SAT Practice Test 1, Section 9: Questions 11  16
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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11. Correct answer: (B)
Given:
The rectangle ABCD is made up of 7 nonoverlapping rectangles
The 2 smallest rectangles have the same area
Each of the other rectangles has twice the area of the next smaller rectangle
To find:
The area of the shaded rectangle is what fraction of the area of the rectangle ABCD
Solution:
Topic(s): Area of rectangle
Fill up the rectangle, each time reducing the area by half.
Answer: (B)
12. Correct answer: (B)
Given:
2x < y < 0
To find:
The answer that is the greatest value
Solution:
Topic(s): Signed operations
We can choose any values for x and y that is true for the inequality.
2x < y < 0
Choose y = – 1 and x = – 2.
Test each of the answers. Be careful about the signed operations.
(A) –2x = –2 (–2) = 4
(B) – (2x + y) = – (2(–2) + (–1)) = – (–4 + (–1)) = – (–4 – 1)
= – (–5) = 5
(C) 2x = 2(–2) = – 4
(D) 0
(E) –y = –(–1) = 1
The greatest value is (B) 5
Answer: (B) 5
13. Correct answer: (C)
Given:
He delivers
n packages on Monday
4 times as many on Tuesday as on Monday
3 more packages on Wednesday than on Monday
To find:
The average number of packages delivered per day over the 3 days
Solution:
Topic(s): Statistics
Given n = Mon
Then, 4n = Tues
n + 3 = Wed
Answer: (C) 2n + 1
14. Correct answer: (E)
Given:
To find:
The answers that must be true
Solution:
Topic(s): Exponents, difference of two squares, distributive rule
Square both sides of the equation.
Recognize that it is a difference of two squares or use the distributive rule.
Answer: (E)
15. Correct answer: (E)
Given:
The graphs:
y = x^{2}
y = a – x^{2}
PQ = 6
To find:
The value of a
Solution:
Topic(s): Coordinate geometry
The two graphs are symmetrical about the yaxis.
If PQ = 6,then the point Q is units from the yaxis.
This means that the xcoordinate of point Q is 3.
The ycoordinate of Q can be obtained by substituting x = 3 into the equation y = x 2.
y = x^{2} = 3^{2} = 9
Point Q is (3, 9).
Point Q also belongs to the graph y = a – x 2.
Substituting x = 3 and y = 9 into y = a – x 2.
9 = a – 3^{2
}a = 9 + 9 = 18
Answer: (E) 18
16. Correct answer: (D)
Given:
Set X has x members
Set Y has y members
Set Z has all members that are either in set X or set Y with the exception of k common members
To find:
The expression that represents the number of members in set Z
Solution:
Topic(s): Sets
Number of members in set X excluding k is x – k.
Number of members in set Y excluding k is y – k.
Number of members in set Z = x – k + y – k = x + y – 2k
Answer: (D) x + y – 2k
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