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Coordinate Geometry - Line Equation - Proportionality

Honore — Sat, 13 Jun 2026 10:11:45 +0000

https://i.ibb.co/cKyFcHFQ/Dancing-question.png
https://www.kaptest.com/sat/free/sat-20-minute-workout
(The first question)

For Earn = f(Hours) linear equation that passes through the points (3.5, 50) and (4, 100) the line function is,
(Earn - 100) / (100 - 50) = (h - 4) / (4 - 3.5) ⇒ Earn = 100(h - 3).

Note: The time during which money is being earned is h - 3 hours. The...

Coordinate Geometry - Line Equation - Proportionality

Trigonometry - Angles in Square and Right Trapezoid

Honore — Thu, 08 Jan 2026 09:56:07 +0000

In quadrilateral ABCD if [AD] // [BC], |CD| = 0.5·|AB|, and [BC] is perpendicular to [CD] what is the measure of angle B?

A) 150°
B) 135°
C) 120°
D) 90°

∡B = [ arccos( |AB| / 2 / |AB| ) + π / 2 ]·180° / π = 150°.

Check by WolframAlpha:...

Trigonometry - Angles in Square and Right Trapezoid

Radical and Exponential Numbers - Principal Argument of Complex Numbers - The Pythagorean Theorem

Honore — Sat, 20 Dec 2025 13:35:40 +0000

A slightly hardened adaptation of an AYT practice problem for the SAT exam:

For a complex number whose real and imaginary parts are positive real numbers x and y, respectively,
if x^0.5·√(2y) = 32^(1 / 2) / 5 and √y / x^(1 / 2) = 3, then what is the principal argument of this number?

A) arctan(1 / 9)
B) arccot(4 / 15)
C) arcsin(15 / 36)
D) arccos(1 / √82)
E) arcsec(36 / √15)

2·x·y = 32 / 5 ⇒ x·y = 16 / 25....(I)
y / x = 9 ⇒ y = 9x....(II)...

Radical and Exponential Numbers - Principal Argument of Complex Numbers - The Pythagorean Theorem

Least Common Multiple Open-End Problem (GRE Level)

Honore — Sat, 08 Nov 2025 11:03:36 +0000

There is a circular running track on which there are 8 points that are equally distant from one another. The starting point to run is colored blue, and the other points are yellow, green, red, orange, pink, gray, and white. Two runners whose names are Ali and Veli, with constant but different speeds, start running nonstop at the same time. Ali and Veli pass each colored point at 2 seconds and 3 seconds, respectively. When they come to the blue point side by side at the...

Least Common Multiple Open-End Problem (GRE Level)

Coordinate Geometry-Hyperbola-Law of Cosines-Radical Numbers-Pythagorean Theorem-Trigonometry

Honore — Thu, 21 Aug 2025 09:22:13 +0000

If the coordinates of two vertices of a triangle, with abscissas of 1 and 2, respectively, lie on the hyperbola y = 1 / x, what is the tangent of the angle opposite the side passing through these points?

Let the vertex opposite the side passing the given points be the origin of the Cartesian plane,
The length of the side: { (1 - 2)^2 + [ (1 / 1)^2 - (1 / 2)^2 ] }^0.5 = (√5) / 2 units
The lengths of the sides connecting those given vertices to the...

Coordinate Geometry-Hyperbola-Law of Cosines-Radical Numbers-Pythagorean Theorem-Trigonometry

Reading Comprehension-Vocabulary-Identifying Grammatically Erroneous, Meaningless or Vague Sentences

Honore — Thu, 03 Apr 2025 14:57:45 +0000

Which of the following sentences is "not" grammatically erroneous, meaningless, or uncertain?

A) After reading the two stories, the class decided that the second one was the best.
B) The task of filling out several college applications are time-consuming and exhausting.
C) Because experience had convinced her that he was both self-seeking and avaricious, she rejected the likelihood that his donation has been ephemeral.
D) The evil of class and race...

Reading Comprehension-Vocabulary-Identifying Grammatically Erroneous, Meaningless or Vague Sentences

Sentence Completion

Honore — Thu, 06 Feb 2025 12:13:21 +0000

Critics of the welfare system argue that rather than aiding people's efforts to govern their own lives, it ________ their independence.

A) supports
B) saps
C) hastens
D) renews
E) abets

Correct Choice: B (saps)

Explanation in the Book:
To sap or weaken the recipient's self-sufficiency would contradict the recipient's true welfare.
The phrase "argument against" is your clue to look for a "negative"...

Sentence Completion

Vocabulary - History of The Turkish Republic

Honore — Thu, 22 Aug 2024 11:56:16 +0000

The Sevres Treaty was never ratified, and much to the Allies' __________, it served as the one electrifying force that __________ the Turks into a determined resistance to the occupation powers and helped to __________ Turkish nationalism around the leadership of the insurgent Mustafa Kemal Atatürk.

A) dismay / stimulated / dissolve
B) regret / thrilled / thaw
C) distress / demoralized / liquefy
D) consternation / galvanized / congeal
E) desperation / dispirited /...

Vocabulary - History of The Turkish Republic

Vocabulary

Honore — Wed, 31 Jul 2024 15:23:24 +0000

Brown, this biography suggests, was an __________ employer, giving generous bonuses one day, and ordering pay cuts the next.

A) indifferent
B) objective
C) unpredictable
D) ineffectual
E) unobtrusive

Correct Choice: C (unpredictable)

Meanings of Some Words:
indifferent: uncaring or mediocre
ineffectual: weak and ineffective
objective: fair and impartial
unobtrusive: hardly...

Vocabulary

Geometry and Probability

Honore — Mon, 01 Apr 2024 12:33:56 +0000

If a real number x is chosen at random in the interval [0, 3] and a real number y is chosen at random in the interval [0, 4], what is the probability that x < y ?

A) 1 / 2
B) 7 / 12
C) 5 / 8
D) 2 / 3
E) 3 / 4

The probability equals the ratio of the area of the trapezoid over y = x to the area of the rectangle within the domain:
[ (4 + 1) / 2]·3 / (4·3) = 5 / 8....

Geometry and Probability

Technical English Vocabulary

Honore — Mon, 03 Oct 2022 10:25:58 +0000

______ can only be removed completely by a dentist or hygienist using special tools.

A) Physics
B) Calculus
C) Geometry
D) Chemistry
E) Biology

Correct Choice: B (Calculus)
Explanation: "Dental calculus is composed of inorganic components and organic matrix."
https://getpocket.com/explore/item/how-to-brush-your-teeth-properly-according-to-a-dentist...

Technical English Vocabulary