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.
16. Correct answer: (E)
y + z
Topic(s): Supplementary angles
a = 180 –115 = 65 (supplementary angles)
z = 65 + b (exterior angle of a triangle = sum of opposite interior angles)
b = 180 – y (supplementary angles)
z = 65 + 180 – y
y + z = 180 + 65 = 245
Answer: (E) 245
17. Correct answer: (D)
The sum of 3 consecutive odd integers = 111
n is the least of the 3 integers
The equation for n
Topic(s): Consecutive integer problems
n + n + 2 + n + 4 = 111
3n + 6 = 111
Answer: (D) 3n + 6 = 111
18. Correct answer: (A)
The figure, which shows part of a circle whose circumference is 45
The arc of length 2 and length b continue to alternate around the entire circle so that there are 18 arcs of each length
The degree measure of each of the arcs of length b
Topic(s): Arc of circle, proportional word problem
18 arcs of each length 2 and b = 45
The length of the arc is proportional to the degree measure.
If 45 then 360º, if then how many degrees?
Answer: (A) 4º
19. Correct answer: (C)
The cost of maintenance increases by 10% each year
Andrew paid $300 for maintenance this year
The cost c for maintenance on Andrew’s automobile n years from now is given by the function: c(n) = 300xn
The value of x
After one year, Andrew would need to pay
300 + 10% × 300
= 300 + 300(0.1)
= 300(1 + 0.1)
After two years, Andrew would need to pay
300(1.1) + 10% × 300(1.1)
= 300(1.1) + 300(1.1)(0.1)
= 300(1.1)(1 + 1.0)
= 300 (1.1)(1.1)
After n years, Andrew would need to pay
Equating with the given function:
c(n) = 300xn = 300(1.1)n
Therefore, x = 1.1
Answer: (C) 1.1
20. Correct answer: (B)
The 5 line segments are congruent
The ratio of the length of to the length of
Topic(s): Rhombus, Pythagorean theorem
This implies that ABCD is a rhombus.
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