How to Solve Challenging Math Problems in SAT

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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 :