How to Solve Challenging Math Problems in SAT

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To solve challenging SAT Math problems, students require deep understanding of the key concepts in Algebra, Geometry and Trigonometry. And also, students may require to master Desmos for graphing, plugging in answer choices (backsolving), and recognizing complex algebraic patterns. Going over the following stuff will help the students to learn, how to solve challenging Math Problems in SAT.

Problem 1 :

2z³ – kxz² + 5xz + 2x – 2

In the polynomial above, k is a constant. If z – 1 is a factor of the polynomial above, what is the value of k?

Solution :

Problem 2 :

The function f is defined by f(x) = 2|x|/k + 15, where k < 0. What is the product f(5k) and f(12k)?

Solution :

Problem 3 :

For the function f, f(kx) = x – 8 for all values of x, where k is a constant. If f(2) = 35, what is the value of k?

Solution :

Problem 4 :

There is a linear relationship between x and y. In the xy-plane, the y-intercept of the line representing this relationship is (0, -16). What is the value of a + b?

A) -32

B) -31

C) -22

D) -21

Solution :

Problem 5 :

Consider the quartic polynomial 60x⁴ + 170x² + 120. It is known that it can be factored in the form

(k)(ax² + b)(cx² + d),

where k, a, b, c and d are integers. Determine the smallest possible value of ab.

Solution :

Problem 6 :

A table gives values of x and the corresponding values of f(x), where f(x) = 3g(x – 2) + 4x and both f and g are linear functions. Determine the value of g(6)?

Solution :

Problem 7 :

The given equation relates the distinct positive real numbers w, x and y. Which equation correctly expresses w in terms of x and y?

Solution :

Problem 8 :

In triangle XYZ, angle Z is a right angle and the length of YZ is 24 units. If tanX = 12/35, what is the perimeter, in units, of triangle XYZ ?

A) 188

B) 168

C) 84

D) 71

Solution :

Problem 9 :

The speed of a vehicle is increasing at a rate of 7.3 meters per second squared. What is this rate, in miles per minute squared, rounded to the nearest tenth? (Use 1 mile = 1,609 meters.)

A) 0.3

B) 16.3

C) 195.8

D) 220.4

Solution :

Problem 10 :

Monthly incomes of two persons are in the ratio 4 : 5 and their monthly expenses are in the ratio 7 : 9. If each saves $500 per month, find their monthly incomes.

A) $5000 and $4000

B) $4000 and $5000

C) $3000 and $6000

D) $3500 and $5500

Solution :

Problem 11 :

The vertex of the function f(x) is given as (9, –13) and the point (3, –4) lies on the parabola. If g(x) = 4f(x – 2), what is the value of g(0) – f(0)?

Answer :

Problem 12 :

The density of a certain type of wood is 770 kilograms per cubic meter. A sample of this type of wood is in the shape of a cube, where each edge has a length of 0.7 meters. To the nearest whole number, what is the mass, in kilograms, of this sample?

A) 264

B) 377

C) 1,571

D) 2,245

Answer :

Problem 13 :

In ΔABC, ∠B is a right angle and the length of AB is 456 millimeters. If the cos C = 7/25, what is the length, in millimeters, of BC?

Answer :

Problem 14 :

In triangle ABC and triangle DEF, sides BC and EF each have a side length of 37 inches, and angles B and E each have an angle measure of 63°. Which of the following additional pieces of information is (are) sufficient to prove whether triangle ABC is congruent to triangle DEF?

I. The measures of angles A and C are equal.

II. The lengths of sides AC and DF are equal.

III. The measures of angles A and D are equal.

A) I is sufficient, but II and III are not.

B) II is sufficient, but I and III are not.

C) III is sufficient, but I and II are not.

B) II and III are sufficient, but I is not.

Answer :

Problem 15 :

77x² + (7j + 11k)x + jk = 0

In the given equation, j and k are positive constants. The product of the solutions to the given equation is ajk, where a is a constant. What is the value of a?

Answer :

Problem 16 :

The number j is 2,400% greater than the number k. The number k is 350% greater than 8. What is the value of j?

Answer :

Problem 17 :

A square is inscribed in a circle with the equation x² + y² – 8x + 10y = 27. What is the area of the square?

Answer :

Question 18 :

The equation below relates distinct positive real numbers a, b and c. Which equation correctly expresses c in terms of a and b?

Answer :

Question 19 :

Triangle ABC is inscribed in a circle with a radius of 85. The length of AC is 170 and the length of BC is 168. What is the value of AB/BC?

Answer :

Question 20 :

For the exponential function f, the value of f(2) is k, where k is a constant. Which of the following equivalent forms of the function f shows the value of k as the coefficient or the base?

A) f(x) = 729(3)^x^{+ 2}

B) f(x) = 6,561(3)^x

C) f(x) = 177,147(3)^{x – 3}

D) f(x) = 59,049(3)^{x – 2}

Answer :