Using Desmos on the DSAT Review Worksheet

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Using Desmos on the SAT
Directions: For every question below, type the expression or equation into the desmos graphing
calculator. Then use the graph to visually find the answer. You can also type in answer choices and
shee which one matches. Some questions may be easier to do in your head, but desmos provides a
nice visual if needed.
Tips to Students Before you Begin
● How to make a table from an equation
● How to type in a table or points
● Using X not w
● Sliders
First Half Questions
1. Which equation has the same solution as the given equation? 3x - 5 = 16
M. 3x = 21
N. 3x = 11
O. 3x = 63
P. 3x = 7
2. Which expression is equivalent to x2 + 5x - 24
R. (x-8)(x+3)
S. (x+8)(x-3)
T. (x-4)(x+6)
U. (x+4)(x-6)
3. Susan walks to the train station at a speed of 4 miles per hour, and then boards the train to
Chicago with an average speed of 65 miles per hour. She walks for w hours and rides the train
for r hours, for a combined total of 50 miles. Which equation represents this scenario?
R. ¼ w + 1/65 r = 50
S. 4w + 65r = 50
T. ¼ w + 1.65 r = 305
U. 4x + 65r = 305
4. 3.5 c + 8d = 120 The given equation describes the relationship between the number of
cats, c, and the number of dogs, d, that can be cared for at a pet store business on a given
day. If the business cares for 12 dogs on a given day, how many cats can it care for on this
day?
5. What is the positive solution to ?45
𝑥+4 = 𝑥
6. What is the positive solution to the given equation -3x2 - 7x = -20? (give your answer as a
simplified fraction)
7. If the given function h is graphed in the xy-plane, where y = h(x), what is the y-intercept of the
graph ?ℎ(𝑥) = 12 1
11( )𝑥
F. (0,11)
G. (0,12)
H.(0,1)
I. (0,132)
8. The exponential function h is defined by h(x) = 17bx , where b is positive constant. If h(4) =
1377, what is the value of h(5)?
9. At how many points do the graphs of the equations y = x - 12 and y = 4x intersect in the
xy-plane?
10.The solution to the given system of equations is (x,y). What is the value of y?
11.Which ordered pair (x,y) is not a solution to the given system of equations?
y = (x+3)(x-7)
y = 4x - 12
I. (9,24)
J. (-1,-16)
K. (2,-25)
L. None of These
12.The given equation defines the function f. For what value of x does f(x) reach its minimum?
f(x) = 4x2 - 7x + 80
13. In the xy plane, line k passes through the point (0,0) and is parallel to the line represented by
the equation y = 3x + 8. If line k also passes through the point (4,d), what is the value of d.
14. In the xy plane, a line with equation 3y = d for some constant d intersects a parabola at exactly
one point. If the parabola has equation y = 2x2 + 5x, what is the value of d?
15.The function f(t) = 300 (3)t / 110gives the number of people at the beach t minutes after an initial
observation. How much time, in minutes, does it take for the number of people at the beach to
quadrouble?
16.Line k is defined by 3x + 9y = 2. Line q is perpendicular to line k in the xy plane. What is the
slope of line q?
17. f(x) = -3x2 + 20x + 182. The function g is defined by g(x) = f(x-3). For what value of x does
g(x) reach its maximum? (write your answer as a simplified fraction)
Second Half Easier Questions
18.What value of x is the solution to the given equation? x + 30 = 55
19.Which expression is equivalent to 10x - (5x + 2x)?
B. 7x
C. -7x
D. -3x
E. 3x
20.Which expression is equivalent to 4x2 + 7x?
G. x(4x+7)
H. 4x(x+7)
I. 7x(x+1)
J. x2(4x+7)
21.Which expression is equivalent to (3x2 + x - 9) - (x2 + 5x + 4)?
K. 3x2 - 5x -13
L. 2x2 - 4x - 5
M. 2x2 + 6x - 5
N. 2x2 - 4x -13
22.The expression is equivalent to where b is a constant and x > 0. What is the value15
12𝑥+21
5
4𝑥+𝑏
of b?
O. 7
P. 14
Q. 63
R. 105
23. If 5 + x = 12, what is the value of 13 + 4x?
24. If y = 3x + 8, what is the value of y when x = 4?
25.What is one possible solution to the given equation |x-3| = 8 ?
26.The function f(x) is defined by f(x) = x4 - 8. What is the value of f(-3)?
27.The total cost f(x) in dollars to rent a boat for 8 hours is given by f(x) = 8x + 800, where x is the
hourly payment, in dollars. What is the total cost to rent the boat when the hourly rate is $125?
28.The function g is defined by g(x) = 3x - 8. What is the value of g(x) when x = 5?
29. If (a,b) is a solution to the given system of equations, what is b - a? x + y = 24 5x = y
30.The graph of 3x + 4y = -15 in the xy-plane has an x-intercept at (a,0) and a y-intercept at (0,b),
where a and b are constants. What is the value of b / a?
S. 4/3
T. ¾
U. - 4/3
V. - ¾
31.Jake paid a total of $215 for a telescope by making a down payment of $47 plus monthly
payments of $18 each. Which of the following equations represents this situation?
W. 18p - 47 = 215
X. 47p - 18 = 215
Y. 18p + 47 = 215
Z. 47p + 18 = 215
32.The table shows three values of x and their corresponding values of y. There is
a linear relationship between x and y. Which of the following equations
represents this relationship.
B. y = 5x + 14
C. y = 5x + 12
D. y = 14x + 5
E. y = 14x + 12
33.A football is kicked from a platform. The equation h = -16t2 + 10t + 7 represents this situation,
where h is the height of the football above the ground, in feet, t seconds after it was kicked.
What number represents the height in meters, from which the object was kicked?
34.Which table gives three values of x and their corresponding values for g(x) for the given
function g(x) = -x2+ 4 ?
F. G. H. I .
35. In the linear function f, f(0) = 4 and f(1) = 6. Which equation defines f?
K. f(x) = 4x + 6
L. f(x) = 6x + 4
M. f(x) = 2x
N. f(x) = 2x + 2
36.For the linear function f, the table shows three values of x and their corresponding values of
f(x). Which equation defines f(x)
P. f(x) = 17x + 23
Q. f(x) = 29x + 23
R. f(x) = 6x + 17
S. f(x) = 23x + 29
37.What is the equation of the graph shown?
T. y = -x - 8
U. y = 4x - 8
V. y = x - 8
W. y = -4x - 8
38.The function f is defined by f(x) = 11x - 77. What is the x-intercept of the graph of y = f(x) in the
xy-plane?
39.The function j is defined by j(n) = 5n2. What is the value of n when j(n) is equal to 180?
M. 2
N. 5
O. 6
P. 18
2nd Half Harder Questions
40.Which expression is equivalent to 4x3 + 2x2+ 3x2?
A. 4x3+ 6x4
B. 6x3 + 3x2
C. 9x7
D. 4x3+ 5x2
41.Which expression is equivalent to 13x4 - 9x4
E. 21x4
F. 21x8
G. 4x4
H. 4x8
42. If 5(2t - 20) + t = 30 + 3t, what is the value of 4t?
43. If 3(x + 5) = 6(x - 3) + 27, what is the value of x + 4?
44.The given equation relates the number p and n, where n is not equal to 0 and p𝑝 = 8 + 15
𝑛
> 8. Which equation correctly expresses n in terms of p?
I . 𝑛 = 𝑝−8
15
J. 𝑛 = 𝑝
15 + 8
K. 𝑛 = 𝑝
15 − 8
L. 𝑛 = 15
𝑝−8
45.Circle A in the xy plane has the equation (x+4)2 + (y-3)2 = 64. Circle B has the same center as
circle A. The radius of circle B is half the radius of Circle A. The equation defining circle B in
the xy-plane is (x+4)2 + (y-3)2 = k, where k is a constant. What is the value of k?
46.The solution to the given system of equations is (x,y). What is the value of y?
7x = 35
-4x + y = -13
47.The graph of the equation in the given system of equations interests at the point (x,y) in the xy
plane. What is a possible value of x?
48.How many solutions does the equation
M. Exactly one
N. Exactly two
O. Infinitely Many
P. Zero
49.How many solutions does the equation
Q. Exactly one
R. Exactly two
S. Infinitely Many
T. Zero
50.How many solutions does the given equation have? 33x = 0
U. Exactly one
V. Exactly two
W. Infinitely Many
X. Zero
51.How many solutions does the given equation have? 33x = 33x + 11
A. Exactly one
B. Exactly two
C. Infinitely Many
D. Zero
52.How many solutions does the given equation have? 33x = 33x
E. Exactly one
F. Exactly two
G. Infinitely Many
H. Zero
53.What is the sum of the solutions to the given equation? x(x+2) - 4 = 6x(x+2)
54.When the quadratic function f is graphed in the xy plane, where y = f(x), its vertex is (-2,5).
One of the x intercepts of the graph is (-15/4 , 0). What is theother x-intercept of the graph?
I. (-¼ , 0)
J. (¼, 0)
K. (-7/4, 0)
L. (7/4, 0)
55.The graph of y = f(x) - 3 is shown. Which equation defines function f?
M. f(x) = ⅓ x + 8
N. f(x) = ⅓ x + 6
O. f(x) = ⅓ x + 2
P. f(x) = ⅓ x - 1
56. In the given system of equations, k is a constant. If the system has no solution, what is the
value of k?
27x - 15y = 9y + 8
ky = ¼ -18x
57. In the given equation 50x2 + bx + 32 = 0, b, is a constant. For which of the following values of
b will the equation have more than one real solution?
Q. 18
R. -18
S. -80
T. -108
58. In the given system of equations, w is a constant. If the system has no solution,
what is the value of w?
59. In the given equation, k is a positive constant. Which of the following is one of the solutions to
the given equation?
𝑥2
(𝑥2−𝑘2)
2 = 𝑘2
(𝑥2−𝑘2)
2 − 3
W. k
X. − 1
3 − 𝑘2
Y. − 1
3 + 𝑘2
Z. 1
3 − 𝑘2
60.For the linear function f, the table shows three values of x and their
corresponding values of f(x). Function f is defined by f(x) = ax + b,
where a and b are constants. What is the value of a - b?
61.The function f is defined by f(x) = 3x - 42. What is the x-intercept of the graph of y=f(x) in the
xy plane?
B. (-3,0)
C. (-14,0)
D. (3,0)
E. (14,0)
62.One of the factors of x4 - 19x3 + 103x2 - 165x is x + b, where b is a negative constant. What is
the largest possible value of b?
63.The function f(x) = -1/9 (x-5)2 + 6 gives the balloons height above the ground in feet, x minutes
after it is released. Which of the following is the best interpretation of the vertex of te graph of
y = f(x) in the xy plane?
F. The balloon’s height was 5 feet above the ground when it started moving
G. The balloon’s height was 6 feet above the ground when it started moving
H. The balloon’s maximum height was 5 feet above the ground
I . The balloon’s maximum height was 6 feet above the ground
64.The function M gives the mass of iron, in grams, that corresponds to the grams of rust on a
bike. If the rust increases by 1.75 grams, by how much did the iron increase, in grams?
M(x) = x (4/159.7) (55.8/2)
65. In the given quadratic function f(x) = ax2+ bx + 10, a and b are constants. The graph of y = f(x)
in the xy-plane is a parabola that opens downwards and has a vertex at the point (h,k), where
h and k are constants. If h>0 and f(-2) = f(4), which of the following must be true?
I. a < 0
II. b < 0
L. I only
M. II only
N. I and II
O. Neither I and II
66.Which point (x,y) is a solution to the given system of inequalities in the xy-plane?
y < 2x + 5
y > -3x - 2
P. (-1,2)
Q. (-2,1)
R. (-2,2)
S. (-1,4)
More Practice
67. A chicken is running from his owner at constant speed. The equation d = 9t gives the distance
d in yards and the time t in minutes. How long does it take the chicken to run 54 yards?
68. A chicken is running from his owner at constant speed. The equation d = 9t gives the distance
d in yards and the time t in minutes. How far does the chicken run in the 4 minutes he is being
chased?
69. A line in the xy plane has a slope of 2 and passes through the point (0,6). Which equation
represents this line?
A. y = 2x + 6
B. y = 2x - 6
C. y = -2x + 6
D. y = -2x -6
70. A line in the xy plane has a slope of -⅓ and passes through the point (-3,6). Which equation
represents this line?
F. y = ⅓ x + 5
G. y = ⅓ x + 6
H. y = -⅓ x + 5
I . y = -⅓ x + 6
71. In the xy-plane, the graph of the linear function f contains the points (0,4) and (9,31). Which
equation defines f, where y = f(x)?
J. f(x) = 4x - 3
K. f(x) = 4x + 3
L. f(x) = 3x - 4
M. f(x) = 3x + 4
72. If x/4 = 2, what is the value of 4/x?
73. If y / x = 5, and 30y / kx = 10, what is the value of k?
74. If y / x = 5, and 30y / kx = 5, what is the value of k?
75. If y / x = 5, and 30y / kx = 2.5, what is the value of k?
76.The function v(x) = 480 - 15t models the volume of sand in the top of a hourglass, in milliliters,
in a container t seconds after the hourglass has been flipped over. According to the model,
how much is the predicted volume, in milliliters, decreasing by in the top of the hourglass each
second?
77.The given equation y = -x2 + 12x - 28 relates the variable x and y. For what value of x does the
value of y reach its maximum?
78.The function g is defined by g(x) = 5x +35. The graph of y = g(x) in the xy plane has an
x-intercept at (a,0) and a y-intercept at (0,b), where a and b are constants. What is the value
of a + b?
79.A student initially measures 800 bateria cells on a piece of bread. 6 hours later, the student
measures 1600 bacteria cells. Assuming exponential growth, the formula P = C(2)rt gives the
number of bacteria on the bread, where r and C are constants, and P is the number of bacteria
cells t hours after the initial measurement. What is the value of r?
Q. 1 / 800
R. 1 / 6
S. 6
T. 800
80.A student initially measures 800 bateria cells on a piece of bread. 4 hours later, the student
measures 3200 bacteria cells. Assuming exponential growth, the formula P = C(2)rt gives the
number of bacteria on the bread, where r and C are constants, and P is the number of bacteria
cells t hours after the initial measurement. What is the value of r?
U. 1 / 4
V. 1 / 2
W. 4
X. 2
81.What is the smallest solution to the given equation?
82.What is the smallest solution to the given equation?
83.Which of the following is a solution to the given equation x - 19 = (x+a)(x-19) , where a is a
constant and a > 20?
B. -a
C. -a + 1
D. a + 1
E. 19
84.The function h is defined by h(x) = 6x. For what value of x does h(x) = 24?
85.The function f is defined by f(x) = 3x2 - 4. For what value of x does f(x) = 23, if x < 0?
86.Which expression is equivalent to ?6
3𝑥 −7 − 1
𝑥 + 2
F. 5
(3𝑥−7)(𝑥+2)
G. 5
2𝑥−9
H. − 3𝑥−19
(3𝑥−7)(𝑥+2)
I . 3𝑥 + 19
(3𝑥−7)(𝑥+2)
87.The point (-3,4) in the xy plane is a solution to which of the following system of inequalities?
J. x > 0 and y > 0
K. x > 0 and y < 0
L. x < 0 and y > 0
M. x < 0 and y < 0
88.Which of the following equations is the most appropriate linear model for the data shown in the
scatterplot?
N. y = -.35x + 6.25
O. y = -.35x - 6.25
P. y = .35x + 6.25
Q. y = .35x - 6.25
89.What is the negative solution to the given equation?
7 |3 - x| - 5 |3 - x| = 21
90.A parent opens a 529 account for their son with an initial balance of $2000. The account earns
interest, and no additional deposits or withdrawals are made. The account balance is given by
an exponential function A, where A(t) is the account balance, in dollars, t years after the
account is opened. The account balance after 18 years is $7992. Which equation could
define A?
R. A(t) = 2000(0.08)t
S. A(t) = 2000(1.08)t
T. A(t) = 5992(0.08)t
U. A(t) = 5992(1.08)t
91.The expression 88y4 - 20y6 is equivalent to ky4(22 - 5y2), where k is a constant. What is the
value of k?
92.For which of the following tables are all the values of x and their corresponding values of y
solutions to the given inequality? y > 4x - 20
W. X. Y. Z.
93.Function f is defined by f(x) = (x + 4) (x -3) (x - 1). Function g is defined by g(x) = f(x-1). The
graph of y = g(x) in the xy plane has x-intercept at (a,0), (b,0), and (c,0), where a, b, and c are
distinct constants. What is the value of a + b + c?
94.The function f is defined by f(x) = (x + 4) (x - 3) (x - 1). In the xy plane, the graph of y = g(x) is
the result of translating the graph of y = f(x) down 5 units. What is the value of g(1)?
95.The function f is defined by f(x) = 180(0.4)x. What is the value of f(0)?
96.The function f is defined by f(x) = 180(⅓)x. What is the value of f(1)?
97.The function f is defined by f(x) = (-6)(4)x + 18. The y-intercept of the graph of y = f(x) in the xy
plane is (0,k). What is the value of k?
98.For the function k, the value of k(x) decreases by 35% for every increase in the value of x by 1.
If k(0) = 12, which equation defines k?
B. k(x) = 1.35 (12)x
C. k(x) = 0.55 (12)x
D. k(x) = 12 (1.35)x
E. k(x) = 12 (0.55)x
99.Which of the following expressions is(are) factors of 3x2 - 10x + 8
I.(3x - 4)
II. (x + 2)
A. I only
B. II only
C. I and II
D. Neither I nor II
100. The function f is defined by the given equation f(x) = 7(3)x. If g(x) = f(x+4), which of the
following equations defines the function g(x)?
E. g(x) = 28(3)x
F. g(x) = 7(7)x
G. g(x) = 28(7)x
H. g(x) = 567(3)x
101. One solution to the given equation x2 - 6x - 11 = 0 can be written as 3 - √k, where k is a
constant. What is the value of k?
J. 6
K. 11
L. 20
M. 80
102. The table shows four values of x and their corresponding values of f(x).
There is a linear relationship between x and f(x) that is defined by the
equation f(x) = mx - 15, where m is a constant. What is the value of m?
103. Which expression is equivalent to , where x and y are positive?
4
𝑥13𝑦26
N. (xy2)13 / 4
O. (xy2)4 / 13
P. (xy2)17
a. Q. (xy2)52
104. Which of the following systems of linear equations has no solution?
R. x = 4 and y = 6
S. y = 3x + 7 and y = 4x + 7
T. y = 5x + 4 and y = 5x + 6
U. y = 7 and y = 7x + 2
105. Which of the following systems of linear equations has infinitely many solutions?
B. 2x + 3y = 5 and 3x + 2y = 5
C. 4x + 7y = 28 and 7x - 4y = -28
D. 5x - 2y = 13 and 10x - 4y = -13
E. x + 5y = 7 and 2x + 10y = 14
106. The first term of a sequence is 8. Each term after the first is 3 times the preceding term. If
w represents the nth term of the sequence, which equation gives w in terms of n?
F. w = 3(8n)
G. w = 8(3n)
H. w = 3(8n-1)
I . w = 8(3n-1)
107. The graph of 3x - 5y = 12 is translated up 7 units in the xy plane. What is the x-coordinate
of the x-intercept of the resulting graph? (Hint, the answer is a decimal)
108. Line q in the xy-plane has a slope of -½ and passes through the point (3,8). Which
equation defines line q?
Q. y = 9.5x - ½
R. y = -x/2 + 9.5
S. y = 3x + 8
T. y = -x/2 + 8
109. Tickets for the Valentine Dance cost $3 per person or $5 per couple. If $475 worth of
tickets were sold and 180 people attended the dance, how many couples were there?
110. A geometry teacher has a set of 60 plastic pentagons and octagons. She happened to
notice that all the figures together have a total of 354 sides (she had lots of spare time to
count). How many pentagons did she have?
111. A group of Mayfield students goes out to lunch. If two have burritos and five have tacos,
the bill will be $19.50. If five have burritos and two have tacos, the bill will be $22.50. Find the
price of a taco.
112. In Lewis Carroll’s Through the Looking Glass, Tweedledum says, “The sum of your weight
and twice mine is 361 pounds.” Then Tweedledee says, “The sum of your weight and twice
mine is 362 pounds.” Find the weight of Tweedledum.
113. The equation (x-1)2 + (y+3)2 = 49 represents circle A. Circle B is obtained by shifting circle
A up 5 units and 2 units left in the xy plane. Which of the following equations represents circle
B?
A. (x+1)2 + (y-2)2 = 49
B. (x-3)2 + (y-2)2 = 49
C. (x+1)2 + (y+8)2 = 49
D. (x-3)2 + (y+8)2 = 49
114. Line p is defined by 4x + 20y = 9. Line k is perpendicular to line p in the xy-plane. What is
the slope of line k?
115. In the given system of equations, a is a positive constant. The system has exactly one
distinct real solution. What is the value of a? y = -3.5 and y = x2 + 6x + a
116. The graph of x2 + 3x + y2 - 6y = 145 / 2 in the xy-plane is a circle. What is the length of the
circle’s radius? (Hint, the answer is a decimal)
117. In the xy-plane, the parabola has a vertex (-7,12) and intersects the x-axis at two points. If
the equation of the parabola is written in the form y = ax2 + bx + c, where a, b, and c are
constants, which of the following could be the value of a + b + c?
M. -34
N. 15
O. -99
P. 24
Directions: For multiple choice questions, put the corresponding letter in the box below the question number.
For short answer questions, match the answer to a letter and then put that letter in the box below the question
number.
Questions 1 - 17
-2 = O 1 = A 3 = H 4 = B 5 = T 6 = N 12 = L
-9.375 = I 0.875 = E 5/3 = P 19/3 = I 139 = N 2005 = J 4131 = W
1 17 2 5 9 11 12 3 9 13 13 10 8
M I S T A K E S A L L O W
5 16 14 15 11 17 4 7 5 10 16 9 6 6 12 15
T H I N K I N G T O H A P P E N
Questions 18-39
7 = I 11 = U 16 = L 20 = P 25 = H 35 = R 41 = M 73 = S
1800 = T 2011 = K
35 33 34 19 37 38 27 18 22 25 27 20 19 39 23 19 30 36 31
L I F E W I T H O U T G E O M E T R Y
28 26 24 22 38 21 27 29 32 26 26
I S P O I N T L E S S
Questions 40-66
-16 = U -10 = B -3 = X -2.4 = R -2 = E -½ = A 1.223 = K 4 = C
6 = F 7 = N 10 = D 16 = S 24 = H 65 = P
51 53 47 58 47 44 41 61 60 58 47 66 65 53 47 45 61
D E A R A L G E B R A P L E A S E
45 57 48 42 47 45 64 54 46 52 50 45 49 55
S T O P A S K I N G U S T O
43 63 46 40 59 55 56 58 62
F I N D Y O U R X
Questions 67-end
-13 = H -7.667=S -7.5 = U -5 = E -3 = E ½ = E 2.5 = E 3 = L
4 = S 5 = H 5.5 = E 6 = M 8 = O 9.152 = V 12 = E 15 = A
17 = T 28 = T 29 = R 30 = C 36 = P 42 = E 60 = O 65 = M
120 = E 155 = B 180 = N
68 76 79 113 93 85 98 87 101 86 103 97 107 100 69 116 112 91 75
P A R A L L E L L I N E S H A V E S O
117 89 83 70 106 95 74 82 67 77 96 88 86 102 84 99
M U C H I N C O M M O N I T ‘ S A
90 114 73 71 105 104 81 94 92 88 110 80 115 108 109 72 111 78
S H A M E T H E Y N E V E R M E E T
Directions: For multiple choice questions, put the corresponding letter in the box below the question number.
For short answer questions, match the answer to a letter and then put that letter in the box below the question
number.
Questions 1 - 17
-2 = O 1 = A 3 = H 4 = B 5 = T 6 = N 12 = L
-9.375 = I 0.875 = E 5/3 = P 19/3 = I 139 = N 2005 = J 4131 = W
1 17 2 5 9 11 12 3 9 13 13 10 8
5 16 14 15 11 17 4 7 5 10 16 9 6 6 12 15
Questions 18-39
7 = I 11 = U 16 = L 20 = P 25 = H 35 = R 41 = M 73 = S
1800 = T 2011 = K
35 33 34 19 37 38 27 18 22 25 27 20 19 39 23 19 30 36 31
28 26 24 22 38 21 27 29 32 26 26
Questions 40-66
-16 = U -10 = B -3 = X -2.4 = R -2 = E -½ = A 1.223 = K 4 = C
6 = F 7 = N 10 = D 16 = S 24 = H 65 = P
51 53 47 58 47 44 41 61 60 58 47 66 65 53 47 45 61
45 57 48 42 47 45 64 54 46 52 50 45 49 55
43 63 46 40 59 55 56 58 62
Questions 67-end
-13 = H -7.667=S -7.5 = U -5 = E -3 = E ½ = E 2.5 = E 3 = L
4 = S 5 = H 5.5 = E 6 = M 8 = O 9.152 = V 12 = E 15 = A
17 = T 28 = T 29 = R 30 = C 36 = P 42 = E 60 = O 65 = M
120 = E 155 = B 180 = N
68 76 79 113 93 85 98 87 101 86 103 97 107 100 69 116 112 91 75
117 89 83 70 106 95 74 82 67 77 96 88 86 102 84 99
‘
90 114 73 71 105 104 81 94 92 88 110 80 115 108 109 72 111 78