DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 10)

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Problem 1 :

If f(x) = x + 7 and g(x) = 7x, find the value of the following :

4f(2) − g(2)

A) -5

B) 1

C) 22

D) 28

Solution :

Problem 2 :

The y-intercept of the graph of y = -6x - 32 in the xy-plane is (0, y). What is the value of y?

Solution :

Problem 3 :

The graph of the function f, where y = f(x), models the total cost y, in dollars, for a certain video game system and x games. What is the best interpretation of the slope of the graph in this context?

A) Each game costs $25.

B) The video game system costs $100.

C) The video game system costs $25.

D) Each game costs $100.

Solution :

Problem 4 :

y < -4x + 4

Which point (x, y) is a solution to the given inequality in the xy-plane?

A) (2, -1)

B) (2, 1)

C) (0, 5)

D) (-4, 0)

Solution :

Problem 5 :

Figure A and figure B are both regular polygons. The sum of the perimeter of figure A and the perimeter of figure B is 63 inches. The equation 3x + 6y = 63 represents this situation, where x is the number of sides of figure A and y is the number of sides of figure B. Which statement is the best interpretation of 6 in this context?

A) Each side of figure B has a length of 6 inches.

B) The number of sides of figure B is 6.

C) Each side of figure A has a length of 6 inches.

D) The number of sides of figure A is 6.

Solution :

Problem 6 :

Which of the following expressions is equivalent to (sin24°)(cos66°) + (cos24°)(sin66°) ?

A) 2(cos66°)(sin24°)

B) 2(cos66°) + 2(cos24°)

C) (cos66°)² + (sin24°)²

D) (cos66°)² + (cos24°)²

Solution :

Problem 7 :

The cost of renting a carpet cleaner is $52 for the first
day and $26 for each additional day. Which of the following functions gives the cost C(d), in dollars, of renting the carpet cleaner for d days, where d is a positive integer?

A) C(d) = 26d + 26

B) C(d) = 26d + 52

C) C(d) = 52d - 26

D) C(d) = 52d + 78

Solution :

Problem 8 :

An investment account was opened with an initial value of $890. The value of the account doubled every 10 years. Which equation represents the value of the account M(t), in dollars, t years after the account was opened?

A) M(t) = 890(1/2)^t/10

B) M(t) = 890(1/10)^t/2

C) M(t) = 890(2)^t/10

D) M(t) = 890(10)^t/2

Solution :

Problem 9 :

For the linear function f, the table shows three values of x and their corresponding values of f(x). If h(x) = f(x) - 13, which equation defines h?

A) h(x) = 5x − 4

B) h(x) = 5x + 7

C) h(x) = 5x + 9

D) h(x) = 5x + 20

Solution :

Problem 10 :

The linear function g is defined by g(x) = b - 15x, where b is a constant. If g(c + 7) = c/4, where c is a constant, which of the following expressions represents the value of b?

A) 15c/4

B) 19c/4 + 7

C) 61c/4 + 105

D) 15c + 105

Solution :

Problem 11 :

If a/2b = 5, what is the value of 15b/2a?

A) 2/3

B) 3/4

C) 7/2

D) 15/2

Solution :

Problem 12 :

Which of the following is equal to a^1/2/a^-1/3?

A) ⁶√a

B) √6⁵

C) ⁶√a⁵

D) ⁵√a⁶

Solution :

Problem 13 :

The equation 3x³ – 5x + 5 = (3x² + 3x – 2)(x – 1) + a is true for all values of x, where a is a constant. What is the value of a?

A) 3

B) 5

C) 7

D) 8

Solution :

Problem 14 :

A pharmaceutical company receives a monthly salary of $3000 plus a commission of k percent of his sales. If the salesperson's monthly wage is $7200, what are his sales in terms of k?

A) 7200k

B) 4200k

C) 4200/k

D) 420000/k

Solution :

Problem 15 :

On a trip downtown, Peter drove his car at an average speed of 50 miles per hour. On the return trip due to bad weather, he drove his car at an average rate of 30 miles per hour and the return trip took 1 hour longer. How much time did he spend on the returning trip?

A) 1.5 hours

B) 2 hours

3) 2.5 hours

D) 3 hours

Solution :

Problem 16 :

If a = x² - 5x + 2 and b = 3x³ + 4x² - 6, what is (3a - b) in terms of x?

A) 4x² - 15x + 12

B) -3x³ - x² - 15x + 12

C) -3x³ - x² - 15x

D) -3x³ + 7x² - 15x + 12

Solution :

Problem 17 :

In the xy-plane above, line l has slope -5/4. What is the area of the triangle bounded by line l, the x-axis and the y-axis?

A) 5

B) 8

C) 10

D) 16

Solution :

Problem 18 :

The price of a textbook this year is 20% greater than the price last year. If this year's price is p, what was last year's price in terms of p?

Solution :

Problem 19 :

y = x² - 2x - 3

A parabola in the xy-plane is given by the equation above. Which of the following equivalent forms of the equation displays the coordinates of the vertex of the parabola as constants or coefficients?

A) y = (x - 1)² - 4

B) y = (x - 1)² - 2

C) y = (x - 3)(x + 1)

D) y + 3 = x(x + 2)

Solution :