
8 10
–10 –8 –6 –4 –2 0 2
4 6
8 10
–10 –8 –6 –4 –2 0 2
4 6
8 10
B.
58
C.
D.
3.
Which inequality is represented on the graph?
–10 –8 –6 –4 –2 0 2 4 6
3 j  1  12
B. 12  3 j  1
C. 3 j  1  12
D.  12  3 j  1
A.
Grade 8 VSC 1.0
8 10
A
Grade 8 Voluntary State Curriculum
4.
Which graph represents the inequality:
12  2 x  14 ?
A
A.
–10 –8 –6 –4 –2 0 2
4 6
8 10
–10 –8 –6 –4 –2 0 2 4 6
8 10
–10 –8 –6 –4 –2 0 2
4 6
8 10
–10 –8 –6 –4 –2 0 2
4 6
8 10
B.
C.
D.
BCR (3 points)
59
Given the inequality:
4m  2  12
Step A
Graph the solutions for the inequality.
0 2 4 6
Step B
Use what you know about graphing inequalities to explain how
you got your answer. Use words, numbers and/or symbols in
your explanation.
Grade 8 VSC 1.0
Solve the inequality using
inverse operations. The
solution is m  5 so use
an open circle at point 5
and the arrow of the line
should point to the right.
Grade 8 Voluntary State Curriculum
e)

Identify equivalent equations
Assessment limit: Use one
unknown no more than 3 times on
one side and up to three operations
(same or different but only one
division) and integers (-2000 to
2000)
1.
Which one of the following equations is NOT equivalent to:
 8a  46a  2  40 ?
A.
B.
C.
D.
2.
60
3.
4.
A.
22 y  14  64
B.
C.
D.
25 y 2  75
25y  75
22 y  3 y  64  11
Which of the following equations is not equivalent to:
800 m  1000 m  100  50  950
C
C
200 m  100  50  950
200 m  800
200 m  100 m  950  100
200 m  900  100
Given 28  8m  4 , choose the equation that is equivalent.
A.
B.
C.
D.
Grade 8 VSC 1.0
16a = 48
16a-8 = 40
-8a+24a-8 = 40
-8a+24a+8 = 40
Given 22 y  3 y  11  64 , choose the equation that is equivalent.
A.
B.
C.
D.
D
8m  28  4
8m  24
m  3
m4
B
Grade 8 Voluntary State Curriculum
5.
Given 125 x  56  15 x   20 , choose the equation that is
equivalent.
D
A. x  5
B. 50 x  50
C. 200 x  30  20
D. 50 x  30  20
f)

Apply given formulas to a problemsolving situation
Assessment limit: Use no more
than four variables and up to three
operations with rational numbers (500 to 500)
d
 1 , where
33
P is the pressure in atmospheres and d is the depth in feet. Find
the amount of pressure experienced by a diver at a depth of 66
feet.
Water pressure can be found using the formula P 
3
2.
1-800-Cell-Connect charges $0.25 for the first minute and $0.15
for each additional minute. The cost of a phone call can then be
expressed by the formula C  0.25  0.15m  1 , where C is the
total cost in dollars and m is the number of minutes. Determine
the cost if you talk for 11 minutes.
1.75
61
1.
Grade 8 VSC 1.0
Grade 8 Voluntary State Curriculum
3.
1
h(b1  b2 ) , to find the area of the
2
trapezoid, given h  8 cm, b1  12 .3 cm, and b2  36 .9 cm.
Use the area formula A 
A. 28.6 cm 2
B. 86.1 cm 2
C. 196.8 cm 2
D. 393.6 cm 2
4.
62
g) Write equations and inequalities that
describe real-world problems
C. Numeric and Graphic Representations of
Relationships
1.
Locate points on a number line and in a
coordinate plane.
Grade 8 VSC 1.0
12.3 cm
8 cm
36.9 cm
Jake deposits $400 into a savings account paying 5% interest.
Use the formula A  P  Pr t , to determine his balance, A, after 4
years, where t is the number of years, r is the annual interest rate,
and P is the principal.
A.
B.
C.
D.
$80
$480
$800
$1200
C
B
Grade 8 Voluntary State Curriculum
a)

Graph linear equations in a
coordinate plane
Assessment limit: Use two
unknowns having integer
coefficients (–9 to 9) and integer
constants (–20 to 20)
1.
2.
63
Grade 8 VSC 1.0
Which of these graphs represents y  2x  1 ?
A.
B.
C.
D.
Which of these graphs represents 3x  2 y  4 ?
A.
B.
C.
D.
B
D
Grade 8 Voluntary State Curriculum
2.
Analyze linear relationships
a)

Determine the slope of a graph in a
linear relationship
Assessment limit: Use an equation
with integer coefficients (–9 to 9)
and integer constants (–20 to 20)
and a given graph of the relationship
1.
Determine the slope of the line given below.
64
Grade 8 VSC 1.0
A.

B.
5
3
C.

D.
3
5
5
3
3
5
C
Grade 8 Voluntary State Curriculum
At 12:05 p.m., a parachutist is 7,000 feet above the ground. At
12:10 p.m., the parachutist is 5,500 feet above the ground. Find
the average rate of change in feet per minute.
Thousands of Feet
2.
8
6
4
12:05 12:10
Time
A.
65
B.
C.
D.
Grade 8 VSC 1.0
1500
5
2500

5
1500
5
2500
5

A
Grade 8 Voluntary State Curriculum
BCR (3 points)
Jason was training for an upcoming long-distance bicycle race.
His coach collected time and distance data at two checkpoints
during his last training session. The data is shown in the graph
below.
66
Step A
During which interval, A or B, was Jason traveling the fastest?
Step B
Use what you know about slope to explain how you determined
your answer. Use words, numbers, and/or symbols in your
explanation.
b) Determine the slope of a linear
relationship represented numerically
or algebraically
Grade 8 VSC 1.0
Jason was traveling the
fastest during interval A.
The slope of interval A is
4 2
 and the slope of
2 1
2 1
interval B is  . The
4 2
higher the slope, the
steeper the line, the
greater the rate of change.
Since interval A has a
greater slope, and steeper
line, it has a greater rate of
change. Thus, he is
traveling faster during the
interval A.
Grade 8 Voluntary State Curriculum
Grade 8 VSC 1.0