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.
16. Correct answer: (C)
The line l that has a positive slope
Line l passes through (0, 0)
Line k is perpendicular to l
The statement that is true for line k
Topic(s): Coordinate geometry
If k is perpendicular to l then the product of their slopes is –1.
Since l has a positive slope, it means that k must have a negative slope.
Answer: (C) line k has a negative slope.
17. Correct answer: (A)
The value of x
Topic(s): Symbol problems
Answer: (A) 4
18. Correct answer: (A)
One shirt costs x dollars
Each additional shirt costs z dollars less than the first shirt
The expression that represents the cost for n shirts
Try to detect the pattern:
1 shirt → x
2 shirts → x +1(x – z)
3 shirts → x +2(x – z)
n shirts → x + (n – 1) (x – z)
Answer: (A) x + (n – 1) (x – z)
19. Correct answer: (A)
QR is the arc of a circle with center P
Length of arc QR is
Area of sector PQR
Topic(s): Circles, angles
Formula of circumference of circle:
Angle QPR is 30º. The sum of angles around a point is 360º.
This means that the arc QR is of the circumference of the circle =
Given Arc QR =
Area of sector PQR is of the area of the circle.
Formula of area of circle:
Substitute r = 36
20. Correct answer: (E)
75 more women than men enrolled
n men enrolled
In terms of n, the percent of those enrolled are men
Let n = men
n + 75 = women
Total = n + n + 75
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