Download (B) 4, 5, 6 - Geometry And Measurement

Math Project Task
(1 & 2)
 Done by: Omar Ali Ahmed Ali Shaheen
 G12-04
 What is SAT Exam?
 Is owned, published, and developed by the College Board, a nonprofit
organization in the United States. It was formerly developed, published, and
scored by the Educational Testing Service[1] which still administers the exam. The
test is intended to assess a student's readiness for college. It was first introduced
in 1926, and its name and scoring have changed several times. It was first called
the Scholastic Aptitude Test, then the Scholastic Assessment Test.
 What is the target score for SAT exam in ATHS?
 It is above 500 for ATHS Students.
 How the SAT test is scored?
 First: Your raw scores are calculated for each section based on the number of
questions you got correct or incorrect, or that you omitted.
 Second: We do a statistical analysis to make sure the test is an accurate
representation of your skills. The unscored section of the test also helps us ensure
the test is fair. Questions in the unscored section are not factored into your SAT
score.
 Third: Your raw score is then converted to a scaled score (reported on a 200-800
scale) by a statistical process called equating.
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 What is the minimum number of correct answers you
need in each section to reach the target?
 For ATHS students minimum of 10 answers in three sections.
 Mention 10 tips to score more in SAT.
 Study concepts.
 Memorize formulas.
 Always show your work to get familiar with the questions.
 Use official tests to practice with.

Read the questions very carefully before you solve.
 Solve multiple choices before the writing questions on math.
 Take SAT courses.
 Practice solving each day.
 Know what are your weaknesses in Math SAT.
 Use the calculator to solve long equations like the divisions
of dominator and nominator.
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 In the figure below, what is the value of y?
(A) 40
(B) 50
(C) 60
(D) 100
(E) 120
 2. A right circular cylinder has a radius of 3 and a height of 5. Which of the following dimensions
of a rectangular solid will have a volume closest to the cylinder.
(A) 4, 5, 5,
(B) 4, 5, 6,
(C) 5,5,5,
(D) 5,5,6,
(E) 5,6,6
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 In the figures above, x = 60. How much more is the perimeter of triangle ABC compared with
the triangle DEF.
(A) 0, (B) 2,
(C) 4,
(D) 6,
(E) 8
 In the figure above, 𝐵𝐸 ⊥ 𝐴𝐷 and 𝐶𝐹 ⊥ 𝐴𝐷 and AE = EF . What is the value of x?
(A) 40,
(B)
45,
(C)
50,
(D)
55,
(E)
60
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 If triangle Abc above is congruent to triangle DEF (not shown), which of the following must be
the length of one side of triangle DEF?
(A) 18
(B) 24
(C) 3√6
(D) 6√3
(E) It cannot be determined from the information given.
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SOLUTIONS
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 In the figure below, what is the value of y?
(A) 40
(B) 50
(C) 60
(D) 100
(E) 120
Step 1: Vertical angles being equal allows us to fill in two angles in the triangle that y° belongs to.
Sum of angles in a triangle = 180°. So, y° + 40° + 80° = 180°
> y° + 120° = 180°
y° = 60°
Answer: (C) 60
 2. A right circular cylinder has a radius of 3 and a height of 5. Which of the following dimensions
of a rectangular solid will have a volume closest to the cylinder.
(A) 4, 5, 5, (B) 4, 5, 6, (C) 5,5,5, (D) 5,5,6, (E) 5,6,6
V = πr2h > V = π × 32 × 5 = 45π V = 45 × 3.142 = 141.39
We now have to test the volume of each of the rectangular to find out which is the closest to 141.39.
(A) 4 × 5 × 5 = 100
(B) 4 × 5 × 6 = 120
(C) 5 × 5 × 5 = 125
(D) 5 × 5 × 6 = 150 (E) 5 × 6 × 6 = 180
Answer: (D) 5, 5, 6
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Note: Figures not drawn to scale
 In the figures above, x = 60. How much more is the perimeter of triangle ABC compared with
the triangle DEF.
(F) 0, (b)
2, (C)
4, (D)
6, (E)
8
Since x = 60°, triangle ABC is an equilateral triangle with sides all equal. The sides are all equal to 8. Perimeter of triangle ABC = 8 + 8 + 8 = 24.
Triangle DEF has two angles equal, so it must be an isosceles triangle. The two equal sides will be
opposite the equal angles.
So, the length of DF = length of DE = 10.
Perimeter of triangle DEF = 10 + 10 + 4 = 24.
Subtract the two perimeters.
24 – 24 = 0
Answer: (A) 0
 In the figure above, 𝐵𝐸 ⊥ 𝐴𝐷 and 𝐶𝐹 ⊥ 𝐴𝐷 and AE = EF . What is the value of x?
(A) 40, (B)
45, (C)
50, (D)
55, (E)
60
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We can find the supplementary angle of 120°, which gives us ∠𝐴𝐹𝐶 60°.
BE is parallel to CF because they are both perpendicular to AD. This means that ∠𝐴𝐸𝐵 = ∠𝐴𝐹𝐶 = 60
since they are corresponding angles.
Triangle ABE and triangle ACF are similar triangles , since ∠𝐴𝐸𝐵 = ∠𝐴𝐹𝐶 and ∠𝐴𝐵𝐸 = ∠𝐴𝐶𝐹 . Given
that AE = EF, we can conclude that AB = BC
Triangle ABE and triangle CBE are congruent triangles . So, x = angle AEB = 60°
So, x = 60
Answer: (E) 60
 If triangle Abc above is congruent to triangle DEF (not shown), which of the following must be
the length of one side of triangle DEF?
(A) 18
(B) 24
(C) 3√6
(D) 6√3
(E) It cannot be determined from the information given.
Triangle ABC is congruent to triangle DEF, so the lengths of the three sides of triangle DEF are the
same as the lengths of the three sides of triangle ABC . Triangle ABC is a 30° - 60° - 90° triangle with
hypotenuse of length 12, so the other two sides of triangle ABC have lengths 6 and 6√3.
Therefore, the lengths of the sides of triangle DEF must be 12, 6, and 6√3. Of the choices given, only
6√3 is one of these values.
Answer: D
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