SAT Practice Test 3, Section 8: Questions 6 - 10

The following are worked solutions for the questions in the math sections of the SAT Practice Tests found in the Official SAT Study Guide.

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6. Correct answer: (B)

Given:
The graph y = g(x)
g(k) = 1

To find:
A possible value of k

Solution:
From the graph, we can see that g(k) = 1, when -1 ≤ k ≤ 0

The only choice of answer, which is between – 1 and 0 (inclusive) is
(B) – 0.5

Answer: (B) –0.5

7. Correct answer: (A)

Given:
2^a × 2^b × 2^c = 64 , where a, b and c are different positive integers

To find:
2^a + 2^b + 2^c

Solution:
Topic(s): Exponents

When we multiply exponents with the same base we can add the exponents.
We can also rewrite 64 as 2⁶.

The equation 2^a × 2^b × 2^c = 64 can be rewritten as 2^a+b+c = 2⁶

With the bases the same, we can equate the exponents
a + b + c = 6

Given that a, b and c are different positive integers.

We can assign a = 1, b = 2 and c = 3.

Then,
2^a + 2^b + 2^c = 2¹ + 2² + 2³ = 2 + 4 + 8 = 14

Answer: (A) 14

8. Correct answer: (E)

Given:
The center of a circle is (3, -7)
One endpoint of a diameter of the circle is (-2, -7)

To find:
Coordinates of the other endpoint of the diameter

Solution:
Topic(s): Coordinate geometry, diameter of circle

Length of AO = 3 – (– 2) = 3 + 2 = 5

Length of AO = length of OB = 5 (both are radii of the circle)

The x-coordinate of B is 5 + 3 = 8. (add 5 units to the x-coordinate of O)

The y-coordinate of B is –7 (in order to form a straight line from A and O)

So, the coordinates of B is (8, -7)

Answer: (E) (8, -7)

9. Correct answer: (D)

Given:
To go for a certain ride, a child must be between 30 inches and 50 inches tall

To find:
The expression that shows the requirement for the child’s height h

Solution:
Topic(s): Absolute value

The absolute value bars can be rewritten as inequalities.

We, then, select the answer that gives the range between 30 and 50.

Answer: (D)

10. Correct answer: (B)

Given:
A right circular cylinder with radius 5 and height 4 and volume v

To find:
The volume of a right circular cylinder with radius 5 and height 8, in terms of v

Solution:
Topic(s): Volume of cylinder

Volume of cylinder:
v = πr²h

The radius of the second cylinder = the radius of the first cylinder

The height of the second cylinder = 2 × the height of the first cylinder

So, volume of second cylinder = 2 × the volume of the first cylinder = 2v

Answer: (B) 2v

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