SAT Practice Test 5, Section 7: Questions 16  20
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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16. Correct answer (B)
Given:
The figure
Diane travels from A to B,from B to C and from C to D
AB = 16
BC = 15
CD = 4
To find:
How much shorter is the trip if she travels directly from A to D
Solution:
Topic(s): Pythagoras theorem
The direct path from A to D is the hypotenuse of the right triangle ADE.
We can use Pythagoras theorem to get the length of AD.
Length of AE = 16 + 4 = 20
Answer (B) 25
17. Correct answer: (D)
Given:
One circle has a radius of
Another circle has a radius of 1
To find:
Ratio of the area of the larger circle to the area of the smaller circle
Solution:
Topic(s): Area of circle
Area of larger circle = π(1)^{2} = π
Area of smaller circle =
Ratio of area of larger circle to the area of smaller circle =
Answer: (D) 4:1
18. Correct answer: (B)
Given:
The sum of consecutive integers from –22 to x, inclusive is 72
To find:
The value of x
Solution:
Topic(s): Consecutive integer problems
The consecutive integers for –22 to x inclusive are
22, 21, 20, …, 1, 0, 1, …,22, 23,.., x
Sum of consecutive numbers from –22 to 22 is 0
We can then add from 23 until we get the sum of 72
23 + 24 + 25 = 72
Answer: (B) 25
19. Correct answer: (A)
Given:
k, n, x and y are positive numbers
To find:
The value of in terms of n and k
Solution:
Topic(s): Exponents
Answer: (A)
20. Correct answer: (E)
Given:
f(x) = x^{2} – 4x
g(x) = f(x + h) + k
To find:
The value of hk
Solution:
This is a graph translation question.
From the graph, we see that the function g(x) is the function f(x) moved 3 units to the right and 2 units down.
Moving 3 units to the right means h = – 3 and moving 2 units down means k = – 2 i.e. g(x) = f(x – 3) – 2
So, hk = (3)(2) = 6
Answer: (E) 6
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