Digital SAT Math Practice Test with Answers (Part - 4)

Question 1 :

Point O is the center of the circle above, and the measure of ∠OAB is 30°. If the length of OC is 18, what is the length of arc AB?

A)  9π

B)  12π

C)  15π

D)  18π

Answer :

Question 2 :

x² + 20x + y² + 16y = -20

The equation above defines a circle in the xy-plane above. What are the coordinates of the center of the circle?

A)  (-20, -16)

B)  (-10, -8)

C  (10, 8)

D)  (20, 16)

Answer :

Question 3 :

A circle in the xy-plane has its center at (-4, -6). Line k is tangent to this circle at the point (-7, -7). What is the slope of line k?

Answer :

Question 4 :

Two identitcal rectangular prisms each have a height of 90 centimeters (cm). The base of each prism is a square, and the surface area of each prism is K cm² . If the prisms are glued together along a square base, the resulting prism has a surface area of (⁹²⁄₄₇)K cm². What is the side length, in cm, of each square base?

A)  4

B)  8

C)  9

D)  16

Answer :

Question 5 :

210 is p% greater than 30. What is the value of p?

Answer :

Question 6 :

The area of rectangle A is 50 m² and the rectangle B is 450 m². Rectangle A has a perimeter of 30 m. If both the rectangles are similar, what is the perimeter of rectangle B?

Answer :

Question 7 :

The solutions to x² + 6x + 7 = 0 are r and s, where r < s. The solutions to x² + 8x + 8 = 0 are t and u, where t < u. The solutions to x² + 14x + c = 0, where c is a constant, are r + t and s + u. What is the value of c?

Answer :

Question 8 :

Function f is a quadratic function. The graph of y = f(x) in the xy-plane has a vertex at (6, 10), contains the point (5, 8), and has a y-intercept at (0, a). The graph of g(x) = 4 ⋅ f(x) has a y-intercept at (0, b). What is the positive difference between a and b?

Answer :

Question 9 :

In the figure above, the radius of the circle is 12. If the length of chord AB is 18, what is the distance between the chord and the diameter?

A)  2√10

B)  3√7

C)  4√5

D)  6√2

Answer :

Question 10 :

0.36x² + 0.63x + 1.17

The given expression can be written as a(4x² + 7x +13),  where a is a constant. What is the value of a?

Answer :

Question 11 :

In the figure above, ΔABC and ΔDBE are right triangles. If AC = 12, BC = 15 and DE = 8, what is the length of BE?

A)  8.5

B)  9

C)  9.5

D)  10

Answer :

Question 12 :

The line y = kx + 4, where k is a constant, is graphed in the xy-plane. If the line contains the point (c, d), where c ≠ 0 and d ≠ 0, what is the slope of the line in terms of c and d?

A)  (d - 4)/c

B)  (c - 4)/d

C)  (4 - d)/c

D)  (4 - c)/d

Answer :

Question 13 :

In the expression 3(2x² + px + 8) – 16x(p + 4), p is a constant. If this expression is equivalent to the expression 6x² – 155x + 24. What is the value of p?

A)  -3

B)  7

C)  13

D)  155

Answer :

Question 14 :

What is the solution set of the equation above?

A)  {-1}

B)  {5}

C)  {-1, 5}

D)  {0, -1, 5}

Answer :

Question 15 :

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?

Answer :

Question 16 :

In the given figure, O is the center of the circle. What is the area of the shaded region?

A)  144 - 8π

B)  72 - 18π

C)  149 - 7π

D)  92 - 4π

Answer :

Question 17 :

The expression 6x⁴ + 17x² + 7 can be written as (3x² + a)(2x² + b), where a and b are positive integers, or as (3x² + c)(2x² + d), where c and d are positive nonintegers. What is the value of a + c?

Answer :

Question 18 :

A data set of 27 different numbers has a a mean of 33 and a median of 33. A new data set is created by adding 7 to each number in the original data set that is greater than the median and subtracting 7 from each number in the original data set that is less than the median. Which of the following measures does NOT have the same value in both the original and new data sets?

A)  Median

B)  Mean

C)  Sum of the numbers

D)  Standard deviation

Answer :

Question 19 :

What is the largest possible value of the constant c such that x + c is a factor of 3x³ + 15x² – 378x?

Solution :

Question 20 :

(3x + p)(5x² – 45)(2x² – 16x + 6p) = 0

In the given equation, p is a constant. The sum of the solutions to the equation is 20/3. What is the value of p?

Answer :

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