MATHEMATICS Leveled Exam 1: Easy
1. Find the discriminant of the quadratic equation 5π₯π₯2 + 7π₯π₯ = 10.
a. 249 b. 350 c. 49 d. 200 e. 560
2. Which of the following equations illustrates the associative law of multiplication?
a. 5 Γ (3 + 7) = 5 Γ 3 + 5 Γ 7 b. (40 + 20) + 5 = 40 + (20 + 5) c. 25 Γ 4 = 4 Γ 25 d. (5 Γ 3) Γ 7 = 5 Γ (3 Γ 7) e. 6 + 7 = 7 + 6
3. Solve the inequality: β16 β€ 5π₯π₯ β 6 β€ 9.
a. (0,4) b. (β2,3) c. (β1,4) d. [β1, 2] e. [β2, 3]
4. Evaluate 4cot2 30Β°
+ 1sin2 60Β°
β cos2 45Β°.
a. 1213
b. 1312
c. 16
d. 136
e. 13
5. Find the range of the function ππ(π₯π₯) = 3π₯π₯ β 4 where π₯π₯π₯π₯{β1,0,1,3,4}.
a. {β7,β4,β1, 5, 8} b. {β8,β4, 1, 2, 5} c. {β8,β5,β2,0,1, 4, 7} d. { 4, 7} e. all real numbers
MATHEMATICS LEVELED EXAM 1 PAGE 2 DEMIDEC Β©2016
6. Simplify (5π₯π₯5 + 7π₯π₯3 + 2π₯π₯2 + 3π₯π₯ + 9) + (4π₯π₯4 + 2π₯π₯3 + 9π₯π₯2 + 3π₯π₯).
a. 5π₯π₯5 + π₯π₯4 + 11π₯π₯3 + 11π₯π₯2 + 6π₯π₯ + 6 b. 7π₯π₯5 + 3π₯π₯4 + 9π₯π₯3 + 9π₯π₯2 + 6π₯π₯ + 6 c. π₯π₯5 + 3π₯π₯4 + 11π₯π₯3 + 9π₯π₯2 + 6π₯π₯ + 9 d. 5π₯π₯5 + 4π₯π₯4 + 11π₯π₯3 + 9π₯π₯2 + 9π₯π₯ + 9 e. 5π₯π₯5 + 4π₯π₯4 + 9π₯π₯3 + 11π₯π₯2 + 6π₯π₯ + 9
7. Find the domain of the function ππ(π₯π₯) = arcsin(2π₯π₯ β 5).
a. (2, 3) b. [2, 3] c. [2, 5] d. (3, 5) e. [3, 5]
8. If sinππ = ππ2βππ2
ππ2+ππ2, cos ππ =
a. 2ππππ2βππ2
b. 2ππππ2+ππ2
c. 2ππππππ2βππ2
d. ππ2+ππ2
ππ2βππ2
e. 2ππππππ2+ππ2
9. If sinππ = ππ2βππ2
ππ2+ππ2, cot ππ =
a. 2ππππ2βππ2
b. 2ππππππ2+ππ2
c. 2ππππππ2βππ2
d. ππ2+ππ2
ππ2βππ2
e. ππ2βππ2
2ππππ
10. Solve 2π₯π₯20βπ₯π₯
= 43 for π₯π₯.
a. 8 b. 5 c. 1 d. 4 e. 3
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11. Solve log(5π₯π₯ β 4) β log(π₯π₯ + 1) = log 4 for π₯π₯.
a. 1 b. 8 c. 3 d. 5 e. 2
12. Solve 64π₯π₯ = 1642π₯π₯
for π₯π₯.
a. 23
b. 12
c. 15
d. 25
e. 13
13. Find the y-intercept of ππ(π₯π₯) = 7π₯π₯2 β 8π₯π₯ + 5.
a. (0, 5) b. (0,β8) c. (0, 8) d. (0, 7) e. (0,β5)
14. Find the radian measure of 520Β°.
a. 16Ο5
b. 21Ο9
c. 26Ο9
d. 32Ο7
e. 35Ο6
15. Solve (π₯π₯+2)π₯π₯
β (π₯π₯β1)2π₯π₯
= 1 for π₯π₯.
a. 6 b. 4 c. 1 d. 2 e. 5
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16. Find the horizontal asymptote of ππ(π₯π₯) = οΏ½12οΏ½2π₯π₯β 12.
a. 6 b. β6 c. 12 d. β12 e. β1
17. Find the solution of tan 3ππ4
= 0.
a. ππ = 2ππππ3
, πππ₯π₯Ξ
b. ππ = 4ππππ3
, πππ₯π₯Ξ c. ππ = ππππ
3, πππ₯π₯Ξ
d. ππ = 3ππππ2
, πππ₯π₯Ξ
e. ππ = 3ππππ4
, πππ₯π₯Ξ
18. Find the centroid of the triangle whose vertices are (1,6), (β1 β 2) and (3,β1).
a. (5,4) b. (2,5) c. (4,1) d. (3,2) e. (1,1)
19. Find the equation of the reflection of ππ(π₯π₯) = β9π₯π₯2 + 5π₯π₯ β 7 across the x-axis.
a. 9π₯π₯2 + 5π₯π₯ + 7 b. 9π₯π₯2 + 5π₯π₯ β 7 c. β9π₯π₯2 + 5π₯π₯ β 7 d. β9π₯π₯2 β 5π₯π₯ + 7 e. 9π₯π₯2 β 5π₯π₯ + 7
20. Solve: π₯π₯2 β 144 < 0.
a. β4 β€ π₯π₯ < 4 b. β2 < π₯π₯ < 4 c. β12 < π₯π₯ < 12 d. β12 β€ π₯π₯ β€ 12 e. β8 < π₯π₯ β€ 8
MATHEMATICS LEVELED EXAM 1 PAGE 5 DEMIDEC Β©2016
21. Solve: cos2 66Β° β sin2 6Β°.
a. β5β18
b. β3β12
c. β5β34
d. 18
e. β12
22. Find the amplitude of the trigonometric function ππ(π₯π₯) = β2 sin οΏ½34π₯π₯οΏ½.
a. 2 b. 4 c. 3 d. β2 e. β1
23. Find the value of cos 210Β°.
a. β34
b. β12
c. ββ32
d. ββ35
e. 14
24. Find the distance AB where A (7, 8) and B (4, 4).
a. 10 units b. 8 units c. 4 units d. 6 units e. 5 units
25. Solve π₯π₯4 β 61π₯π₯2 + 900 = 0 for x.
a. π₯π₯ = Β±3 ; π₯π₯ = Β±4 b. π₯π₯ = Β±5 ; π₯π₯ = Β±6 c. π₯π₯ = Β±2 ; π₯π₯ = Β±5 d. π₯π₯ = Β±4 ; π₯π₯ = Β±2 e. π₯π₯ = Β±7 ; π₯π₯ = Β±6
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26. ππ(π₯π₯) = πππ₯π₯3 + 9π₯π₯2 + 4π₯π₯ β 10 has remainder 2 when divided by (π₯π₯ + 1). Find ππ.
a. β3 b. β7 c. 5 d. β1 e. 3
27. Find the value of cos(90Β°+ππ) sec(βππ) tan(180Β°βππ)sec(360Β°βππ) sin(180Β°+ππ) cot(90Β°βππ)
.
a. 5 b. 2 c. β3 d. β1 e. 1
28. Solve βπ₯π₯ + β9π₯π₯ = 12 for π₯π₯.
a. 10 b. 16 c. 12 d. 9 e. 8
29. If π§π§ = 8 β 6ππ, find the value of |π§π§|.
a. 10 b. 7 c. 12 d. 5 e. 8
30. Find the domain of the real valued function ππ(π₯π₯) = π₯π₯β1π₯π₯β2
.
a. all real numbers except 3 b. all real numbers except 1 c. all real numbers except 1 and 2 d. all real numbers e. all real numbers except 2
31. Solve sinππβsin3ππsin2 ππβcos2 ππ
.
a. cos ππ b. 2 sinππ c. 2 cos ππ d. sinππ e. 2 tanππ
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32. If (2π₯π₯ + 1) is a factor of 6π₯π₯3 + 5π₯π₯2 + πππ₯π₯ β 2, find ππ.
a. β5 b. 3 c. 5 d. β3 e. β1
33. Fill in the missing term: (π₯π₯ + 4)(4π₯π₯3 + 2π₯π₯2 + 5) = 4π₯π₯4 + 18π₯π₯3 + _____ + 5π₯π₯ + 20.
a. 10π₯π₯2 b. 16π₯π₯2 c. 5π₯π₯2 d. 2π₯π₯2 e. 8π₯π₯2
34. If cosπΌπΌ = β12 and ππ < πΌπΌ < 3ππ
2, find the value of 4 tan2 πΌπΌ β 3 csc2 πΌπΌ.
a. 2 b. 8 c. 5 d. 7 e. 3
35. Express (1 β ππ)4 in the form of ππ + ππππ.
a. 4 + 1ππ b. β4 + 1ππ c. β4 + 0ππ d. 2 + 2ππ e. β2 + 2ππ
1. If the points π(π + 1, β10), π(6, π + 1), π (3,16) and π(2,2) are the vertices of a parallelogram πππ π, find the values of π and π.
a. π = 2 πππ π = 4 b. π = 4 πππ π = 3 c. π = 1 πππ π = 2 d. π = 4 πππ π = 1 e. π = 2 πππ π = 5
2. Find the real number π₯ and π¦, if (π₯ β ππ¦)(3 + 5π) is the conjugate of β6 β 24π.
a. π₯ = 2 πππ π¦ = β4 b. π₯ = 2 πππ π¦ = β2 c. π₯ = 1 πππ π¦ = 3 d. π₯ = 3 πππ π¦ = β3 e. π₯ = 6 πππ π¦ = 3
3. Find the range of π(π₯) = β16 β π₯2.
a. [0,4] b. (β4,4) c. [β4,4] d. [2,4] e. (2,4)
4. Solve: π(π₯) β π(π₯) β 2β(π₯), where π(π₯) = π₯3 + 3π₯2 + 5π₯ β 4 , π(π₯) = 3π₯3 β 8π₯2 β 5π₯ +6 and β(π₯) = βπ₯3 + 5π₯ β 5.
a. 11π₯2 + 5 b. 15π₯2 c. 11π₯2 d. 12π₯2 e. 15π₯2 + 3π₯ + 5
5. A pole casts a shadow β3 times longer the poleβs height. Find the angle of elevation to the sun.
a. 75Β° b. 15Β° c. 60Β° d. 45Β° e. 30Β°
6. Find the π₯ β πππ‘ππππππ‘ and π¦ β πππ‘ππππππ‘ of the line π¦ + 6 = β3(π₯ β 8).
a. x-intercept (6, 0); y-intercept (0, 18) b. x-intercept (3, 0); y-intercept (0, 9) c. x-intercept (5, 0); y-intercept (0, 10) d. x-intercept (6, 0); y-intercept (0, 12) e. x-intercept (4, 0); y-intercept (0, 12)
7. Simplify arcsin (sin π₯+cos π₯
β2) , β
π
4< π₯ <
π
4.
a. π₯ +π
3
b. π₯ βπ
4
c. π₯ +π
2
d. π₯ +π
4
e. π₯ +π
6
8. Find the quotient when π(π₯) = βπ₯3 + 3π₯2 β 3π₯ + 5 divides π(π₯) = βπ₯2 + π₯ β 1 with remainder 3.
a. π₯ β 1 b. π₯ β 2 c. π₯ + 2 d. π₯ + 1 e. π₯ + 3
9. In any βπ΄π΅πΆ, find the value of (π β π)2 cos2 πΆ
2+ (π + π)2 sin2 πΆ
2.
a. π2 + π2 b. π2 + π2 c. π2 d. π2 e. π2
10. Find the point on the π₯ β axis which is equidistant from the points π(β2,5) and π(2, β3).
a. (2,0) b. (β1,0) c. (β2,0) d. (1,0) e. (4,0)
11. The price of a notebook has been marked up by 20% and is being sold for $105. How much did the shopkeeper pay the manufacturer of the notebook?
a. $87.50 b. $92.50 c. $113.50 d. $850 e. $97.50
12. The sum of the squares of two positive integers is 650. If the square of the larger number is 25 times the square of the smaller number, find the numbers.
a. 5 πππ 10 b. 8 πππ 11 c. 7 πππ 12 d. 5 πππ 25 e. 8 πππ 13
13. Simplify sin 5π₯β2 sin 3π₯+sin π₯
cos 5π₯βcos π₯ .
a. sin π₯ b. tan π₯ c. cot π₯ d. sec π₯ e. cos π₯
14. Solve the inequality π₯2 + 13π₯ + 12 > 0.
a. π₯ > β12 or π₯ β€ β1 b. π₯ β€ β10 or π₯ β₯ β2 c. π₯ β€ β12 or π₯ β₯ β1 d. π₯ < β2 or π₯ > 1 e. π₯ < β12 or π₯ > β1
15. Evaluate: 2
3csc2 58Β° β
2
3cot 58Β° tan 32Β° β
5
3tan 13Β° tan 45Β° tan 77Β°.
a. 3 b. 1 c. β1 d. β2 e. 2
16. Find the axis of symmetry of the graph of π(π₯) = π₯2 + 6π₯ β 20.
a. π₯ = 3 b. π₯ = 7 c. π¦ = 2 d. π¦ = 1 e. π₯ = 4
17. Find the domain of π(π₯) =|π₯β4|
π₯β4.
a. β β {β4} b. β β {8} c. β β {2} d. β β {4} e. β
18. If 52π₯β1 = 25π₯β1 + 100, find the value of 31+π₯.
a. 24 b. 27 c. 30 d. 21 e. 81
19. Evaluate sin(β420Β°) cos(390Β°) + cos(β660Β°) sin(330Β°).
a. 4 b. β2 c. 2 d. 1 e. β1
20. Find the life span of this person who spent 3
13 of her life in childhood and school,
4
39 of her life
in medical school, 1
2 of her life as a doctor, and died 13 years into retirement.
a. 82 π¦ππππ b. 80 π¦ππππ c. 78 π¦ππππ d. 85 π¦ππππ e. 75 π¦ππππ
21. Evaluate sin 12Β° sin 48Β° sin 54Β°.
a. 1
3
b. 1
8
c. 1
6
d. 2
3
e. 5
8
22. Find the angle between the hour hand and the minute hand of a clock at half past three.
a. 5π
6πππππππ
b. 3π
12πππππππ
c. π
12πππππππ
d. 5π
12πππππππ
e. 7π
6πππππππ
23. Solve βπ₯ + 6 + β10 β π₯ = β16.
a. π₯ = β6, 10 b. π₯ = β3, 8 c. π₯ = 6, 10 d. π₯ = 6 , β10 e. π₯ = 3, β8
24. Find the range of π(πΎ) = 4 sin πΎ β 3 cos πΎ + 7.
a. [3, 14] b. [4, 10] c. [4, 12] d. [2, 10] e. [2, 12]
25. If π₯ = log10 12 , π¦ = log4 2 Γ log10 9 and π§ = log10 0.4, evaluate π₯ β π¦ β π§.
a. 3 b. 1 c. 5 d. 2 e. 4
26. Simplify 1+sin 2π+cos 2π
1+sin 2πβcos 2π .
a. sin π b. tan π c. cos π d. cot π e. sec π
27. If 10 sin4 πΌ + 15 cos4 πΌ = 6, evaluate 27 csc6 πΌ + 8 sec6 πΌ.
a. 300 b. 125 c. 250 d. 100 e. 275
28. Let π(π₯) = π₯. If π was further stretched vertically by a factor of 3, then reflected over the π₯ βaxis and then translated vertically by 5 units, find the new equation of the graph.
a. β6π₯ + 5 b. β3π₯ β 5 c. 3π₯ β 5 d. 5 + 3π₯ e. β3π₯ + 5
29. Solve π₯5 β 29π₯3 + 100π₯ = 0 for x.
a. π₯ = 0, Β±1, Β±15 b. π₯ = 0, Β±2, Β±5 c. π₯ = 0, Β±4, Β±3 d. π₯ = 0, Β±2, Β±3 e. π₯ = 0, Β±3, Β±5
30. Evaluate cos2 33Β°βcos2 57Β°
sin221Β°
2β sin269Β°
2
.
a. β3
b. β2 c. 1
d. ββ2
e. 3β2
31. Find the equation of the graph of π(π₯) = π₯3 β 2π₯2 + 6π₯ β 1 reflected across the y-axis.
a. π₯3 β 2π₯2 β 6π₯ β 1 b. βπ₯3 + 2π₯2 β 6π₯ + 1 c. βπ₯3 β 2π₯2 β 6π₯ + 1 d. βπ₯3 β 2π₯2 β 6π₯ β 1 e. π₯3 + 2π₯2 + 6π₯ + 1
32. Solve for π₯: π2π₯ + ππ₯ β 12 = 0.
a. ln 3 b. ln 5 c. βln 5 d. 2ln 3 e. ln 5
33. Find a and b if (π₯ β 2) and (π₯ β 3) are both factors of π(π₯) = π₯3 + ππ₯2 + 2ππ₯ β 7.
a. π = β14
3 and π =
74
3
b. π = β73
4 and π =
71
6
c. π = β37
6 and π =
71
12
d. π = β71
3 and π =
74
12
e. π = β74
30 and π =
71
6
34. Which of the following expressions has the GREATEST period?
a. 2 cos π₯ b. tan 7π₯ c. sin 4π₯
d. 1
3cos 6π₯
e. cos1
3π₯
35. Solve tan π½ + tan 2π½ + tan 3π½ = tan π½ tan 2π½ tan 3π½ for π½.
a. π
3, ππΞ
b. ππ
3, ππΞ
c. 2ππ
3, ππΞ
d. ππ
2, ππΞ
e. 5ππ
3, ππΞ
MATHEMATICS Leveled Exam 3: Hard
1. A two digit number is four times the sum and three times the product of its digits. Find the number.
a. 20 b. 24 c. 18 d. 15 e. 22
2. If π΄π΄(0,1) is equidistant from π΅π΅(5,β3) and πΆπΆ(π₯π₯, 6). The sine of the angle to C from the origin is positive. Find x.
a. 5 b. -4 c. -5 d. 4 e. 2β41
3. In a βππππππ, find the value of οΏ½ππ2βππ2
ππ2οΏ½ sin 2ππ + οΏ½ππ
2βππ2
ππ2οΏ½ sin 2ππ + οΏ½ππ
2βππ2
ππ2οΏ½ sin 2ππ.
a. 0 b. 2 c. 7 d. 4 e. 1
4. Evaluate: οΏ½π₯π₯ππ+πποΏ½2οΏ½π₯π₯ππ+πποΏ½
2οΏ½π₯π₯ππ+πποΏ½2
(π₯π₯πππ₯π₯πππ₯π₯ππ)4 .
a. 0 b. 2 c. 3 d. 4 e. 1
5. Find the value of tan 6Β° tan 42Β° tan 66Β° tan 78Β°.
a. 4 b. 1 c. 4 d. 6 e. 5
MATHEMATICS LEVELED EXAM 3 PAGE 16 DEMIDEC Β©2016
6. The line joining ππ(3,3) and ππ(6,β9) is trisected at the points π΄π΄ and π΅π΅ where π΄π΄ divides the line in the ratio 1:2. If point π΄π΄ lies on the line 2π₯π₯ β π¦π¦ + β = 0, find the value of β.
a. β2 b. β4 c. β9 d. β7 e. β3
7. Which of the following expressions is equivalent to tanπΌπΌ1βcotπΌπΌ
+ cotπΌπΌ1βtanπΌπΌ
?
a. 1 + tanπΌπΌ + cotπΌπΌ b. 1 + sinπΌπΌ + cosπΌπΌ c. 1 + cotπΌπΌ + secπΌπΌ d. tanπΌπΌ + cosπΌπΌ e. 1 + cotπΌπΌ + cscπΌπΌ
8. Solve for π½π½: tanπ½π½ + tan 2π½π½ + β3 tanπ½π½ tan 2π½π½ = β3.
a. 2ππππ3
+ 2ππ9
, ππππΞ b. ππππ
3,ππππΞ
c. ππππ3
+ ππ9
, ππππΞ
d. 2ππππ3
+ ππ4
, ππππΞ e. ππππ
3+ ππ
2, ππππΞ
9. If ππ(π₯π₯) = (ππ β π₯π₯ππ)1/ππ,ππ > 0 ππππππ ππ β Ξ, then find the value of ππ(ππ(π₯π₯)).
a. π₯π₯2 b. 2π₯π₯ c. 1 d. π₯π₯ππ e. π₯π₯
10. If sinππ + sin ππ = ππ ππππππ cos ππ + cos ππ = ππ, find the value of cos(ππ β ππ).
a. 2ππ2+ππ2+22
b. ππ2βππ2β22
c. ππ2+ππ2β22
d. 3ππ2+2ππ2β22
e. ππ2+2ππ2+22
MATHEMATICS LEVELED EXAM 3 PAGE 17 DEMIDEC Β©2016
11. What must be added to the polynomial ππ(π₯π₯) = 2π₯π₯4 β 4π₯π₯3 β π₯π₯2 + 3π₯π₯ β 1 so that the resulting polynomial is exactly divisible by ππ(π₯π₯) = π₯π₯2 + 2π₯π₯ β 3?
a. β63π₯π₯ β 61 b. 63π₯π₯ β 62 c. β60π₯π₯ β 62 d. β63π₯π₯ + 62 e. β60π₯π₯ + 62
12. Find the value of 3(sinπΌπΌ β cosπΌπΌ)4 + 6(sinπΌπΌ + cosπΌπΌ)2 + 4(sin6 πΌπΌ + cos6 πΌπΌ)4 + sin2 πΌπΌ +cos2 πΌπΌ β 13.
a. 3 b. 0 c. 4 d. 1 e. 5
13. If ππ(π₯π₯) = π₯π₯β1π₯π₯+1
. π₯π₯ β β1, πποΏ½ππ(π₯π₯)οΏ½=
a. β4π₯π₯
b. 1π₯π₯
c. β32π₯π₯
d. β1π₯π₯
e. β13π₯π₯
14. Simplify οΏ½4ππ3
+ 8πποΏ½ + (β2ππ + 6ππ) β οΏ½10ππ6β 40πποΏ½ + οΏ½14ππ
6β 24πποΏ½.
a. 30ππ b. 40ππ c. β7ππ + 33ππ d. 33ππ e. 5ππ + 30ππ
15. Which of the following expressions is equivalent to sin 2π¦π¦ + 2 sin 4π¦π¦ + sin 6π¦π¦?
a. sin2 4π¦π¦ cos2 π¦π¦ b. 4 sin2 4π¦π¦ cos2 π¦π¦ c. 4 sin 4π¦π¦ cos2 π¦π¦ d. 2 sin 4π¦π¦ cos2 π¦π¦ e. sin 4π¦π¦ cos2 π¦π¦
MATHEMATICS LEVELED EXAM 3 PAGE 18 DEMIDEC Β©2016
16. Find the value of cos ππ8
.
a. 2β2 β 1
b. οΏ½β2β12β2
c. οΏ½β2β1β2
d. 2β2
e. οΏ½β2+12β2
17. Evaluate 3π₯π₯5 + 5π₯π₯4 β 75π₯π₯ β 125 = 0.
a. π₯π₯ = Β±5 ; π₯π₯ = β53
b. π₯π₯ = +β5 ;π₯π₯ = ββ5ππ ; π₯π₯ = 53
c. π₯π₯ = Β±β3 ;π₯π₯ = Β±β3ππ ; π₯π₯ = 43
d. π₯π₯ = Β±β5 ;π₯π₯ = Β±β5ππ ; π₯π₯ = β53
e. π₯π₯ = Β±β3 ;π₯π₯ = Β±β3ππ ; π₯π₯ = β43
18. Solve the inequality: π₯π₯2 + 15π₯π₯ < β14.
a. β15 < π₯π₯ < β1 b. β14 β€ π₯π₯ β€ 1 c. β13 < π₯π₯ < 1 d. β13 < π₯π₯ < 1 e. β14 < π₯π₯ < β1
19. Convert π₯π₯ = 0.235353535 β¦ to fractional form.
a. 23399
b. 2399
c. 233660
d. 33690
e. 233990
20. In an election for the mayor of a city, there were two candidates. A total of 10,000 votes were polled. 253 votes were declared invalid. The successful candidate got 5 votes for every 4 votes his opponent had. By what margin did the successful candidate win?
a. 1050 votes b. 1080 votes c. 1083 votes d. 1081 votes e. 1085 votes
MATHEMATICS LEVELED EXAM 3 PAGE 19 DEMIDEC Β©2016
21. Find the period of the trigonometric function ππ(π₯π₯) = cos 4π₯π₯ + cot 3π₯π₯.
a. 2ππ b. ππ c. 3ππ d. 7ππ e. 5ππ
22. Solve for π₯π₯: π₯π₯π₯π₯β12
+ 5π₯π₯β2
= π₯π₯2
π₯π₯2β14π₯π₯+24.
a. 25 b. 20 c. 30 d. 28 e. 31
23. Which of the following equations represents the graph given below?
a. ππ(π₯π₯) = π₯π₯2 β 4 b. ππ(π₯π₯) = βπ₯π₯ + 4 c. ππ(π₯π₯) = π₯π₯2 + 4 d. ππ(π₯π₯) = βπ₯π₯ + 4 e. ππ(π₯π₯) = π₯π₯3 + 4
24. A kite is flying at a height of 95 meters from ground level, attached to a string inclined at 60Β° to the horizontal. Find the length of the string to the nearest meter.
a. 110 meters b. 115 meters c. 102 meters d. 105 meters e. 112 meters
(0,4)
Y
X
MATHEMATICS LEVELED EXAM 3 PAGE 20 DEMIDEC Β©2016
25. If three consecutive natural numbers are such that the sum of one-third of the first, one-fourth of the second, and one-fifth of the third is at most 22, find the LARGEST of the numbers.
a. 20 b. 24 c. 26 d. 29 e. 31
26. Find the range of the function ππ(π₯π₯) = οΏ½(π₯π₯ β 1).
a. (1,β) b. (β1,β) c. [0,β) d. [0,1) e. [β1, 1]
27. If ππ(π₯π₯) = 2π₯π₯3 + πππ₯π₯2 + πππ₯π₯ β 2 has a factor (π₯π₯ + 2) and leaves a remainder 7 when divided by 2π₯π₯ β 3, find the values of ππ and ππ.
a. ππ = 3 and ππ = β1 b. ππ = 1 and ππ = β3 c. ππ = β3 and ππ = β1 d. ππ = 3 and ππ = 3 e. ππ = 3 and ππ = β3
28. Find the domain and range of the function ππ(π₯π₯) = 4 β |π₯π₯ β 10|.
a. Domain = β and Range = (ββ, 2) b. Domain = β and Range = (ββ, 4] c. Domain = β and Range = (ββ, 1) d. Domain = β and Range = (ββ, 10) e. Domain = β and Range = (ββ, 8]
29. Solve for π₯π₯: 421β 2(π₯π₯+8)
12= 6(π₯π₯β3)
15β 6
10.
a. π₯π₯ = 7131
b. π₯π₯ = 1211
c. π₯π₯ = 11113
d. π₯π₯ = 138119
e. π₯π₯ = 17121
MATHEMATICS LEVELED EXAM 3 PAGE 21 DEMIDEC Β©2016
30. Evaluate cot(β15ππ4
).
a. 3 b. 4 c. 1 d. 2 e. 5
31. Find π₯π₯ if π₯π₯ cot(90Β° + ππ) + tan(90Β° + ππ) sinππ + csc(90Β° + ππ) + tan 45Β° = 1.
a. cos ππ b. sinππ c. tanππ d. cot ππ e. csc ππ
32. Evaluate 1log2 126
+ 1log7 126
+ 1log9 126
.
a. 3 b. 7 c. 9 d. 1 e. 5
33. Express the angular measurement of the angle of a regular octagon in radians.
a. 4ππ3
radians
b. 3ππ5
radians
c. 2ππ5
radians
d. 2ππ3
radians
e. 3ππ4
radians
34. Solve for : β3π₯π₯2 + 4π₯π₯ + 32 = 4 β π₯π₯.
a. β8 ππππ β 4 b. 4 ππππ 2 c. β4 ππππ β 2 d. β8 ππππ 2 e. β4 ππππ 8
35. If πππ§π§3 + π§π§2 β π§π§ β ππ2 + ππ = 1, then find the value of |π§π§|.
a. 1 b. 3 c. 2 d. 0 e. 4