Rules and Equations
What is the equation of a circle AND what letters represent the center?
(x-h)2 + (y-k)2 = r2 - Center is (h,k)
Two units of length used in ancient Egypt were
cubits and palms, where 1 cubit is equivalent to
7 palms. The Great Sphinx statue in Giza is
approximately 140 cubits long. Which of the
following best approximates the length, in palms, of
the Great Sphinx statue?
A) 0.05
B) 20
C) 140
D) 980
Choice D is correct. Since 1 cubit is equivalent to 7 palms, 140 cubits
are equivalent to 140(7) palms, or 980 palms.
Choice A is incorrect and may result from dividing 7 by 140. Choice B
is incorrect and may result from dividing 140 by 7. Choice C is
incorrect. This is the length of the Great Sphinx statue in cubits,
not palms.
3x + x + x + x − 3 − 2 = 7 + x + x
In the equation above, what is the value of x ?
A) −
5
7
B) 1
C)
12
7
D) 3
Choice D is correct. Combining like terms on each side of t he
given equation yields 6x − 5 = 7 + 2x. Adding 5 to both sides of
6x − 5 = 7 + 2x and subtracting 2x from both sides yields 4x = 12.
Dividing both sides of 4x = 12 by 4 yields x = 3.
Choices A, B, and C are incorrect because substituting those values
into the equation 3x + x + x + x − 3 − 2 = 7 + x + x will result in a
false statement. For example, in choice B, substituting 1 for x in the
equation would give 3(1) + 1 + 1 + 1 – 3 – 2 = 7 + 1 + 1, which yields the
false statement 1 = 9; therefore, x cannot equal 1.
How much time should you spend on each question of the exam.
About 30 seconds
What is the ERW Score you should achieve to be college ready?
480
What is the difference of two square rule?
If our quadratic equation may be written as a difference between two squares, then it may be factored into two binomials, one a sum of the square roots and the other a difference of the square roots. This is sometimes shown by the expression A² - B² = (A + B) (A - B)
What value of x satisfies the equation 3x + 3 = 27 ?
A) 3
B) 8
C) 10
D) 27
Choice B is correct. Subtracting 3 from both sides of the equation
yields 3x = 24. Dividing both sides of this equation by 3 yields x = 8.
Choice A is incorrect and may result from finding a common factor
among the three given terms instead of finding x. Choice C is incorrect
and may result from incorrectly adding 3 to, instead of subtracting 3
from, the right-hand side of the equation. Choice D is incorrect. This is
the value of 3x + 3, not the value of x.
The width of a rectangular dance floor is w feet. The
length of the floor is 6 feet longer than its width.
Which of the following expresses the perimeter, in
feet, of the dance floor in terms of w ?
A) 2w + 6
B) 4w + 12
C) w2 + 6
D) w2 + 6w
Choice B is correct. It is given that the width of the dance floor is
w feet. The length is 6 feet longer than the width; therefore, the length
of the dance floor is w + 6. So the perimeter is w + w + (w + 6) + (w + 6) =
4w + 12.
Choice A is incorrect because it is the sum of one length and one
width, which is only half the perimeter. Choice C is incorrect and may
result from using the formula for the area instead of the formula for
the perimeter and making a calculation error. Choice D is incorrect
because this is the area, not the perimeter, of the dance floor.
What are 3 major items you should have with you for your exam?
2) A charged calculator
3) Your I.D.
What is the college ready Math Score you must receive on the SAT?
530
What is SoCahToa?
Sin = opposite over hypotenuse
Cos = adjacent over hypotenuse
Tan = Opposite over adjacent
If 2n/5 = 10, what is the value of 2n − 1 ?
A) 24
B) 49
C) 50
D) 99
Choice B is correct. Multiplying both sides of the given equation by
5 yields 2n = 50. Substituting 50 for 2n in the expression 2n − 1 yields
50 − 1 = 49.
Alternate approach: Dividing both sides of 2n = 50 by 2 yields n = 25.
Evaluating the expression 2n − 1 for n = 25 yields 2(25) − 1 = 49.
Choice A is incorrect and may result from finding the value of n − 1
instead of 2n − 1. Choice C is incorrect and may result from finding the
value of 2n instead of 2n − 1. Choice D is incorrect and may result from
finding the value of 4n − 1 instead of 2n − 1.
(x − 6)2 + (y + 5)2 = 16
In the xy-plane, the graph of the equation above is a
circle. Point P is on the circle and has coordinates
(10, −5). If PQ is a diameter of the circle, what are
the coordinates of point Q ?
A) (2, −5)
B) (6, −1)
C) (6, −5)
D) (6, −9)
Choice A is correct. The standard form for the equation of a circle is
(x – h)2 + (y – k)2 = r 2, where (h, k) are the coordinates of the center
and r is the length of the radius. According to the given equation, the
center of the circle is (6, –5). Let (x1, y1) represent the coordinates of
point Q. Since point P (10, –5) and point Q (x1, y1) are the endpoints
of a diameter of the circle, the center (6, –5) lies on t he diameter,
halfway between P and Q. Therefore, the following relationships hold:
x1 + 10
_2 = 6 and
y1 + (−5)
_2 = −5. Solving the equations for x1 and y1,
respectively, yields x1 = 2 and y1 = −5. Therefore, the coordinates of
point Q are (2, –5).
Alternate approach: Since point P (10, −5) on the circle and the center
of the circle (6, −5) have the same y-coordinate, it follows that the
radius of the circle is 10 – 6 = 4. In addition, the opposite end of the
diameter
_
PQ must have the same y-coordinate as P and be 4 units away
from the center. Hence, the coordinates of point Q must be (2, –5).
Choices B and D are incorrect because the points given in these
choices lie on a diameter that is perpendicular to the diameter
_
PQ . If
either of these points were point Q, then
_
PQ would not be the diameter
of the circle. Choice C is incorrect because (6, −5) is t he center of the
circle and does not lie on t he circle.
What is something you should do the morning of your exam?
Eat a hardy breakfast and drink a lot of water!
When will you take the SAT again with Southeast?
In October of Senior Year.
What are the 4 methods of factoring?
The Greatest common factor (GCF), the Grouping method, the difference in two squares, and the sum or difference in cubes.
Washington High School randomly selected
freshman, sophomore, junior, and senior students
for a survey about potential changes to next year’s
schedule. Of students selected for the survey,
1/4 were freshmen and 1/3 were sophomores. Half of the remaining selected students were juniors. If
336 students were selected for the survey, how many were seniors?
A) 240
B) 140
C) 120
D) 70
Choice D is correct. It is given that the number of students surveyed
was 336. Finding of 336 yields , the number of
freshmen, and finding of 336 yields , the number of
sophomores. Subtracting these numbers from the total number of
selected students results in 336 − 84 − 112 = 140, the number of juniors
and seniors combined. Finding half of this total yields ,
the number of juniors. Subtracting this number from the number of juniors
and seniors combined yields 140 − 70 = 70, the number of seniors.
Choices A and C are incorrect and may result from calculation errors.
Choice B is incorrect. This is the total number of juniors and seniors.
A group of 202 people went on an overnight camping
trip, taking 60 tents with them. Some of the tents
held 2 people each, and the rest held 4 people each.
Assuming all the tents were filled to capacity and
every person got to sleep in a tent, exactly how many
of the tents were 2-person tents?
A) 30
B) 20
C) 19
D) 18
Choice C is correct. Let x represent the number of 2-person tents
and let y represent the number of 4-person tents. It is given that the
total number of tents was 60 and the total number of people in the
group was 202. This situation can be expressed as a system of two
equations, x + y = 60 and 2x + 4y = 202. The first equation can be
rewritten as y = −x + 60. Substituting −x + 60 for y in the equation
2x + 4y = 202 yields 2x + 4(−x + 60) = 202. Distributing and combining
like terms gives −2x + 240 = 202. Subtracting 240 from both sides
of −2x + 240 = 202 and then dividing both sides by −2 gives x = 19.
Therefore, the number of 2-person tents is 19.
If you do not know the answer, you should?
Guess.
What is the exam you will need to take if you do not score college ready scores on your SAT?
The TSI: Texas Success Initiative Assessment
πr2h is the formula used to measure this.
What is the volume of a cylinder.
If f (x) = 5x2 − 3 and f (x + a) = 5x2 + 30x + 42,
what is the value of a ?
A) −30
B) −3
C) 3
D) 30
Choice C is correct. Substituting x + a for x in f(x) = 5x 2 − 3 yields
f(x + a) = 5(x + a)2 − 3. Expanding the expression 5(x + a)2 by multiplication
yields 5x 2 + 10ax +5a2, and thus f(x + a) = 5x 2 + 10ax + 5a2 − 3. Setting
the expression on the right-hand side of this equation equal to the
given expression for f(x + a) yields 5x 2 + 30x + 42 = 5x 2 + 10ax + 5a2 − 3.
Because this equality must be true for all values of x, the coefficients of
each power of x are equal. Setting the coefficients of x equal to each other
gives 10a = 30. Dividing each side of this equation by 10 yields a = 3.
Choices A, B, and D are incorrect and may result from a calculation error.
g (x) = 2x-1
h (x) = 1 - g (x)
The functions g and h are defined above. What is the
value of h(0) ?
A) −2
B) 0
C) 1
D) 2
Choice D is correct. Since h (x) = 1 − g (x), substituting 0 for x yields
h (0) = 1 − g (0). Evaluating g (0) gives g (0) = 2(0) − 1 = −1. Therefore,
h (0) = 1 − (−1) = 2.
Choice A is incorrect. This choice may result from an arithmetic
error. Choice B is incorrect. This choice may result from incorrectly
evaluating g(0) to be 1. Choice C is incorrect. This choice may result
from evaluating 1 − 0 instead of 1 − g(0).
Is it better to answer all questions or to leave what you do not know blank?
Answer all questions.
What is the importance of SAT Scores.
They assist in Auto Admissions to some schools and increase chances of scholarship opportunities.