1. PSAT Review #3
*Questions adapted from the released Fall 2017 College Board PSAT/NMSQT

2. B is the correct answer #1
432( 1.027) ( 1.027) 1 =432( 1.027) 5−1 =432( 1.027) 4

3. #2-4

4. #2
Write the equations that model the growth for the two types of trees, set equal to each other, and solve.
ℎ=0.49𝑡+82.50
ℎ=0.30𝑡+85.35
0.49𝑡+82.50= 0.30𝑡+85.35
0.19𝑡= 2.85
t=15

5. #3
Solve ℎ=𝑔𝑡+𝑏 for 𝑔:
ℎ=𝑔𝑡+𝑏
ℎ−𝑏=𝑔𝑡
ℎ−𝑏 𝑡 =𝑔
𝑔= ℎ−𝑏 𝑡

6. #4
The problem tells us: The growth factor for a species is the factor by which the diameter of a tree trunk of the species, measured in inches at 5 feet above the ground level, is multiplied to determine the age of the tree.
Using the table, we see that the growth factor for the silver maple is 3, therefore, the function that determines age is
𝑎 𝑑 =3𝑑.

7. #5 Algebraically, use substitution to solve: 𝑦=− 𝑥 2 +10𝑥−27 𝑦=𝑥−9
𝑥−9=− 𝑥 2 +10𝑥−27
𝑥 2 −9𝑥+18=0
𝑥−6 𝑥−3 =0
𝑥=6 𝑜𝑟 𝑥=3
Plug these values in to either equation and solve for y to find the y – coordinates.
6, −3 𝑜𝑟 3, −6
Graphically, solve both equations for y and type into graphing calculator. Use the intersect feature to find the points of intersection.

8. #6
First, set up a proportion to determine the distance between the two cities in miles: 𝑖𝑛 25 𝑚 = 𝑖𝑛 𝑥 𝑚 Cross multiply and solve: 𝑥= 𝑥=325 miles
Next, use unit conversion to convert 325 miles to kilometers:
325 𝑚𝑖𝑙𝑒𝑠 1 ∗ 1 𝑘𝑚 𝑚 = 𝑘𝑚

9. #7 Solve the quadratic equation by factoring: 𝑡−3 𝑡 −12 =0
𝑡−3 𝑡 −12 =0
𝑡−3=0 𝑜𝑟 𝑡−12=0
t=3 𝑜𝑟 𝑡=12
To find the positive difference subtract the smaller number from the larger number: = 9

10. #8
11X + 8Y ≤ 178
11(13) + 8Y ≤ 178
Y ≤ 178
8Y ≤ 35
Y ≤
Round down to the next highest whole number: Y = 4
The store manager can buy at most 4 units of Product Y.

11. #9
𝑥 𝑦 = 3 2 = 3𝑧 2𝑧 Let z be the factor of the ratio 3:2 that has been cancelled out.
Then 3𝑧+2𝑧=100, or 5z = 100, making z = 20.
x = 3z = 3(20) = 60
y = 2z = 2(20) = x = 60

12. #10 Calculate the percent of votes for Candidate A: 100 150 =66.667%
Calculate the percent of votes for Candidate B: =33.333%
Subtract the percentages: % % = %.
Round to tenths 33.3%.