NEW GOLANI ACT PREP 2022-2023 COMPLETE EAM SOLUTION FOR A GRADE STUDENT
Angles that look the same can be assumed to be the same, even if you can't prove it, since
there is no other way to solve it.
For example, ACD can be assumed to be 25° - You are asked to solve for DBC and are stuck.
What might be a reasonable assumption to help solve it?
Just from eyeballing it, the answer is greater than 180, which is a straight line.
It also seems less than 270, which would leave only a 90° angle. 252° is a reasonable answer. -
What answer seems most reasonable without doing any math?
Plug in a number for n. - What technique could be used to solve this problem? If n is any integer
greater than 10, which of the following expressions is closest in value to ½?
a) n/(n+2)
b) n(2n+1)
c) (n-1)/(n+2)
d) (2n+1)/n
Make every value equal to 18 - The average of 5 numbers is 18. What technique comes to
mind?
a) If asked to solve for a variable, like x, and the answers have numbers, can you:
i) Backsolve? (plug in the answer choices )
ii) Solve the equation using Solver on the calculator?
b) If the answer choices have variables, can you plug in? (Make up a number for the variable
and see where it leads to)
c) If it is a measurement, like the length of a segment or an angle measure, can you can ballpark
if from other lengths, or estimate the angle measure?
d) If you think you can solve it with time, star it and come back to it later
e) If you are completely guessing, eliminate the oddball answer - I'm stuck on a problem and
have no idea how to solve it. What do I do?
"Min-Max". In order to maximize one number, minimize the others. (In this case, make the
others all one) - What technique comes to mind? "Each of 5 people had a blank card on which
they wrote a positive integer. If the average of these 5 integers is 15, what is the greatest
possible integer that could be on one of the cards?
Either
a) Backsolve; that is, use the answer choices and plug them in. OR
b) Use solver on the calculator - You do not know how to solve this algebraically. What would
you do?
If 5ⁿ = 25²ⁿ⁺³ , solve for x.
a) 1
b) 0
,c) -1
d) -2
Casio:
shift , then a b/c button
TI: Alpha, F1 - Type 2¾ on the calculator
Casio: EQUA, POLY, degree 2.
TI: Apps, polysiml, polynomial root finder - Solve the quadratic: X²+ 19x +48 =0
Method A:
By hand: 2x²-8x = 0
Factor out a 2x: 2x(x-4) =0
2x = 0 or x-4 =0
so x = 0 or 4
Method B: Solve on calculator:
EQUA (Casio) or Polysiml (TI) - Solve: 2x² = 8x
Casio: EQUA, SIML.
TI: Apps, Poly Siml, Simulataneous Equations - Solve this system of equations.
3x-7y = 18
4x + 3y = 9
On the calculator:
Casio: EQUA, SOLV
TI: MATH, SOLVER - Solve for x:
5x/3 + 1 = 18x/17
...2, -1, 0, 1, 2,... - Integers
Can be written as a fraction.
For example, ¾, 7, 0 are all rational.
Also, any decimal with a pattern is rational, such as 2.45454545..." - Rational Numbers
Cannot be written as fraction.
Pi and √5, for example. - Irrational Numbers
The answer in an addition problem - Sum
The answer in a multiplication problem - Product
The answer in a division problem - Quotient
, There are TEN digits. They are 0-9 - Digits
The digit in the ones place.
In the number 6,789, it's the nine - Units digit
Any number that can only be divided by one and itself. - Prime number
2 is the first prime number.
ONE is NOT PRIME! - What is the first prime number?
The factors of 18 are 1,2,3,6,9, and 18 - What are the factors of 18?
The answers you get when you multiply by a number. - Multiple
The Multiples of 7 are 7, 14, 21... - List the multiples of 7
9.41 X 10⁻⁷ - Write in scientific notation: 0.000000941
4.3 X 10²
right/reduce and left/lift. That is, when moving the decimal to the right, reduce the exponent -
Convert 0.43 X 10³ into scientific notation
5.6 X 10⁶ or 5,600,000 - How would you interpret 5.67 E+6 when it appears on the calculator?
1.3x - A value x, increased by 30% can be written as:
0.8x - A value x, decreased by 20% can be written as:
2/8 or 25%.
Percent change:
change /original = percent / 100 - An increase from 8 to 10 is a percent increase of what?
Let x = original.
1.4x = 25
x=$17.86 - After a 40% increase, the new price is $25. Find the original
"V for Victory"
3/a + a/a = 3/a +1 - What comes to mind?
(3+a)/a
Cross multiply:
5x = 3
x = 3/5 - If 3/x = 5, solve for x.
Angles that look the same can be assumed to be the same, even if you can't prove it, since
there is no other way to solve it.
For example, ACD can be assumed to be 25° - You are asked to solve for DBC and are stuck.
What might be a reasonable assumption to help solve it?
Just from eyeballing it, the answer is greater than 180, which is a straight line.
It also seems less than 270, which would leave only a 90° angle. 252° is a reasonable answer. -
What answer seems most reasonable without doing any math?
Plug in a number for n. - What technique could be used to solve this problem? If n is any integer
greater than 10, which of the following expressions is closest in value to ½?
a) n/(n+2)
b) n(2n+1)
c) (n-1)/(n+2)
d) (2n+1)/n
Make every value equal to 18 - The average of 5 numbers is 18. What technique comes to
mind?
a) If asked to solve for a variable, like x, and the answers have numbers, can you:
i) Backsolve? (plug in the answer choices )
ii) Solve the equation using Solver on the calculator?
b) If the answer choices have variables, can you plug in? (Make up a number for the variable
and see where it leads to)
c) If it is a measurement, like the length of a segment or an angle measure, can you can ballpark
if from other lengths, or estimate the angle measure?
d) If you think you can solve it with time, star it and come back to it later
e) If you are completely guessing, eliminate the oddball answer - I'm stuck on a problem and
have no idea how to solve it. What do I do?
"Min-Max". In order to maximize one number, minimize the others. (In this case, make the
others all one) - What technique comes to mind? "Each of 5 people had a blank card on which
they wrote a positive integer. If the average of these 5 integers is 15, what is the greatest
possible integer that could be on one of the cards?
Either
a) Backsolve; that is, use the answer choices and plug them in. OR
b) Use solver on the calculator - You do not know how to solve this algebraically. What would
you do?
If 5ⁿ = 25²ⁿ⁺³ , solve for x.
a) 1
b) 0
,c) -1
d) -2
Casio:
shift , then a b/c button
TI: Alpha, F1 - Type 2¾ on the calculator
Casio: EQUA, POLY, degree 2.
TI: Apps, polysiml, polynomial root finder - Solve the quadratic: X²+ 19x +48 =0
Method A:
By hand: 2x²-8x = 0
Factor out a 2x: 2x(x-4) =0
2x = 0 or x-4 =0
so x = 0 or 4
Method B: Solve on calculator:
EQUA (Casio) or Polysiml (TI) - Solve: 2x² = 8x
Casio: EQUA, SIML.
TI: Apps, Poly Siml, Simulataneous Equations - Solve this system of equations.
3x-7y = 18
4x + 3y = 9
On the calculator:
Casio: EQUA, SOLV
TI: MATH, SOLVER - Solve for x:
5x/3 + 1 = 18x/17
...2, -1, 0, 1, 2,... - Integers
Can be written as a fraction.
For example, ¾, 7, 0 are all rational.
Also, any decimal with a pattern is rational, such as 2.45454545..." - Rational Numbers
Cannot be written as fraction.
Pi and √5, for example. - Irrational Numbers
The answer in an addition problem - Sum
The answer in a multiplication problem - Product
The answer in a division problem - Quotient
, There are TEN digits. They are 0-9 - Digits
The digit in the ones place.
In the number 6,789, it's the nine - Units digit
Any number that can only be divided by one and itself. - Prime number
2 is the first prime number.
ONE is NOT PRIME! - What is the first prime number?
The factors of 18 are 1,2,3,6,9, and 18 - What are the factors of 18?
The answers you get when you multiply by a number. - Multiple
The Multiples of 7 are 7, 14, 21... - List the multiples of 7
9.41 X 10⁻⁷ - Write in scientific notation: 0.000000941
4.3 X 10²
right/reduce and left/lift. That is, when moving the decimal to the right, reduce the exponent -
Convert 0.43 X 10³ into scientific notation
5.6 X 10⁶ or 5,600,000 - How would you interpret 5.67 E+6 when it appears on the calculator?
1.3x - A value x, increased by 30% can be written as:
0.8x - A value x, decreased by 20% can be written as:
2/8 or 25%.
Percent change:
change /original = percent / 100 - An increase from 8 to 10 is a percent increase of what?
Let x = original.
1.4x = 25
x=$17.86 - After a 40% increase, the new price is $25. Find the original
"V for Victory"
3/a + a/a = 3/a +1 - What comes to mind?
(3+a)/a
Cross multiply:
5x = 3
x = 3/5 - If 3/x = 5, solve for x.
