Test 16

January 2023
1.
The range y of the function f defined by 𝑓(𝑥 ) = 1 − 2𝑥 − 𝑥 2 is

A) 𝑦<2 B) 𝑦≤2
C) 𝑦 ≥ −2 D) 𝑦 < −2

2.
If the graphs of xy = 1 and xy = -1 are drawn on the same set of axes, how many
points (s) will they have in common?

A) 0 B) 1
C) 2 D) Infinite
3.
1
If y = 4 and x = , then the value of y in terms of x is:
8

2
A) y = B) y = 2x
𝑥
1
C) y = D) x = 2y
2𝑥

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4.
What is the range of the exponential function y = -5, 3𝑥+2 − 2 ?

A) {𝑦/𝑦 > 2} B) {𝑦/𝑦 < −2}

C) {𝑦/𝑦 < 2} D) {𝑦/𝑦 < −5}

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5.
If 𝑥𝑦 < −1 and 𝑥 < 𝑦 , which of the following must be always positive ?

A) 𝑥 − 𝑦 B) 𝑦−𝑥
C) 2𝑥 + 𝑦 D) 𝑥 2 − 𝑦 2
6.
Amr and his friends compared the amount of time x (in hours) ------------------
studying versus their ------------------------------------- (over 10) on a --------------- .
This results is modeled by the linear equation 𝑦 = 2.93𝑥 + 1.21 . which of the
below predications could be made?
I. It is impossible for anyone to score below 1.21.
II. The minimum number of studying hours needed to get a full score is 3.
III. Studying for 2 hours would guarantee a score above the average.

A) I only B) II only
C) I and II D) I, II, and III
7.
If x and y are two consecutive integers and 𝑦 2 = 𝑥 2 + 𝑧 2 , which of the following
is true?

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

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8.
How does 𝑔(𝑥) change over the interval {−2, 2} ?

A) 𝑔(𝑥) decreases by 6. B) 𝑔(𝑥) decreases by 12.

C) 𝑔(𝑥) decreases by 4. D) 𝑔(𝑥) increases by 12.
9.
𝐵𝐷 and ̅̅̅̅
In the isosceles triangle ABC shown below, ̅̅̅̅ 𝐶𝐷 are the bisectors of the
base angles. What is the value of x ? (Figure not drawn to scale)

A) 20 B) 60
C) 100 D) 120

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10.
3
What is/are the real values (s) of x for which –x = √𝑥 ?

A) 1 B) -1
C) 0 D) -1,0 and 1
11.
The graph below shows a sketch of the curve with equation 𝑦 = 𝑓(𝑥) .

There is only one maximum point on the curve of coordinates (3, 7). What are the
coordinates of the maximum point on the curve with equation 𝑦 = 𝑓(𝑥 + 3) ?
(Figure not shown to scale)

A) (6, 7) B) (0, 4)
C) (3, 4) D) (0, 7)

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12.
A library charges a cents for the 5 days that a book is borrowed and b cents for
each day over the 5 days. What is the total cost for borrowing a book for c days
where c is greater than 10 ?

A) 𝑎 + 𝑏𝑐 B) 𝑎 + 𝑏 (𝑐 − 5)
C) 𝑎 + 𝑏(𝑐 − 10) D) 𝑏 + 𝑎(𝑐 − 10)
13.
𝑐𝑎2 −𝑐𝑏2
is equivalent to ca plus
𝑎+𝑏

A) cb B) −𝑐𝑏
C) −𝑏 D) 1 + 𝑐𝑏
14.
In the figure below, ̅̅̅̅
𝐵𝑓 is perpendicular to ̅̅̅̅
𝐵𝐸 , and 𝑚∠𝐹𝐵𝐴 = 60° . What is the
value of x ? (Figure not drawn to scale)

A) 60 B) 120
C) 150 D) 160

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15.
How many students are there in a class if 8 students remain unsealed after 3 rows
of seats are filled, and 2 students remain unsealed after 4 rows of seats are filled,
knowing that all rows are the same ?

A) 24 B) 26
C) 38 D) 42
16.
1
When 5 is subtracted from of a number, the result is 10. What is the number?
5

A) -25 B) 10
C) 25 D) 75
17.
A factor of the polynomial 𝑥 2 − 5𝑥 + 6 is:

A) 𝑥 − 2 B) 𝑥+1
C) 𝑥 + 3 D) 2 + 𝑥

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18.
If 3x – 5 = 10, what is the value of 10x + 5 ?

A) 21.7 B) 55
C) 125 D) 455
19.
Line L is perpendicular to line T of equation 5𝑥 − 3𝑦 + 2 = 0 . What is the slope
of line U perpendicular to L ?

5
A) 5 B)
3
−3
C) D) -5
5
20.
2𝑥−5𝑦 −3𝑦
If = -2 , what is the value of +1?
2𝑦 𝑥

A) -2 B) -3
C) -4 D) -5

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1.
1 2 1
Of Ibrahim's salary, is spent for clothing, for food, and for transportation.
3 5 10
What part of Ibrahim's salary is left for other expenditures and savings?

1 5
A) B)
6 6
2 2
C) D)
9 7

Questions 2 and 3 refer to the following information:

2.
Consider Karim's sales record from month 5 to month 6. What is the percent change?

A) Increase by 20% B) Increase by 25%

C) Decrease by 20% D) Decrease by 25%
3.
How much greater are the sales for Amir's best month than Karim's best month?

A) $500 B) $1000
C) $1500 D) $5000

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4.
In my school, the robotics club (R) has 20 students, and the public speech club (P)
has 9 students. If a total of 15 members belong to only one of the two clubs, which
of the following Venn diagrams is a correct representation of the students in both
clubs?

A) B)

C) D)

5.
Consider the system of inequalities below.
𝑦≥0
{𝑥 − 2 ≤ −3
𝑦−𝑥 ≤3
The solution set is a triangular region. What are the coordinates of its vertices?

A) (-3,0), (1, 0), (-2,1) B) (-3,0), (-1,0), (-1,2)

C) (0,-3), (-1,0), (2,1) D) (3,0), (-1,0), (-1,-4)

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Questions 6 and 7 refer to the following information:
Majed walks from home to the coffee shop. He spends 20 minutes drinking his
coffee. He then walks back to his home at a constant speed of 4.8 km/h. The
distance-time graph below shows part of his journey.

6.
Find the speed, in km/h, at which Majed walks to the coffee shop?

A) 0,8 km/h B) 2,4 km/h

C) 3,2 km/h D) 8 km/h
7.
At what time does he arrive back home?

A) 9:10 B) 9:45
C) 9:55 D) 10:05

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8.
During the festive season, a $500 item is reduced 15 percent. If a 15 percent
charge is made on the reduced price for packaging and delivery, what is the final
cost of this item?

A) $500 B) $361.25
C) $350 D) $488.75
9.
On a TV show, competitors have to prepare a specific meal in x minutes. The
minimum length is 15 minutes, and the maximum length is 20 minutes.
Which equation represents the given situation?

A) |𝑥 − 20| ≤ 15 B) |𝑥 − 17.5| ≤ 2.5

C) |𝑥 − 15| ≤ 20 D) |𝑥 − 2.5| ≤ 20
10.
B and C are points On segment AD such that AB = BC = CD. What ratio of BC is
AD ?

1 2
A) B)
3 3
4
C) D) 3
3

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11.
If log 𝑥 6 = m, log 𝑥 3 = 𝑛, and 6𝑎 = 3, then a =

𝑛
A) m, n B)
𝑚
𝑚
C) D) n - m
𝑛
12.
If the circumference of a circle increases from π cm to 2π cm, what change occurs
in the area?

A) It remains the same. B) It is halved.

C) It is doubled. D) It is quadrupled.
13.
In the figure below, what is the length of AB? (Figure not drawn to scale).

A) 5 B) 8
C) 10 D) 13

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14.
In the figure below, three equal circles of center A, C, and E and each of radius 3
cm are inscribed in a rectangle JGHI. If x = 1 cm, then what is the perimeter of
rectangle JGHI? (Figure not drawn to scale)

x x

A) 32 cm B) 44 cm
C) 48 cm D) 96 cm
15.
5 kilograms of zucchini costs as much as 7 kilograms of tomato and 1 kilogram of
cucumber. 5 kilograms of tomato costs as much as 1 kilogram of zucchini and 3
kilograms of cucumber. How many kilograms of tomato can be purchased for the
amount of money needed to purchase 8 kilograms of zucchini?

A) 8 B) 11
C) 13 D) 15
16.
1 5
The gasoline indicator in Adam's car goes from to when he adds 4 gallons into
3 9
the tank. What is the total capacity of the tank, in gallons, in Adam's car?

A) 4 B) 4.5
C) 7.2 D) 18

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17.
A company has 6 departments, each with 10 to 14 bureaus. In each bureau, there
are at least 30 but no more than 50 workers. If 20% of the workers are web
developers, what is the minimum number of web developers in a department?

A) 36 B) 60
C) 360 D) 1800
18.
Nabil can do a job in 6 hours, and his son can do it in 10 hours. How long would it
take them to do the job if they worked together?

A) 0.27 hours B) 3 hours

C) 3.75 hours D) 6 hours
19.
If the length of an object y is directly proportional to its weight x, and a 5 meters
length weighs 2 kilograms, how many kilograms is a 2 meters length of object y ?

A) 0.4 B) 0.8
C) 2.5 D) 5

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20.
A basketball team plays 78 games in the regular season. After a certain date, the
team won 30 and lost 10 games. How many of the remaining games must the team
win to finish the regular season winning at least 55% of the games?

A) 9 B) 13
C) 15 D) 21
21.
Tomatoes originally sold at 4 kilograms for $1 were reduced in price to 2
kilograms for $0.4. By how much was the price per kilogram reduced?

A) 0.05 B) 0.2
C) 0.25 D) 0.6
22.
If the straight line d of equation 3𝑥 + 𝑎𝑦 − 1 = 0 passes through the y- intercept
of straight line L of equation 2𝑥 − 3𝑦 = −2 , what is the slope of d ?

2
A) -2 B)
3
−1
C) D) -3
2

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23.
Which point has the shortest distance to the origin of a coordinate plane?

A) (0, -4) B) (2, 6)

C) (-4, 1) D) (-1, -5)
24.
A man works "a" times as fast as any one of his helpers. If the man does a job in
"h" hours, how many hours are required for "w" helpers to do the same job?

ℎ𝑤
A) ahw B)
𝑎
𝑎𝑤 𝑎ℎ
C) D)
ℎ 𝑤
25.
If you walk 4 laps on a specific track, you cover 3 miles. How many miles are
expected to be covered in total by making an additional 1 lap?

A) 0.75 B) 2.25
C) 3.75 D) 4.75

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26.
𝑡 2𝑟 𝑠 𝑢
If = 3, = 16, and = 2, then =
2𝑢 𝑠 𝑡 𝑟

6 1
A) B)
16 96
8
C) D) 96
3
27.
𝑥 1 1
2 ( − ) − 3𝑥 =
5 3 5
What is the solution to the equation above?

−1
A) 𝑥 = −3 B) 𝑥=
3
−15 15
C) 𝑥 = D) 𝑥=
24 8
28.
3
√8𝑥6 −2√𝑦4
If 𝐸 = 3
, then the simplified form of E is:
√(𝑥−𝑦)3

A) 2𝑥 − 2𝑦 B) −2𝑥 − 2𝑦
C) -2 D) 2𝑥 + 2𝑦

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29.
If 𝑔(𝑓(𝑥 )) = 8𝑥 2 + 2𝑥 and 𝑔(𝑥 ) = 2𝑥 2 + 𝑥 , then 𝑓(𝑥 ) =

A) 𝑥 + 1 B) 𝑥2
C) 2x D) 𝑥 − 1
30.
1
Which of the following represents 𝑥2 + 𝑥 + 2 in the form 𝑎 + (𝑏𝑥 + 𝑐)2 where
4
𝑎, 𝑏, and c are real numbers ?

2 2
A) 2 + (1 𝑥 + 1) B) -3 + (1 𝑥 + 2)
2 2
1 2 1 1 2
C) 1 + ( 𝑥 + 1) D) + (𝑥 + )
2 4 2
31.
A function 𝑓(𝑥) increases by a factor of 4 over every unit interval in x and
𝑓(0) = 1 . Which could be a function rule for 𝑓(𝑥) ?

A) 𝑓 (𝑥 ) = 4𝑥 B) 𝑓 (𝑥 ) = 4𝑥
𝑥
C) 𝑓 (𝑥 ) = 1 − 4 D) 𝑓 (𝑥 ) = 1.04𝑥

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32.
What kind of transformation converts the graph of 𝑓(𝑥 ) = −6|𝑥 + 2| − 2 into the
graph of 𝑔(𝑥 ) = −6|𝑥 + 4| + 5 ?

Horizontal translation 2 units to the right and vertical translation 5 units

A)
upwards.
Horizontal translation 4 units to the left and vertical translation 3 units
B)
downwards.
Horizontal translation 2 units to the left and vertical translation 7 units
C)
upwards.
Horizontal translation 5units to the right and vertical translation 2 units
D)
upwards.

Questions 33 to 37 refer to the following information:

The table below shows a payroll example in a certain company.
Position Number of employees Salaries paid (in thousands dollars)
Worker 400 550
Supervisor 15 120
Manager 3 36

33.
The salaries paid to supervisors make up approximately what percent of the total
payroll?

A) 15 B) 16
C) 17 D) 18

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34.
What is the average salary for all employees?

A) $1689 B) $4725
C) $1375 D) $592
35.
What is the ratio of the average salary of a manager to the average salary of a
supervisor?

2 3
A) B)
3 2

1 3
C) D)
5 10

36.
The owner of the company decided to increase the salaries of the workers by 20%,
of the supervisors by 3%, and of the managers by 2%. By what percent did the
average salary increase?

A) 114.32 B) 16.19
C) 13.94 D) 25

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37.
The employees decided to form a committee of 3 members. In electing the 3
members, what is the probability to have one employee from each position?

18000 3
A) B)
12085216 418
418 1 1 1
C) D) × ×
1254 400 15 3
38.
If 𝑓 (𝑎) = 𝑎2 + 5 for all real values of a, which of the following is a possible value
of 𝑓(𝑎) ?

A) -1 B) 3
C) √5 D) 2√7

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 Mark Scheme
No Calculator
(1) B (6) C (11) D (16) D
(2) A (7) B (12) B (17) A
(3) C (8) B (13) B (18) B
(4) B (9) A (14) C (19) B
(5) B (10) C (15) B (20) D

Calculator
(1) A (9) B (17) C (25) C (33) C
(2) C (10) D (18) C (26) B (34) A
(3) A (11) B (19) B (27) B (35) B
(4) D (12) D (20) B (28) D (36) B
(5) B (13) B (21) A (29) C (37) A
(6) C (14) B (22) A (30) C (38) D
(7) B (15) C (23) A (31) A
(8) D (16) D (24) D (32) C

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