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Quant Practice Questions for ACT - 3 | Mathematics for ACT PDF Download

Q1: Draw the graph of y = 2 sin 1/2 x.

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Ans: 

Quant Practice Questions for ACT - 3 | Mathematics for ACT
Quant Practice Questions for ACT - 3 | Mathematics for ACT

Q2: Find the value of sin(30° + 45°)

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Ans: Expand the formula:
sin(30° + 45°) = sin 30° cos 45° + cos 30° sin 45°
Substitute values:

Quant Practice Questions for ACT - 3 | Mathematics for ACT
The cosine of the sum of two angles equals the product of their cosines minus the product of their sines. Memorize: cos(α + β) = cos α cos β – sin α sin β

Q3: Simplify cos A tan A, when cos A ≠ 0.

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Ans:

Quant Practice Questions for ACT - 3 | Mathematics for ACT

Q4: Simplify tan2 θ cos2 θ csc θ.

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Ans:

Quant Practice Questions for ACT - 3 | Mathematics for ACT

Q5: A kite has 80 meters of string out. The string makes an angle of 30° with the ground. How far above the ground is the kite?

Quant Practice Questions for ACT - 3 | Mathematics for ACT

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Ans:
Quant Practice Questions for ACT - 3 | Mathematics for ACT

Q6: Evaluate sin 45° • cos 60°

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Ans: Substitute the trigonometric function values:

Quant Practice Questions for ACT - 3 | Mathematics for ACT

Q7: If ∠A is an acute angle and sin A = 3/5 , find tan A.

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Quant Practice Questions for ACT - 3 | Mathematics for ACT

Quant Practice Questions for ACT - 3 | Mathematics for ACT
Quant Practice Questions for ACT - 3 | Mathematics for ACT

Q8: What is the area of the shaded portion?

Quant Practice Questions for ACT - 3 | Mathematics for ACT

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Ans: The area of the shaded portion equals the area of the rectangle minus the area of the triangle. Area of rectangle = length × width = 7 inches × 3 inches = 21 square inches. Area of triangle = 1/2 × base × height =1/2 × 2 inches × 3 inches = 3square inches. Area of shaded region = 21square inches – 3 square inches = 18 squareinches. To solve this problem: (1) Find the areaof the outside, larger figure; (2) Find the area ofthe smaller, undefined figure; (3) Subtract thearea of the unshaded figure from the area of theoutside larger figure.

Q9: Inscribed ∠CAD measures 50°. Find the inscribed angle whose measure is x.

Quant Practice Questions for ACT - 3 | Mathematics for ACT

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Ans:

Quant Practice Questions for ACT - 3 | Mathematics for ACT
Therefore, x = 50°
The measures of two inscribed angles are equal if they intercept the same arc.

Q10: O is the center. Chords Quant Practice Questions for ACT - 3 | Mathematics for ACT form aninscribed angle of 30°. Find the central anglewhose measure is x

Quant Practice Questions for ACT - 3 | Mathematics for ACT

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Quant Practice Questions for ACT - 3 | Mathematics for ACT

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FAQs on Quant Practice Questions for ACT - 3 - Mathematics for ACT

1. How can I improve my quant score on the ACT?
Ans. To improve your quant score on the ACT, it is essential to practice regularly, review fundamental math concepts, and familiarize yourself with the format of the exam. Additionally, consider seeking help from a tutor or using online resources for additional support.
2. What are some common topics covered in the quant section of the ACT?
Ans. The quant section of the ACT typically covers topics such as algebra, geometry, trigonometry, and data analysis. It is important to review these concepts thoroughly to perform well on the exam.
3. Are there any strategies for managing time during the quant section of the ACT?
Ans. To manage time effectively during the quant section of the ACT, it is recommended to pace yourself, skip difficult questions and come back to them later, and use process of elimination to narrow down answer choices. Practice time management strategies during your preparation to improve your performance on test day.
4. How can I stay calm and focused during the quant section of the ACT?
Ans. To stay calm and focused during the quant section of the ACT, it is important to practice mindfulness techniques, such as deep breathing or visualization, before and during the exam. Additionally, make sure to get plenty of rest the night before the test and stay hydrated to maintain focus.
5. Are there any resources available for additional practice for the quant section of the ACT?
Ans. Yes, there are several resources available for additional practice for the quant section of the ACT, including official ACT prep materials, online practice tests, and review books. Consider using these resources to supplement your preparation and improve your quant score.
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