EST II – Individual Subject Test
Level 2
Student’s Name
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National ID
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Test Center:
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Subject: Math
Duration: 60 minutes
50 Multiple Choice Questions
Instructions:
-
Place your answer on the answer sheet. Mark only one answer for each of the multiple
choice questions.
-
Avoid guessing. Your answers should reflect your overall understanding of the
subject matter.
-
Calculator is allowed. When a calculator is used, be aware of switching between
radian mode and median mode.
-
Formula sheet is available at the end of the booklet for your reference.
1. What is the distance between the two points 𝐴 2, 5, 7 and B
A.
B.
C.
D.
E.
5.2
7.14
12.77
38.17
51
2. What is the value of 𝑚 if
A.
B.
C.
D.
E.
3, 4, 2 ?
𝑚
𝑚
𝑚
𝑚
𝑚
3𝑚 4
1.01 or 𝑚
1.65
1.01 or 𝑚
1.65
1.01 or 𝑚 1.65
1.01 or 𝑚 1.65
1.01
is a unit vector ?
3. Lorenzo invested $14000 at an annual rate of 3.5%. What will be his balance after 4 years
if the type of compounding is continuous?
A.
B.
C.
D.
E.
$16090.79
$16094.03
$16100.55
$16103.83
$16677.45
4. In triangle 𝐻𝐺𝐹, 𝐹𝐺
length of 𝐹𝐻 ?
A.
B.
C.
D.
E.
11 𝑐𝑚, and 𝐺𝐻
17.29 𝑐𝑚
19 𝑐𝑚
21.88 𝑐𝑚
23.26 𝑐𝑚
26.94 𝑐𝑚
5. What are the solutions of the system:
A.
B.
C.
D.
E.
3; 4
4; 3
4; 3
3; 4
3; 4
2𝑥
and 0.5; 7.5
and 0.5; 7.5
and 7.5; 0.5
and 7.5; 0.5
and 0.5; 7.5
20.5 𝑐𝑚 with 𝑚∠𝐺𝐹𝐻
3𝑥
𝑥 𝑦
44°. What is the
2𝑦 17
?
7 0
2
January 2021
6. Which of the following functions, compared to 𝑔 𝑥
𝑥 , represents a reflection across
the 𝑥-axis, a vertical shift 7 units up, and a vertical compression?
A. 𝑓 𝑥
𝑥
7
B. 𝑓 𝑥
𝑥
3
4
C. 𝑓 𝑥
𝑥
3
4
D. 𝑓 𝑥
E. 𝑓 𝑥
2𝑥
2𝑥
3
3
4
4
7. What are the asymptotes of 𝑓 𝑥
1?
A. Vertical asymptote at 𝑥
and an oblique asymptote at 𝑦
B. Vertical asymptote at 𝑥
and an oblique asymptote at 𝑦
𝑥
C. Vertical asymptote at 𝑥
and a horizontal asymptote at 𝑦
1
D. Vertical asymptote at 𝑥
and a horizontal asymptote at 𝑦
and a horizontal asymptote at 𝑦
E. Vertical asymptote at 𝑥
8. What is the solution of 400
A.
B.
C.
D.
E.
𝑡
𝑡
𝑡
𝑡
𝑡
6
.
ℎ
ℎ
ℎ
ℎ
ℎ
1
1
1300 ?
146.9
132
1.32
0.66
1.84
9. What is the inverse function of ℎ 𝑥
A.
B.
C.
D.
E.
𝑥
𝑥
𝑥
𝑥
𝑥
𝑥
𝑒
𝑒
𝑒
𝑒
2𝑒
ln 𝑥
2
2?
2
2
2
2
10. What is the slope of the line perpendicular to the line with equation
1
5?
A.
B. 5
C.
D.
E.
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January 2021
11. 2𝑥
4𝑦
ellipse?
9 is the equation of an ellipse. What is the value of the eccentricity of this
√
A.
B. 2
C.
D. √2
E.
√
12. What is the sum of 5
A.
B.
C.
D.
E.
12
19
26
… to 30 terms?
2385
3088.5
3120
3195
3300
13. Kevin has 4 blue pens and 3 red pens in his pencil case. He chose two pens randomly, one
by one, without replacing any of the chosen pens. What is the probability that both chosen
pens are blue?
A.
B.
C.
D.
E.
0.07
0.24
0.29
0.38
0.77
14. The chart below shows the “life expectancy at birth” from 2008 to 2015 in Egypt. From
this data set, what could be the quotient of
, given that 𝑚 represents the median of the
data, and 𝑀 is its mean?
A.
B.
C.
D.
E.
0.012
0.667
1
1.334
1.5
4
January 2021
15. Which of the following functions is graphed below?
A. 𝑓 𝑥
B. 𝑓 𝑥
C. 𝑓 𝑥
D. 𝑓 𝑥
E. 𝑓 𝑥
𝑥 3;
2𝑥 1;
𝑥 2;
𝑥 3;
2𝑥 1;
𝑥 2;
𝑥 3;
2𝑥 1;
𝑥 2;
𝑥 3;
2𝑥 1;
𝑥 2;
𝑥 3;
2𝑥 1;
𝑥 2;
𝑥
2
𝑥
𝑥
𝑥
2
𝑥
𝑥
𝑥
2
𝑥
𝑥
𝑥
2
𝑥
𝑥
𝑥
2
𝑥
𝑥
2
3
3
2
3
3
2
3
3
2
3
3
2
3
3
16. If ℎ and 𝑔 are two negative numbers, and ℎ is an odd number while 𝑔 is an even number,
which of the following always has a positive answer?
A. √ℎ
𝑔
B. ℎ 𝑔
C. ℎ ℎ
D. ℎ𝑔 𝑔
E.
𝑔
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January 2021
17. If 2𝑥 3 represents the side of a base of a square prism, and 𝑥 3 represents the
height of the same prism, which expression denotes the lateral surface area of the square
prism?
A.
B.
C.
D.
E.
96𝑥
96𝑥
96𝑥
96𝑥
96𝑥
16𝑥
16𝑥
16𝑥
16𝑥
16𝑥
𝑥
18. If
1
A.
√41
B.
√
C.
√
D.
E.
2√41
36𝑥
36𝑥
36𝑥
36𝑥
36𝑥
540𝑥
540𝑥
540𝑥
540𝑥
540𝑥
324𝑥
324𝑥
324𝑥
324𝑥
324𝑥
972
972
972
972
972
3 , then what is the value of ?
19. What is the value of lim
?
→
A. 2
B. 2
C. 0
D. 0
E.
20. Given the function 𝑓 𝑥
A.
B.
C.
D.
E.
𝑅
𝑅
𝑅
𝑅
𝑅
2 sin 3𝑥
1
5. What is the range R of the function?
7, 3
7, 3 ∪ 3, 7
3, 7
7, 3 ∪ 3, 7
3, 7
21. In the adjacent figure,
𝐵𝐹,
𝐵𝐷 26 𝑐𝑚, 𝐸𝐹
and 𝐹 is the midpoint of 𝐵𝐷 .
What is the length of segment
𝐴𝐵? (the figure is not drawn
to scale)
A.
B.
C.
D.
E.
21.23 𝑐𝑚
19.38 𝑐𝑚
17.33 𝑐𝑚
8.66 𝑐𝑚
4.33 𝑐𝑚
6
January 2021
22. Which of the following could be a solution to 3
2𝑥
11 ?
A.
B.
C.
D.
E.
√
23. Given that 𝜃 is an obtuse angle, and sin 𝜃
√
, what is the value of 1
tan 𝜃 ?
A. 12.93
B. 7.46
C. 0.08
D. 0.57
E. 13.93
24. A restaurant recorded how many pizzas were sold every day during the past week. The list
of
sold
pizzas per
day
is the
following: 42, 37, 26, 40, 42, 50, 41.
What is the half of the standard deviation of the list?
A.
B.
C.
D.
E.
2.84
3.61
5.85
7.22
19.86
25. What is the product of the roots of 3𝑥
2 2𝑥
√3
0?
√
A.
B.
1 𝑥
√
C.
√
D.
√
E.
√
26. Which of the following is true about the graph of the function 𝑓 𝑥
A.
B.
C.
D.
E.
3
1?
It is always increasing and it has a vertical asymptote at 𝑥 1
It is always increasing and it has a horizontal asymptote at 𝑥
1
It is always increasing and it has a horizontal asymptote at 𝑦 1
It is always decreasing and it has a horizontal asymptote at 𝑦 1
It is always decreasing and it has a horizontal asymptote at 𝑦
1
7
January 2021
27. What is the value of 𝑥 when
A.
B.
C.
D.
E.
𝑥
𝑥
𝑥
𝑥
𝑥
3?
1
1 √5
√5
1 √5
1 √5
28. What is the radius of the circle with the equation 𝑥
A.
B.
C.
D.
E.
6𝑥
𝑦
16𝑦
20 ?
√93
93
√20
20
10
29. If log 3
A. 𝑥
2𝑥
8 , which of the following is true?
4
B. 𝑥
C. 𝑥
3
D. 𝑥
2
E. 𝑥
2
30. Fady is now 7 years older than Tina. In 12 years, the product of their age will be equal to
540. What is the age of Tina right now?
A.
B.
C.
D.
E.
4 years old
8 years old
15 years old
32 years old
39 years old
31. Given 𝑓 𝑥
3 sin 2𝑥
shift of this function?
1 , what is the value of the amplitude and the value of the phase
A. The amplitude is 3 and the phase shift is to the left.
B. The amplitude is and the phase shift is 3 to the left.
C. The amplitude is 3 and the phase shift is to the right.
D. The amplitude is and the phase shift is 3 to the right.
E. The amplitude is 3 and the phase shift is 2 to the right.
8
January 2021
32. Three positive odd integers have a product equal to 231. What is the sum of these integers?
A.
B.
C.
D.
E.
9
19
21
33
77
33. 𝐴 1, 7 is a point on the graph of the function 𝑔 𝑥
2𝑥
6𝑥 1. What are the
coordinates of point 𝐵, symmetric of 𝐴 with respect to the axis of symmetry of 𝑔 ?
A.
B.
C.
D.
E.
𝐵 7 ,7
𝐵 3.5 , 7
𝐵 1.5 , 7
𝐵 4 ,7
𝐵 1, 7
34. Which of the following is a solution of 3 sin 𝑥
A.
B.
C.
D.
E.
𝑥
𝑥
𝑥
𝑥
𝑥
and
C.
and
E.
, what are the two coterminal angles of 𝜃 ?
and
B.
D.
and
and
2
3
36. What is the value of one third the determinant of
0
2
A.
B.
C.
D.
E.
0?
3.86 𝜋𝑛 , with 𝑛 is an integer
2𝜋𝑛 , with 𝑛 is an integer
2.42 𝜋𝑛 , with 𝑛 is an integer
3.86 𝜋𝑛 , with 𝑛 is an integer
2.42 2𝜋𝑛 , with 𝑛 is an integer
35. Given the angle 𝜃
A.
2 sin 2𝑥
3
5
6
4
0
1
2
7
11
10
?
4
5
232
348
696
2088
9
January 2021
37. The adjacent table shows the prices of some
items in need to be replaced in Farid’s car after
the accident he had last month.
If he has to pay 26% of the prices of the items,
in addition to $100 as extra charges for the
garage, how much should he pay to fix the car?
A.
B.
C.
D.
E.
$206.67
$306.67
$332.67
$406.67
$1279.49
38. The adjacent table shows the
distance, in kilometers, between
different places in Egypt. What is
, given that 𝑥
the value of 2𝑥
represents the lower quartile, and 𝑦
represents the upper quartile of the
set of data given?
A.
B.
C.
D.
E.
626.73
87.06
82.89
17.98
8.99
Price (in $)
120.74
450.11
30.4
77.84
500.4
Item
Mirror
Towbars
Horn
Battery
Front bumper
Starting Point
Destination
Distance (𝑲𝒎
Al Qubbaah Palace
Giza Necropolis
35.2
Burj Al Arab
10th of Ramadan City
281
Qarun Lake
Pond El Sied
317
Kafr El Sheikh
Tanta
43.6
Alexandria
Burullus Lake
119
Wadi El Rayan
Kharga
542
39. The area of an oblique
triangle, is equal to half the
product of the lengths of two
sides times the sine of their
included angle. What could
be the area of triangle ABC ?
(the figure is not drawn to
scale)
A.
B.
C.
D.
E.
15.89 𝑐𝑚
21.12 𝑐𝑚
44.22 𝑐𝑚
253.8 𝑐𝑚
930.15 𝑐𝑚
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January 2021
40. The expression
A.
𝑥
𝑥
B.
𝑥
𝑥
C.
𝑥
D.
𝑥
𝑥
E.
𝑥
𝑥
is equivalent to which of the following?
𝑥
41. In the xy-plane, line 𝐷 passes through 𝐵 2, 5 and 𝑀 3, 8 while line 𝐿 passes through
𝑁 3, 7 and a point 𝐴. If 𝐷 and 𝐿 are parallel, what is the ordinate of point 𝐴 if its
abscissa is equal to 5 ?
A.
B.
C.
D.
E.
31
24
17
7
3
42. If 𝑥
A.
B.
C.
D.
E.
𝑎 and 𝑗
𝑥
𝑥
𝑥
2𝑥
𝑞
𝑞, which one is always true?
𝑗
𝑞
𝑗
𝑎 𝑞
𝑎 𝑗
𝑎 𝑞
3𝑎 𝑗
𝑥 2𝑗 𝑎
43. Given that 2𝑥
3𝑦𝑖
5
A. 𝑥
and 𝑦
B. 𝑥
and 𝑦
6
C. 𝑥
and 𝑦
6
D. 𝑥
and 𝑦
E. 𝑥
6 and 𝑦
2𝑦
3
6𝑥
1 𝑖 , what are the values of 𝑥 and 𝑦?
11
January 2021
44. In an arithmetic sequence, 𝑢
sequence?
A.
B.
C.
D.
E.
14 and 𝑢
23. What is the value of the 12th term in this
29
30.5
32
33.5
35
45. Using the adjacent figure, what is the value of
tan 𝛽 ?
A. 0.524
B. 0.62
C. 0.85
D. 1.17
E. 1.622
46. Marlene prepares handmade mugs and sells
them online. She has 6 different samples which
are sold for the following prices respectively:
$14, $16.5, $17, $19, $22, and $30. What is the
product of the range and three times the median of the list of prices shown?
A.
B.
C.
D.
E.
288
672
864
948
1066.5
47. Given 𝐴
2
3
5
2
1
and 𝐵
3
4
8
4
10
2
1
7
3 . Find 2𝐴
3
𝐵.
52 11
4
8 37 18
52 11
4
2
8 37 18
52 11
4
8 37 18
8 52
4 11 37
52
4
52
8
4 37 11
4
18
A. 4
B.
C.
D.
E.
12
January 2021
48. In the adjacent figure, if the side of the large cube
is equal to 8 𝑖𝑛, what is the surface area of the large
cube if we subtract the small shaded cubes?
A.
B.
C.
D.
E.
32 𝑖𝑛
192 𝑖𝑛
288 𝑖𝑛
336 𝑖𝑛
384 𝑖𝑛
49. Which function below represents the graph above? Determine its amplitude and its period.
A.
B.
C.
D.
E.
𝑓
𝑓
𝑓
𝑓
𝑓
𝑥
𝑥
𝑥
𝑥
𝑥
sin 2𝑥. The amplitude is equal to 1 and the period is 𝜋.
sin 2𝑥. The amplitude is equal to 1 and the period is 𝜋.
sin 2𝑥. The amplitude is equal to 1 and the period is 2𝜋.
sin 2𝑥. The amplitude is equal to 1 and the period is 2𝜋.
cos 2𝑥. The amplitude is equal to 1 and the period is 𝜋.
50. What are the asymptotes of
A.
B.
C.
D.
E.
𝑦
𝑦
𝑦
𝑦
𝑦
25 ?
5√13 𝑥
0
√13 𝑥
𝑥
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January 2021
THE FORMULAS BELOW MAY BE USEFUL IN ANSWERING QUESTIONS ON THIS
TEST.
𝑆
4𝜋𝑟
is the formula for the surface area of a sphere with a radius of 𝑟.
𝑉
𝜋𝑟 ℎ is the formula for a right circular cone with a radius of 𝑟 and a height of ℎ.
𝑉
𝜋𝑟
𝑉
𝐵ℎ is the formula for a pyramid with a base area of 𝐵 and a height of ℎ.
is the formula for a sphere with a radius of 𝑟.
14
January 2021