Comprehensive Overview of the Preliminary
SAT/National Merit Scholarship Qualifying Test
(PSAT/NMSQT) 2024 2025 latest (UPDATED EXAMS)
Math: Includes algebra, geometry, and data analysis.
Reading: Focuses on reading comprehension and analysis of various passages.
Writing and Language: Assesses grammar, vocabulary, and editing skills.
1.Math
a babysitter earns $8 an hour for babysitting 2 children and an additional $3 tip when both
children are put to bed on time, what expression could be used to determine how much the
babysitter earned?
8x+3, where x is the number of hours
3(x+y) = y
if (x,y) is a solution to the equation above and y does't equal zero, what is the ratio x/y?
-2/3
1/2x-1/4y = 10
1/8x- 1/8y = 19
which ordered pair (x,y) satisfies the system of equations above?
(-112, -264)
,In a certain game, a player can solve easy or hard puzzles. A player earns 30 points for solving
an easy puzzle and 60 points for solving a hard puzzle. Tina solved a total of 50 puzzles playing
this game, earning 1,950 points in all. How many hard puzzles did Tina solve?
15
2x^2 + 7x - 15 = 0
if r and s are two solutions of the equation above and r > s, which of the following is the value
of r-s?
13/2
To cut the lawn, Allen charges a fee of $15 for his equipment and $8.50 per hour spent cutting a
lawn. Taylor charges a fee of $12 for his equipment and $9.25 per hour spent cutting a lawn. if x
represents the number of hours spent cutting a lawn, what are all the values of x for which
Taylor's total charge is greater than Allen's total charge?
X >4
n = 456 - 3T
The equation above is used to model the relationship between the number of cups, n, of hot
chocolate sold per day in a coffee shop and the average daily temperature, T, in degrees
Fahrenheit. According to the model, what is the meaning of the 3 in the equation?
For every decrease of 1 degree F. three more cups of hot chocolate will be sold.
A truck enters a stretch of road that drops 4 meters in elevation for every 100 meters along the
length of the road. The road is at 1,300 meters elevation where the truck entered, and the truck
is traveling at 16 meters per second along the road. What is the elevation of the road, in
meters, at the point where the truck passes t seconds after entering the road?
,1,300 - .04t
if f(x-1) = 2x + 3 for all the values of x, what is the value of f(-3) ?
-1
which of the following is equivalent to (s-t) ?
s^2/t - s
p(x) = 3(x^2 + 10x + 5) - 5(x-k)
in the polynomial p(x) defined above, k is a constant. if p(x) is divisible by x, what is the value of
k?
-3
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In the xy-plane, if the parabola with equation y = ax^2 + bx + c, where a, b, and c are constants,
passes through the point (-1,1), which of the following must be true?
a-b=1
for what value of h is 24 = h/10 - 6?
300
what is the value of a if (2a + 3) - (4a -8) = 7 ?
, 2
If x is not equal to zero, what is the value of 4(3x)^2 / (2x)^2 ?
9
if x-2 is a factor of x^2 - bx + b, where b is a constant, what is the value of b?
4
Tyra subscribes to an online gaming service that charges a monthly fee of $5.00 and $0.25 per
hour for time spent playing premium games. which of the following functions gives Tyra's cost,
in dollars, for a month in which she spends x hours playing premium games?
C(x) = 5 + .25x
A grocery store sells a brand of juice in individual bottles and in packs of 6 bottles. On a certain
day, the store sold a total of 281 bottles of the brand of juice, of which 29 were sold as the
individual bottles. which equation shows the number of packs of bottles, p, sold that day?
P = 281-29/6
A rectangle has a perimeter P, length l and with w. which of the following represents l in terms
of P and w?
l = p-2w/2
which ordered pair (x,y) satisfies the system of equations shown above?
