Download quadratic functions

‫مدرســـة الحصــن الثانويــة‬
‫المراجعة النهائية‬
‫رياضيات‬
‫الفصل الدراسي‬
‫األول ‪2022/2021‬‬
‫(‪)10 – G‬‬
‫أبنائي الطالب‪....‬‬
‫‪ ..‬العلم هو الوسيلة الوحيدة التي يرتفع بها شأن االنسان إلى مراتب الكرامة‬
‫والشرف‪.‬‬
‫إعداد‬
‫أ‪ .‬مصطفى عبد العزيز‬
‫مصـطــفى عبد العزيز‬
‫مدرسة الحصن الثانويــة‬
‫مراجعــــة الوحــــــدة األولى‬
The Quadratic Function
1.Which is an equation for the function shown in
the graph?
A.
B.
C.
D.
𝑦 = (𝑥 + 2)2 − 3
𝑦 = 2𝑥 2 − 3
𝑦 = (𝑥 − 2)2 + 3
𝒚 = (𝒙 − 𝟐)𝟐 − 𝟑
2.Find the zeros of function shown in the graph?
A. 2, 4
B. 4, 4
C. 1, 3
D. 1, 5
3.Which is the graph of 𝒚 = −𝟑𝒙𝟐 + 𝟏 ?
H
1
Mr. Moustafa Abdelaziz
Al-hosn Secondary School
10- G
4.The value of C that makes 𝑥2 − 4𝑥 + 𝑐 perfect square trinomial:
A. 18
B. -4
C. 4
D. 81
5.The parabola has a:
A. maximum value at x=4
B. minimum value at x =4
C. maximum value at x= 0
D. minimum value at x=0
6.Find the equation of the axis of symmetry.
A.
B.
C.
D.
𝑥 = −1
𝒙 = −𝟑
𝑦 = −1
𝑥=4
7.What is the equation of the axis of symmetry?
𝒚 = 𝟑𝒙2 − 𝟔𝒙 + 𝟒
A. x=1
B. x=-6
C. x=2
D. x=-1
2
Mr. Moustafa Abdelaziz
Al-hosn Secondary School
10- G
8.The sign of coefficient of 𝑥2 should be:
A. Positive
B. Negative
C. May either positive or negative
D. zero
9.Domain and range of the quadratic function:
A. Domain R, Range y≥ -3
B. Domain R, Range y ≥ -2
C. Domain R, Range y> -3
10.Determine the values of 𝑎, 𝑏, and 𝑐 for the quadratic equation:
4x2 – 8x = 3
𝐴. 𝑎 = 4, 𝑏 = −8, 𝑐 = 3
𝑩. 𝒂 = 𝟒, 𝒃 = −𝟖, 𝒄 = −𝟑
𝐶. 𝑎 = 4, 𝑏 = 8,
𝑐 = 3
3
Mr. Moustafa Abdelaziz
Al-hosn Secondary School
10- G
11.Use the discriminant to determine the number of solutions 4x2 + 4x + 1 = 0 has?
A. 0
B. 1
C. 2
D. More than 2
12.Square root of 16 is.
A. 4 or -4
B. 32
C. 8
D. 4
13. Use the quadratic formula to solve 2x2 + 2x - 12=0?
A. -2, 3
B. 2, 3
C. 2, -3
D. -2, -3
14.What is the y-intercept for 𝒇(𝒙) = −𝟐𝒙𝟐 + 𝟒𝒙 – 𝟔?
(0, 6)
B. (0, -6)
C. (6, 0)
D. (-6, 0)
A.
4
Mr. Moustafa Abdelaziz
Al-hosn Secondary School
10- G
15.What are the x-intercepts for 𝒇(𝒙) = 𝒙𝟐 − 𝟓𝒙 + 𝟔
A. (-2, 0), (-3, 0)
B. (2, 0), (3, 0)
C. (0,2), (3, 0)
16.Simplify:
A.
−𝟔
𝟏𝟑
+
𝟒
𝟏𝟑
−2
3 + 2𝑖
𝒊
B. -6 +4i
C.
D.
𝟔
𝟏𝟑
+
−𝟔
𝟏𝟑
𝟒
𝟏𝟑
𝒊
𝟒
-𝟏𝟑 𝒊
17.Which equation corresponds to the graph shown?
A. 𝒚 = 𝒙𝟐 + 𝟏
B. 𝑦 = 𝑥 2 − 1
C. 𝑦 = −𝑥 2 − 1
D. 𝑦 = 𝑥 2
18.Find the values of C that makes 𝑦 = 𝑥 2 − 6𝑥 + 𝐶 perfect square trinomial.
A. 3
B. 6
C. -9
D. 9
5
Mr. Moustafa Abdelaziz
Al-hosn Secondary School
10- G
19.Which equation is equivalent to 𝑥 2 + 2𝑥 − 3 = 0 ?
a) (𝑥 + 1)2 = 2
b) (𝒙 + 𝟏)𝟐 = 𝟒
c) (𝑥 − 1)2 = 2
d) (𝑥 − 1)2 = 4
20. State the value of the discriminant for 𝑦 = 𝑥 2 − 8𝑥 + 10
a) 4.9
b) 104
c) 24
d) 10.2
21. Simplify:(𝟐 − 𝟑𝒊) + (𝟓 + 𝟕𝒊) =?
a) 𝟕 + 𝟒𝒊
b) 7 − 4𝑖
c) −7 + 3𝑖
d) −7 − 4𝑖
22.How many x-intercepts has the graph of 𝒚 = − 𝒙𝟐 – 𝟑
A. 2
B. 1
C. 0
D. 3
23.the graph of 𝑦 = 𝑥 2 + 𝑥 − 6 has the y-intercept of
A.6
B. -6
C. 3
D. -2
6
Mr. Moustafa Abdelaziz
Al-hosn Secondary School
10- G
24. What are the solutions?
A. 0 and 2.5
B. 0 and 3
C.1 and -1
D. 2 and 4
25.How many zeros does this parabola have?
A. 3
B. 2
C. 0
D. 1
26.Solve 𝑥 2 − 9𝑥 + 8 = 0 by factoring.
A. x = 8 and 1
B. x = -8 and 1
C. x = 8 and -1
D. x = -8 and -1
7
Mr. Moustafa Abdelaziz
Al-hosn Secondary School
10- G
27. What are the x- intercepts?
A. x= 0 and x= -4
B. x= -3 and x= 1
C. y= 0
D. x= 2
28.What is another word that describes the zeroes of a quadratic function?
A. y-intercept
B. vertex
C. x-intercepts
D. maximum
29. What is the solution set for this quadratic equation? 𝒂𝟐 =16
A. {𝟒, −𝟒}
C.{2, −2}
B. {2}
D. {16, −16}
30. What is the solution set for this quadratic equation? 4 𝒂𝟐 = 𝟔𝟖
A.
{
10 −10
3
,
3
}
C. {9, −9}
B. {3, −3}
D.{√𝟏𝟕 , −√𝟏𝟕}
31. What is the solution set for this quadratic equation? 𝑥
2
− 1 = 80
A
8
Mr. Moustafa Abdelaziz
Al-hosn Secondary School
10- G
32. Does 𝒚 = −𝟒𝒙𝟐 have a maximum or minimum value?
A. maximum
B. minimum
33.Standard form of a quadratic equation
A. 𝑦 = 𝑥²
B. 𝒚 = 𝒂𝒙² + 𝒃𝒙 + 𝒄, 𝒂 ≠ 𝟎
C. 𝑦 = 𝑚𝑥 + 𝑏
D. 𝑦 = 𝑥
34. The
axis of symmetry line passes through which point?
A. y-intercept
B. any random point
C. vertex
D. symmetrical point for the vertex
35. Determine the line of symmetry. 𝒚 = 𝒙𝟐 + 𝟏𝟔𝒙 + 𝟔𝟒
A. x=4
B. x=2
C. x=-8
D. x=64
36. Find the vertex of 𝒇(𝒙) = −𝒙𝟐 − 𝟒𝒙 + 𝟏𝟐.
A.(-2, 16)
B. (2, 0)
C. (2, 4)
D. (-2, 4)
37. What is the y-intercept of 𝒇(𝒙) = −𝟐𝒙 𝟐 + 𝟒𝒙 − 𝟔
A. (0, 6)
B. (0, -6)
C. (6, 0)
D. (-6, 0)
9
Mr. Moustafa Abdelaziz
Al-hosn Secondary School
10- G
38. What is the solution set to the inequality 𝒙𝟐 − 𝟒𝒙 − 𝟓 > 𝟎
𝑨. 𝒙 < −𝟏 𝒐𝒓 𝒙 > 𝟓
𝐵. 𝑥 < −5 𝑜𝑟 𝑥 > 1
𝐶 . −1 < 𝑥 < 5
𝐷. −5 < 𝑥 < 1
39. Is (2, 3) part of the solution set?
𝒚 < 𝟐𝒙2 − 𝟑𝒙 + 𝟏
A. Yes
B. No
40. Solve the inequality: 𝟐𝒙𝟐 + 𝟓𝒙 ≥ 𝟏𝟐
A. [-4, 1.5]
B. (∞, -4) U (1.5, ∞)
C. (∞, -4] U [1.5, ∞)
D. no solution
41. What is the solution set for this quadratic equation? 𝒙𝟐
+ 𝟔𝟒 = 𝟎
A. 8i, -8i
B. -8, 8
C. 4, -4
D. 32, -32
42. Determine the number of solutions to the equation 𝒙𝟐 − 𝟑𝒙 − 𝟒 = 𝟎
A. One real solution only.
B. No real solutions.
C. Infinitely many real solutions.
D. Two real solutions.
10
Mr. Moustafa Abdelaziz
Al-hosn Secondary School
10- G
43.For the given graph, the correct function is
A. 𝒇(𝒙) = (𝒙 − 𝟑)𝟐
B. 𝑓(𝑥) = (𝑥 + 3)2
C. 𝑓(𝑥) = 𝑥 2 + 3
D. 𝑓(𝑥) = 𝑥 2 − 3
44. the roots of any quadratic equation can be found by using
A.
𝒙=
B.
𝑥=
C.
𝟐
D.
−𝒃
𝟐𝒂
−𝑏 ±√𝑏2 −4𝑎𝑐
2𝑎
𝒃 − 𝟒𝒂𝒄 = 𝟎
𝒚 = 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄
45. Ali shoots an arrow. The height of the arrow can be modeled
by 𝒚 = −𝟏𝟔𝒙𝟐 + 𝟏𝟎𝟎𝒙 + 𝟒, where 𝑦 represents the height (ft) of
the arrow 𝑥 seconds after it is shot into the air.
a.
At what height is the arrow shot?
𝑃𝑢𝑡 𝑥 = 0
⇒𝑦=4
Height = 4 ft
b. What is the maximum height of the arrow? How long does it take the arrow to reach this
height?
−𝑏
−100
𝑥=
2𝑎
=
2(−16)
= 3.125
⇒ 𝑦 = −16(3.125)2 + 100(3.125) + 4 = 160.25
●𝑀𝑎𝑥𝑖𝑚𝑢𝑚 ℎ𝑒𝑖𝑔ℎ𝑡 𝑖𝑠 160.25 𝑓𝑡.
●𝑥 = 3.125 seconds.
11
Mr. Moustafa Abdelaziz
Al-hosn Secondary School
10- G
Alhosn Secondary School
10- General
Mr. Moustafa Abdelaziz
‫مراجــعــــــــــة الوحدة الثانيـــة‬
1- In an exponential function, what does the 'a' represent?
A: slope
B: Rate of change
C: y-intercept
D: Common ratio
x
2. What is a, the starting term, for the function: f(x) = 300(1.16) ?
A: 300
B: 1.16
C: 16
D: x
3. Which of the following functions shows an initial amount of $15 and an increase of
35% each year?
A: y = 15(35)x
B: y = 15(1.35)X
C: y = 15(0.35)x
D: y = 35(1.15)x
4. Classify the model as Exponential GROWTH or DECAY. A=1200(.85)6
A: Growth
B: Decay
5. Is the pictured graph growth, decay, or linear or none?
A: Exponential Growth
B: Exponential Decay
C: Linear
D: None
1
Mr. Moustafa Abdelaziz
Alhosn Secondary School
10 -G
6. Is this exponential growth or decay?
A: Growth
B: Decay
7. Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an
equation that represents this situation.
A: 𝑦 = 5000(0.7)x
B: y=30(5000)x
C: y=5000(1.3)x
D: y=5000xx
8. The number of mosquitoes at the beginning of the summer was 4,000. The
population of mosquitoes is expected to grow at a rate of 25% a month. How many
mosquitoes will there be after 4 months?
A: 9766
B: 9006
C: 9765
D: 5433
9.Identify the y-intercept (initial value) of the function 𝑓(𝑥) = 2(4) 𝑋 .
A: 2
B: 4
C: (2)x
D: 8
10. Is the graph linear, exponential or neither?
A: Linear
B: Exponential
C: Neither
2
Mr. Moustafa Abdelaziz
Alhosn Secondary School
10 -G
11. Convert 3% to a decimal.
A: 3
B: 0.3
C: 0.03
D: 0.003
12. Which of the equations below represent this table?
A: y=3• (36)x
B: y=36• (3)x
C: y=3•(⅓)x
D: y=36•(⅓)x
13.What is the equation for the exponential function?
A: y = 2(3(x
B: y = 3(2(x
𝑥
C: y = 3 (1)
2
D: y = -2(3(x
14. What is the common ratio for the sequence: 3, 15, 75...?
A: 12
B: 1/5
C: 5
15.What is the explicit rule for the sequence: 11, 22, 44, 88...
A: an = 2(11)n-1
B: an = 11x2
C: an = 11(2)n-1
3
Mr. Moustafa Abdelaziz
Alhosn Secondary School
10 -G
An arithmetic sequence
Recursive formula
Explicit formula
𝒂𝒏 = 𝒂𝒏−𝟏 + 𝒅
𝒂𝒏 = 𝒂𝟏 + (𝒏 − 𝟏)𝒅
Geometric sequence
Recursive formula
Explicit formula
𝒂𝒏 = 𝒂𝒏−𝟏 ∙ 𝒓
𝒂𝒏 = 𝒂𝟏 ∙ 𝒓𝒏−𝟏
16. Which formula is used to find the explicit equation for geometric sequences?
𝐴: 𝑎𝑛 = 𝑎𝑛−1 + 𝑑
𝐵: 𝑎𝑛 = 𝑎𝑛−1 • 𝑟
𝐶: 𝑎𝑛 = 𝑎1 + 𝑑(𝑛 − 1)
𝐷: 𝑎𝑛 = 𝑎1●rn-1
17.Write the explicit formula for the geometric sequence.10,20,40, 80....
𝐴: 𝑎𝑛 = 10(2)𝑛−1
𝐵: 𝑎 𝑛 = 2(10)𝑛−1
𝐶: 𝑎𝑛 = 10(2)𝑛
𝐷: 𝑎𝑛 = 2(10)𝑛
18. Find the common ratio for the geometric sequence.7, -7,7, -7, ...
A:1
B: -1
C: 7
D: -7
19. Write the explicit formula for the geometric sequence.
𝐴: 𝑎 𝑛 = 162(2/3) 𝑛−1
𝐵: 𝑎 𝑛 = (2/3) (162)𝑛
𝐶: 𝑎 𝑛 = 162(3/2) 𝑛
𝐷: 𝑎𝑛 = 162 + (𝑛 − 1) (−54)
20. What is the 11th term of the geometric sequence 3,6,12, 24 ...?
A: 48
B: 97
C: 96
D: 3072
4
Mr. Moustafa Abdelaziz
Alhosn Secondary School
10 -G
what are the first fourth terms of the sequence in which𝑎1 = −2 and
𝑎𝑛 = (−3)𝑎𝑛−1 + 4, 𝑖𝑓 𝑛 ≥ 2
21.
A. -2, 10, -26, 82
B: 2,10, -26, 82
C: -2, -10, 26, -82
D: -2, -10, -26, -82
22.What is recursive formula for the following sequence: 5, 9, 13, 17, ...
A: 𝒂𝟏 = 𝟓, 𝒂𝒏 = 𝒂𝒏−𝟏 + 𝟒 , 𝒏 ≥ 2
B:
𝑎1 = −5, 𝑎𝑛 = 𝑎𝑛−1 − 4 , 𝑛 ≥ 2
𝐶: 𝑎1 = −5, 𝑎𝑛 = 𝑎𝑛−1 + 4 , 𝑛 ≥ 2
23. Solving the exponential equation:
4 2x + 3 = 1
A: 1
B: 1.5
C: 0
D: -1.5
24. Solving the exponential inequality 162𝑥−3 < 8
A: 𝑥 <
15
B: 𝑥 >
C: 𝑥 >
8
15
3
8
2
25. Solving the exponential equation: 42𝑛−1 = 64
A: -2
B: 2
C: 3
D: -3
5
Mr. Moustafa Abdelaziz
Alhosn Secondary School
10 -G
Al Hosn Secondary School
Grade 10 G
Mr. Moustaf Abdelaziz
‫مرا جعـــــــــــــــــة الوحـــــــــــــــدة الثالثة‬
1-What is the equation of the function graphed?
A: 𝒇(𝒙) = √𝒙 − 𝟐 + 5
B: 𝒇(𝒙) = √𝒙 + 𝟓 - 2
C: 𝒇(𝒙) = √𝒙 + 𝟐 + 5
D: 𝒇(𝒙) = √𝒙 − 𝟐 - 5
2. Which is the graph of the square root parent function?
A
B
A
B
3.What are the transformations of this function compared to
the parent function 𝒇(𝒙) = √𝒙 + 𝟐 ?
A: Shifted down 2
B: Shifted up 2
C: Shifted right 2
D: Shifted left 2
4. Solve
the radical equation 11= 2 + √𝟗𝟎 − 𝑿
A: 9
B: -9
C: 82
D: -82
1
Mr. Mr.Moustafa Abdelaziz
10 - G
5. Solve the radical equation: 6= √𝑿 − 𝟐
A: 8
B: 34
C: 38
D: 14
6. What does the Direct Variation Equation look like?
A: 𝒚 = 𝒌𝒙
𝑩: 𝒚 = 𝒙
𝑪: 𝒚 = 𝒎𝒙 + 𝒃
𝑫: 𝒚 =
𝒌
𝒙
7. y varies directly with x, and y is 84 when x is 16. Which equation
represents this situation?
A: y=1344x
B: y=100x
C: y=5.25x
D: y= 4 x
21
8.Is the given table a direct variation? If so, what is the constant of variation?
X
Y
5
15
6
18
7
21
8
24
A: Yes; 1/3
B: Yes; 3
C: Yes; 5
D: No
2
Mr. Mr.Moustafa Abdelaziz
10 - G
9. The number of kilograms of water in a person’s body varies directly as the person’s
mass. A person with a mass of 90 kg contains 60 kg of water. How many kilograms of
water are in a person whose mass is 75 kg?
A: 50 kg water
B: 72 kg water
C: 94 kg water
D: 150 kg water
10. Which of the given graphs is a direct variation?
A
B
C
D
𝟏𝟏. 𝑪𝒍𝒂𝒔𝒔𝒊𝒇𝒚 𝒕𝒉𝒆 𝒆𝒒𝒖𝒂𝒕𝒊𝒐𝒏: 𝟏𝟓 𝒙 = 𝟑 𝒚
A: Direct Variation
B: Inverse Variation
C: Joint Variation
D: Linear Equation
3
Mr. Mr.Moustafa Abdelaziz
10 - G
𝟏𝟐. 𝑾𝒉𝒂𝒕 𝒌𝒊𝒏𝒅 𝒐𝒇 𝒆𝒒𝒖𝒂𝒕𝒊𝒐𝒏 𝒊𝒔 𝒕𝒉𝒊𝒔? 𝒙 𝒚 = 𝟖
A: Linear Equation
B: Direct Variation
C: Inverse Variation
D: Joint Variation
13. Is the given table a direct or inverse variation? What is the constant
of variation?
X
Y
1
12
2
6
3
4
4
3
A: Direct, 12
B: Inverse, 12
C: Direct, 1/12
D: Inverse, 1/12
14. Determine the type of variation:
A: Direct
B: Inverse
C: Neither
15. Trina's paycheck earnings varies directly as the number of hours she works. If she works
19 hours and earns $187.15, what should she earn if she worked 40 hours?
A: $394
B: $443.25
C: $472.80
D: $512.20
4
Mr. Mr.Moustafa Abdelaziz
10 - G
16. An inverse variation is always a curve, and a direct variation is always a line?
A: True
B: False
17. True or False:
In a direct relationship the constant of variation is the product of x and y, and in an
inverse relationship the constant of variation is the quotient of x and y.
A: True
B: False
18. State the vertical asymptote:
𝑓(𝑥) =
A: x = -2/5
B: x = -5/2
C: x = -5
D: x = 2
𝑥−2
𝑥+5
19. State the horizontal asymptote of the function 𝒇(𝒙)
A: y =2
B: y = 1
C: y = 0
=
𝟐𝒙𝟐 −𝟓𝒙+𝟏
D: There is no HA
20. State the excluded value for the function:
𝒚=
𝒙𝟐 −𝒙
𝟒
𝟐𝒙 − 𝟖
𝑨: 𝒙 = 𝟒
𝑩: 𝒙 = −𝟒
𝑪: 𝒙 = 𝟖
𝑫: 𝒙 = −𝟖
5
Mr. Mr.Moustafa Abdelaziz
10 - G
21. Solve:
A: x = 5
B: x = -3
C: x = 3
D: x = -5
22. Solve:
𝟏
𝒙
=
𝒙+𝟏
𝟑
𝟏
𝟓𝒙
−
−
𝒙
𝟓
A: x = 20
B: x = -20
C: No Solution
D: x = 3
23. Solve:
𝟒
𝒙 +𝟐
A: x = 2
B: No Solution
C: x = -10
D: x = 10
=
𝒙 −𝟏
𝟓𝒙
= 𝟑
𝟔
𝒙−𝟐
𝟏𝟔
?
𝟑𝟐
24. which expression is equivalent to √
A:
𝟏
𝟐
√𝟐
B:
𝟐
C: 2
D:4
6
Mr. Mr.Moustafa Abdelaziz
10 - G
Mr. Moustafa Abdelaziz
10 G
‫مراجعــــــــــــــــــــــة الوحـــــــــــــــــــــدة الرابعـــــــــــــــــــة‬
1. The point of concurrency of the 3 perpendicular bisectors of a triangle is called
the ___?
A. Midsegment
B. Incenter
C. Circumcenter
D. Centroid
2. Define: INCENTER OF A TRIANGLE
A. the intersection point of the three angle bisectors of a triangle
B. when three or more lines intersect at a single point
C. the intersection point of the three perpendicular bisectors of a triangle
D. the point of intersection of three or more lines
3. Name the point of concurrency shown.
A.
B.
C.
D.
Circumcenter
Incenter
center
Neither
4. The circumcenter of a triangle is equidistant from the _______ of the triangle.
A. vertices
B. sides
C. center
D. midsegment
1
Mr. Moustafa Abdelaziz
Al Hosn Secondary School
10- G
5. The figure is an example of a(an) ...
A.
B.
C.
D.
altitude
perpendicular bisector
midsegment
angle bisector
6. Find the length of AD
A.
B.
C.
D.
2
4
6
8
7. Any point on a perpendicular bisector of segment is equidistant from both ends
of the segment.
A. True
B. False
8. The centroid is the point of concurrency of the 3 ____ of a triangle.
A. Medians
B. Midsegments
C. Perpendicular Bisectors
D. Angle Bisectors
9. The centroid cuts each median into two segments. The shorter segment is
___________ the length of the entire segment.
A. one third
B. two thirds
C. three fourths
D. one half
2
Mr. Moustafa Abdelaziz
Al Hosn Secondary School
10- G
10.The figure is an example of a(an) ...
A. angle bisector
B. midsegment
C. altitude
D. median
11. The altitudes of a triangle intersect at the _________________________.
A. Centroid
B. Circumcenter
C. Incenter
D. Orthocenter
12. CF, BE, and AD are the medians of the triangle. If BF =10, find AF.
A.
B.
C.
D.
20
10
5
Not Enough Information.
13. The circumcenter and orthocenter can be outside the triangle if the triangle is
A. obtuse
B. acute
C. isosceles
D. right
14. Which of the following words describes the point shown in the figure?
A. CenterPoint
B. Orthocenter
C. Centroid
D. Midpoint
3
Mr. Moustafa Abdelaziz
Al Hosn Secondary School
10- G
15. AD = 12. Find AG
A.
B.
C.
D.
6
8
18
12
16. Can a triangle have sides with the given lengths?
15 m, 1 cm, 15 cm
A. Yes
B. No
17. The lengths of two sides of a triangle are 5 in and 16 in. What is the range of
possible lengths for the third side?
A. 11 in < x < 21 in
B. x > 0
C. 11 or 21
D. 5 < x < 16
18. Can a triangle have sides with the given lengths:
4 m, 5 m, 9 m
A. Yes
B. No
19. Which of the following is a possible length for segment AC
A.
B.
C.
D.
10
15
17
9
4
Mr. Moustafa Abdelaziz
Al Hosn Secondary School
10- G
20. Using the hinge theorem, we can say that AB _____ DC
A.
B.
C.
D.
Greater than
Less than
Equal to
Half of
21. Use the Hing Theorem and the diagram below to choose the statement which must be true.
𝐴. 𝑚∠1 > 𝑚∠3
𝐵. 𝑚∠1 = 𝑚∠3
𝑪. 𝒎∠𝟏 < 𝒎∠𝟐
𝐷. 𝑚∠1 < 𝑚∠3
22. Two sides of a triangle have side lengths of 17 meters and 12 meters. What is
the range of possible lengths for the third side?
A. 12 < x < 17
B. 12 < x < 29
C. 5 < x < 17
D. 5 < x < 29
5
Mr. Moustafa Abdelaziz
Al Hosn Secondary School
10- G
Mr. Moustafa Abdelaziz
Transformation and symmetry
10-G
)2( ‫مراجــعـة‬
Rotation on the coordinate plane (About the origin)
Counterclockwise
900 Rotation (𝑥, 𝑦) → (−𝑦, 𝑥)
180 0 Rotation (𝑥, 𝑦) → (−𝑥, −𝑦)
2700 Rotation (𝑥, 𝑦) → (𝑦, −𝑥)
Clockwise
900 Rotation (𝑥, 𝑦) → (𝑦, −𝑥)
180 0 Rotation (𝑥, 𝑦) → (−𝑥, −𝑦)
2700 Rotation (𝑥, 𝑦) → (−𝑦, 𝑥)
1.Triangle ABC is reflected on the 𝑡ℎ𝑒 𝑥 − 𝑎𝑥𝑖𝑠. What is the location of the image of point B?
A. (-3, 2)
B. (-3, -2)
C. (3, -2)
D. (-2, 3)
2.The fixed point around which the rotation occurs is called
A. Centre of rotation
B. Degree of rotation
C. Angle of rotation
D. None of these
1
Mr. Moustafa Abdelaziz
Al-hosn Secondary School
10-G
3. Which best describes a possible step that is used to determine the location
of the image of point B when it is reflected in the line y= x?
a. Move down and right one from (0, 0)
b. Move down one and right one from (-1, 1)
c. Move right two from (1, 1)
d. Move down two from (-1, 1)
4.The order of rotational symmetry for an alphabet "O" is
A. One
B. Two
C. Eight
D. Infinite
5. A figure is rotated around a center point, and it still appears exactly as it did before the
rotation, it is said to have
A. reflection
B. Translation
C. Rotation
D. None of these
6. Find the vector that translate A (-2, 7) to A’ (6, 4)
A. 〈−8, 3〉
B. 〈−3, 8〉
C. 〈3, 8〉.
D. 〈8, −3〉.
2
Mr. Moustafa Abdelaziz
Al-hosn Secondary School
10-G
7. Which is the image of P (3, 0) after a counterclockwise rotation of 900 about (2, 4)?
A. P’ (-2, 5)
B. P’ (6, 5)
C. P’ (6, 3)
D. P’ (-4, 2)
8. State the order and magnitude of symmetry for the object below.
A. Order= 24, magnitude=150
B. Order= 20, magnitude=150
C. Order= 24, magnitude=300
D. Order= 12, magnitude=300.
9. How many lines of symmetry does this figure have?
A. 2
B. 3
C.1
D.0
10. Triangle ABC is rotated 900 counterclockwise about the origin. What is
the location of the image of point B?
A. (3, 2)
B. (-3, -2)
C. (-2, 3)
D. (-3, -2)
3
Mr. Moustafa Abdelaziz
Al-hosn Secondary School
10-G
11. Identify the transformation from ABCD to A'B'C'D'.
A. Translation
B. Reflection across the x-axis
C. Reflection across the y-axis
D. 90o counterclockwise rotation
12. A transformation that “turns” a figure about a fixed point at a given
angle and a given direction.
A. rotation
B. translation
C. reflection
D. dilation
13. Identify the transformation from ABC to A'B'C'.
A. (x+8, y+4)
B. (x-8, y-4)
C. (x+4, y+8)
D. (x-4, y-8)
4
Mr. Moustafa Abdelaziz
Al-hosn Secondary School
10-G
14. G (-4,1), ---------
After a translation of 3 units down and 5 units right
A. G’ (-1,6)
B. G’ (1, -2)
15. Triangle ABC has vertex A (5,2). Find the coordinates of 𝑨′ after a
reflection over the x-axis.
A. A’ (5, -2)
B. A’ (-5, -2)
C. A’ (-5, -2)
5
Mr. Moustafa Abdelaziz
Al-hosn Secondary School
10-G
‫اختبار الفصل األول ‪ 10‬عام وزارة ‪2012/2020‬‬