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

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This is for SAT in Jan 2016 or before.

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

It would be best that you go through the SAT practice test questions in the Study Guide first and then look at the worked solutions for the questions that you might need assistance in. Due to copyright issues, we are not able to reproduce the questions, but we hope that the worked solutions will be helpful.

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

Let A be the point (-2, -7), O be the point (3, -7) and B be the other endpoint of the diameter.

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