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

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: 1.2

Given: a Δ b = a + 3b a □ b = a + 4b

4 Δ (5y) = (5y) □ 4

To find:
The value for y

Solution: Topic(s): Symbol problems

Given a Δ b = a + 3b 4 Δ (5y) = 4 + 3(5y) = 4 + 15y

Given a □ b = a + 4b (5y) □ 4 = 5y + 4(4) = 5y + 16

Equating the two expressions

4 + 15y = 5y + 16 ⇒ 10y = 12 ⇒ y = 1.2

Answer: 1.2

17. Correct answer: 1

Given:
The graph x = y 2 – 4 intersects the line l at (0, p) and (5, t)

To find:
The greatest possible value of the slope of line l

Solution: Topic(s): Coordinate geometry, difference of two squares

To get the values of p for the points (0,p), substitute x = 0 for the graph x = y^{2} – 4.

y^{2} – 4 = 0 (difference of two squares)
(y – 2)(y + 2) = 0 y = ± 2

The possible points are A(0, 2) and A 1(0, –2)

To get the values of t for the points (5,t), substitute x = 5 for the graph x = y^{2} – 4.
5 = y^{2} – 4

y^{2} – 9 = 0 (difference of two squares)
(y – 3)(y + 3) = 0 y = ± 3

The possible points are B(5, 3) and B 1(5, –3)

Answer: 1

18. Correct answer: 18

Given:
She goes to work at 45 mph
She returns home along the same route at 30 mph
Total among of time spent traveling is 1 hour

To find:
The number of miles she drove to work

Solution: Topic(s): Distance word problem

This is a distance word problem . Use the rtd table.

Let t = time to go to work

r

t

d

to work

45

t

45 × t

from work

30

1 – t

30(1 – t)

Distance to work = distance from work

45t = 30(1 – t)
45t = 30 – 30t 75t = 30

Distance to work =

Answer: 18

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