OFFICIAL TEST 1 Ms Ánh Dạy SAT 1600 MS TUYET

OFFICIAL TEST 1 – MODULE 1

1.
For groups of 18 or more people, a museum charges $42 per person for the first
18 people and $28 for each additional person. Which function f gives the total
charge, in dollars, for a tour group with n people, where n ≥ 18 ?
A) f(n) = 28n + 756
B) f(n) = 28n + 252
C) f(n) = 42n + 504
D) f(n) = 70n + 756

2.

Data set A: 130, 136, 136, 185

Data set B: 130, 136, 136, 185, m

The lists give the values in data sets A and B. Which statement correctly
compares between the data set X and the data set Y ?

I. The mean and median of data set A are less than data set B if m > 185.

II. The standard deviation of data set B is equal data set A if m ≤ 185.

A) I

B) II

C) Both

D) Neither
OFFICIAL TEST 1 Ms Ánh Dạy SAT 1600 MS TUYET

3.

Triangle 𝑨𝑩𝑪 and triangle 𝑫𝑬𝑭 are similar triangles, where ̅̅̅̅𝑨𝑩 and ̅̅̅̅
𝑫𝑬 are
corresponding sides. If 𝑫𝑬 = 𝟐𝑨𝑩 and the perimeter of triangle 𝑨𝑩𝑪 is 20, what
is the perimeter of triangle 𝑫𝑬𝑭 ?

A) 10
B) 40
C) 80
D) 120

4.

A circle in the 𝑥𝑦-plane has equation (𝒙 + 𝟑)𝟐 + (𝒚 − 𝟏)𝟐 = 𝟐𝟓. Which of the
following points does NOT lie in the interior of the circle ?

A) (–7, 3)
B) (–3, 1)
C) (0, 0)
D) (3, 2)

5.
A special camera is used for underwater ocean research. When the camera is at a
depth of 33.8 fathoms, what is the camera's depth in feet ? (1 fathom = 6 feet)

6.
𝒉(𝒙) = 𝟐(𝒙 − 𝟒)𝟐 − 𝟑𝟐
The quadratic function h is defined as shown. In the xy-plane, the graph of 𝒚 = 𝒉(𝒙)
intersects the x-axis at the points (0, 0) and (t, 0) , where t is a constant. What is the
value of t ?
OFFICIAL TEST 1 Ms Ánh Dạy SAT 1600 MS TUYET

A) 1
B) 2
C) 4
D) 8

7.

Which of the following expressions is(are) a factor of 𝟒𝒙𝟐 + 𝟐𝟎𝒙 − 𝟕𝟓 ?

I. x – 3
II. 2x – 5
A) I only
B) II only
C) I and II
D) Neither I nor II

8.

The scatterplot above shows the federal-mandated minimum wage every 10

years between 1940 and 2010. A line of best fit is shown, and its equation is
y = 0.096x − 0.488. What does the line of best fit predict about the increase
in the minimum wage over the 70-year period ?
OFFICIAL TEST 1 Ms Ánh Dạy SAT 1600 MS TUYET

A) Each year between 1940 and 2010, the average increase in minimum wage
was 0.096 dollars.
B) Each year between 1940 and 2010, the average increase in minimum wage
was 0.49 dollars.
C) Every 10 years between 1940 and 2010, the average increase in minimum
wage was 0.096 dollars.
D) Every 10 years between 1940 and 2010, the average increase in minimum
wage was 0.488 dollars.

9.

In the xy-plane, the graph of line 𝑦 = mx + c intersects the curve of the exponential
function f(x) = 2𝑥 at points 𝑃(a, b) and 𝑄(a – 5, d) and a, b, c, d are a constant. If
15
b–d= . What is the value of 𝑚 ?
32

10.
𝟏
=𝟒
𝒙𝟐 + 𝟏𝟎𝒙 + 𝟐𝟓

If x is a solution to the given equation, which of the following is a possible value

of x + 5 ?

1
A)
2
5
B)
2
9
C)
2
11
D)
2
OFFICIAL TEST 1 Ms Ánh Dạy SAT 1600 MS TUYET

11.

𝟓 𝟔
√𝟕𝟎𝒏( √𝟕𝟎𝒏)𝟐
For what value of x is the given expression equivalent to (𝟕𝟎𝒏)𝟑𝟎𝒙 , where n > 1 ?

12.
𝟐 𝟑 𝒓𝒙 + 𝒕
+ =
𝒙 − 𝟐 𝒙 + 𝟓 (𝒙 − 𝟐)(𝒙 + 𝟓)
The equation above is true for all x > 2 , where r and t are positive constants.
What is the value of rt ?

A) – 20
B) 15
C) 20
D) 60

13.

The glass pictured above can hold a maximum volume of 473 cubic centimeters,
which is approximately 16 fluid ounces. What is the value of 𝒌, in centimeters ?
OFFICIAL TEST 1 Ms Ánh Dạy SAT 1600 MS TUYET

A) 2.52
B) 7.67
C) 7.79
D) 10.11

14.
For the function f, if f(3x) = 6x − 16 for all values of x, what is the slope of
g(x) = f(x − 36) ?

A) 6
1
B)
2
C) 1
D) 2

15.
Energy per Gram of Typical Macronutrients
Macronutrient Food calories Kilojoules
Protein 4.0 16.7
Fat 9.0 37.7
Carbohydrate 4.0 16.7
The table above gives the typical amounts of energy per gram, expressed in both
food calories and kilojoules, of the three macronutrients in food. If the 180 food
calories in a granola bar come entirely from p grams of protein, f grams of fat, and
c grams of carbohydrate, which of the following expresses f in terms of p and c ?
OFFICIAL TEST 1 Ms Ánh Dạy SAT 1600 MS TUYET

4
A) f = 20 + (p + c)
9
4
B) f = 20 − 9 (p + c)
4
C) f = 20 − 9 (p − c)
9
D) f = 20 + (p + c)
4

16.

̂ is 𝟓𝝅, and 𝒙 = 𝟏𝟎𝟎. What

The circle above has center O, the length of arc 𝐴𝐷𝐶
̂?
is the length of arc 𝑨𝑩𝑪

A) 9𝜋
B) 13𝜋
C) 18𝜋
13
D) 𝜋
12

17.

If s and t are two roots of 𝒙𝟐 − 𝟕𝒙 + 𝟐𝒄 = 𝟎 the quadratic equation whose roots

are s + 1 and t + 1 is
OFFICIAL TEST 1 Ms Ánh Dạy SAT 1600 MS TUYET

A) 𝑥 2 − 10𝑥 + 2𝑐 + 2 = 0
B) 𝑥 2 − 10𝑥 + 2𝑐 + 8 = 0
C) 𝑥 2 − 9𝑥 + 2𝑐 + 2 = 0
D) 𝑥 2 − 9𝑥 + 2𝑐 + 8 = 0

18.
𝒇(𝒙) = 𝟗, 𝟎𝟎𝟎(𝟎. 𝟔𝟔)𝒙
The given function 𝒇 models the number of advertisements a company sent to its
clients each year, where 𝒙 represents the number of years since 1997,
and 𝟎 ≤ 𝒙 ≤ 𝟓. If 𝒚 = 𝒇(𝒙) is graphed in the xy-plane, which of the following
is the best interpretation of the y-intercept of the graph in this context ?

A) The minimum estimated number of advertisements the company sent to its

clients during the 𝟓 years was 1,708.
B) The minimum estimated number of advertisements the company sent to its
clients during the 𝟓 years was 9,000.
C) The estimated number of advertisements the company sent to its clients in
1997 was 1,708.
D) The estimated number of advertisements the company sent to its clients in
1997 was 9,000.

19.
(x – 18) is factor of g(x), g(x) cross x-axis at –2, g(x) has vertex point (m, n).
What is value of m ?

20.
There are 800 students at a school. Each student has either a school dinner or a
packed lunch. 31% of the students have packed lunches. 55% of the students are
boys. 60% of the boys have school dinners. How many girls have packed lunches ?
OFFICIAL TEST 1 Ms Ánh Dạy SAT 1600 MS TUYET

21.

Line 𝑣 in the xy-plane is represented by the equation 7x – 2y = 9. The slope of line

v is half of the slope of line w and line 𝑥 is perpendicular to line 𝑣. Line w and line
x intersect at (2, b), b is a positive constant integer. Which of the following
equations could represent line 𝑤 and line 𝑥 ?

A) 14x – 2y = 27 ; 4x + 14y = 15
B) 14x – 4y = 24 ; 2x – 7y = –3
C) 28𝑥 – 4𝑦 = 32 ; 6𝑥 + 21y = 138
D) 28x – 4y = 48 ; 6x – 21y = –30
22.

In the 𝑥𝑦-plane above, points 𝑃, 𝑄, 𝑇, and 𝑹(a, b), lie on the circle with center 𝑂.
The area of the sector OQR is 7.5𝝅 and measures of angles 𝑃𝑂𝑄 is 𝟒𝟓° . What is
the value of b ?
1
A)
2
√3
B)
2
C) 3√3
D) 3
OFFICIAL TEST 1 Ms Ánh Dạy SAT 1600 MS TUYET

OFFICIAL TEST 1 – MODULE 2

1.

The volume of a certain right circular cylinder is 16. A larger right circular
cylinder has radius 25 percent greater and height 50 percent greater than the
radius and height, respectively, of the smaller cylinder. What is the volume of the
larger cylinder ?
2.
𝟏𝟑
Which expression is equivalent to 𝒂𝟏𝟓 , where 𝒂 > 𝟎 ?

15
A) √𝑎13
165
B) √𝑎143
143
C) √𝑎165
13
D) √𝑎15

3.

In the figure above, O is the center of the circle with radius 1, and line CD is
tangent to the circle at A. If the measure of ‫ ے‬AOC is 30° and the length of ̅̅̅̅
𝑪𝑫
̅̅̅̅̅ ?
is 3, what is the length of 𝑩𝑫
A) 2.62
B) 2.93
C) 3.14
D) 3.42
OFFICIAL TEST 1 Ms Ánh Dạy SAT 1600 MS TUYET

4.

In a radio station a writer is paid $475 every month and $0.25 per a song
additionally. If the writer gave n songs to the radio station, 40% of the total
money that he earned can be expressed as ⸏

A) 0.2(n + 0.2) + 475

B) 0.4(n + 0.2) + 475
C) 0.4(0.25n + 475)
D) (0.4)0.25n + 475

5.

If 𝒂𝟒 = √√𝒃𝟑 , where 𝒃 > 𝟎, what is the value of 𝒂 in terms of 𝒃 ?

3
A) 𝑏4
3
B) 𝑏2
5
C) 𝑏 12
3
D) 𝑏 16

6.

What is the first term of the geometric sequence whose the fourth terms, the fifth
term and the sixth term are 486, 162, and 54 respectively ?

A) 39366
B) 13112
C) 4374
D) 1458
OFFICIAL TEST 1 Ms Ánh Dạy SAT 1600 MS TUYET

7.

P(x) = (x + 3)Q(x) + R

The equation above shows when P(x) is divided by (x + 3), the remainder is R, where
Q(x) is the quotient. If P(x) = 5𝒙𝟐 − 3x + 4, what is the value of R ?

8.

The figure above is the graph of which of the following ?

A) 𝑦 = |𝑥 − 2| − 1
B) 𝑦 = |𝑥 − 1| − 2
C) 𝑦 = |𝑥 + 2| − 1
D) 𝑦 = |𝑥 + 1| − 2

9.
A cell phone provider charges $0.40 for the first minute of a call and $0.20 for each
additional minute or each additional portion of a minute. The cost of a call, C, is
given by the model C = 0.40 + 0.20 ⎡t⎤ where t is the number of minutes over the
first minute and ⎡t⎤ is the least integer greater than or equal to t. What is the cost of
a 12.25-minute call ?
A) $2.60
B) $2.65
C) $2.80
D) $2.85
OFFICIAL TEST 1 Ms Ánh Dạy SAT 1600 MS TUYET

10.
t, 8, 5, 4, 12, 8
In the list above, t is an integer. For the list, if the mean is equal to the median
and the range is less than 10, what is the value of t ?

11.

𝒙+𝟗 𝒙+𝟗
If = , the value of x + 9 is between which of the following pairs of values ?
𝟑 𝟏𝟓

A) −7 and −3
B) –1 and 1
C) 2 and 9
D) 8 and 15

12.
𝟏
𝟔𝟖𝒙𝟐 −
(𝒂 + 𝒃 )𝒙 + 𝒂𝒃 = 𝟎
𝟔𝟖
In the given equation, a and b are positive constants. The sum of the solutions to
the given equation is k(a + b) , where k is a constant. What is the value of k ?

A) 1
B) 4624
1
C)
4624
1
D)
68
OFFICIAL TEST 1 Ms Ánh Dạy SAT 1600 MS TUYET

13.

Seven integers are arranged from least to greatest. If the median is 9 and the only
mode is 7, what is the least possible range for the 7 numbers

A) 4
B) 5
C) 6
D) 8

14.

Immanuel purchased a certain rare coin on January 1. The function

𝒇(𝒙) = 𝟔𝟓(𝟏. 𝟎𝟑)𝒙 , where 𝟎 ≤ 𝒙 ≤ 𝟏𝟎, gives the predicted value, in dollars, of
the rare coin x years after Immanuel purchased it. What is the best interpretation
of the statement “f(8) is approximately equal to 82” in this context ?

A) When the rare coin's predicted value is approximately 82 dollars, it is 8%

greater than the predicted value, in dollars, on January 1 of the previous year.
B) When the rare coinʼs predicted value is approximately 82 dollars, it is 8
times the predicted value, in dollars, on January 1 of the previous year.
C) From the day Immanuel purchased the rare coin to 8 years after Immanuel
purchased the coin, its predicted value increased by a total of approximately 82
dollars.
D) 8 years after Immanuel purchased the rare coin, its predicted value is
approximately 82 dollars.
OFFICIAL TEST 1 Ms Ánh Dạy SAT 1600 MS TUYET

15.
Alan drives an average of 180 miles each week. His car can travel an average of 45
miles per gallon of gasoline. Alan would like to reduce his weekly expenditure on
gasoline by $5. Assuming gasoline costs $12 per gallon, which equation can Alan
use to determine how many fewer average miles, m, he should drive each week ?
45
A) m = 15
5
5
B) m=5
12
12
C) m = 175
5
4
D) m=5
15

16.
A triangle has sides measuring 4, 4, and 6 inches. What is the measure of its
largest angle ?

A) 82.8°
B) 97.2°
C) 41.4°
D) 120.0°

17.

𝒙 𝒏𝒙
If 𝒚 = 28 and 𝟕𝒚 = 28, what is the value of n ?

18.
Which of the following is NOT a factor of 𝒙𝟓 + 𝒙𝟑 + 𝟐𝒙𝟐 − 𝟏𝟐𝒙 + 𝟖 ?

A) 𝑥−1
B) 𝑥+2
C) 𝑥2 + 4
D) 𝑥−2
OFFICIAL TEST 1 Ms Ánh Dạy SAT 1600 MS TUYET

19.

If 𝒙(𝒙 + 𝟑)(𝟗 − 𝒙 ) > 𝟎, then which of the following is the solution set ?

A) −3 < x < 9
B) x < −3 or 0 < x < 9
C) x>9
D) 9 < x or x < −3

20.

√𝟑 √𝟐
𝒔𝒊𝒏𝜶 = , 𝒄𝒐𝒔𝜷 = 𝟎° < 𝜶 < 𝟑𝟔𝟎°, and 𝟎° < 𝜷 < 𝟑𝟔𝟎°. Which of the
𝟐 𝟐
following can not be 𝜶 + 𝜷 ?

A) 165°
B) 110°
C) 375°
D) 435°

21.

P, Q, R and S are four points on a circle with centre O. Given that PS is a diameter
of the circle and OPQ = 50°, and SPR larger RPQ is 4°. The measure of length
PQ is a. The measure of length SR is b. What is different between a and b ?
OFFICIAL TEST 1 Ms Ánh Dạy SAT 1600 MS TUYET

22.

The cube in Figure has edges of length 4 cm. If point B is the midpoint of the
edge, what is the perimeter of ΔABC ?

A) 11.31
B) 12.94
C) 14.60
D) 15.87