Revision Pack

Grade 10
Quarter four
Solve:
1. Solve |x +4| > 10.

( ) = 81
m
1 m +1
2. Solve .
9

3. Solve 25 4 t+ 1 ≥ 1252 t .

4. Use 𝐥𝐨𝐠𝟏𝟎 5 ≈ 0.6990 and 𝐥𝐨𝐠𝟏𝟎 7 ≈ 0.8451 to approximate the value of each expression.

1. log1035

2. log10 7/125

3. log10 1.4

4. Solve each equation. Check your solutions.

a) log10 (3m – 5) + log10 m = log10 2

b) log8 (n – 3) + log8 (n + 4) = 1

c) log7 x + 2log7 x – log7 3 = log7 72

1. 𝑎1 = 18, r = 3, n = 6
6. Find an for each geometric sequence.

7. Write an equation for the nth term of each geometric sequence.

3. 3, 9, 27, … 4. –1, –3, –9, …

8. Find the geometric means of each sequence.

1. 1, ? , ? , ? , 81

9. The terminal side of () in standard position contains each point. Find the exact values of the six
trigonometric functions of (). 2. (3, 4)

3. (8, -15) 4. (-4, 3)

 9. Find the area of 6ABC to the nearest tenth, if necessary.
1.A = 20°, c = 4 cm, b = 7 cm

2. c = 15 in., b = 13 in., A = 53°

10. Determine whether each triangle has no solution, one solution, or two solutions. Then solve the
triangle. Round side lengths to the nearest tenth and angle measures to the nearest degree.

1. .A = 29°, a = 6, b = 13

2.A = 113°, a= 21, b = 25

11. Determine whether each triangle should be solved by begining with the Law of
Sines or the Law of Cosines. Then solve the triangle.

.
1 . A = 11 °' C = 27°' C = 50

2.A = 71°, C = 62°, a= 20

Find the exact value of each trigonometric function.

1. tan 330

2. cot 30°

Choose:

1. What is the common ratio of the geometric sequence 2, 6, 18, 54, ...?

a) 2 b) 3 c) 4 d) 6

2. The first term of a geometric sequence is 5, and the common ratio is -2. What is the 4th term?

a) -40 b) 40 c) -20 d) 20

3. What is the formula for the nth term of a geometric sequence?

a) an = a1 + (n-1)d b) an = a1 * rn-1 c) an = a1 * rn d) an = a1 + n*d

4. Find the sum of the fifth terms of the geometric sequence 1, 3, 9, 27, ...

a) 121 b) 242 c) 363 d) 1093

5. The sum of an infinite geometric series is 20, and the first term is 10. What is the common ratio?

a) 1/2 b) -1/2 c) 2 d) -2
 6. Which of the following is a geometric sequence?

a) 1, 2, 3, 4, ... b) 1, 4, 9, 16, ... c) 2, 4, 8, 16, ... d) 1, 3, 5, 7, ...

7. What is the next term in the geometric sequence 5, -10, 20, -40, ...?

a) -80 b) 80 c) -60 d) 60

8. The common ratio of a geometric sequence is 1/3. If the third term is 9, what is the first term?

a) 1 b) 27 c) 81 d) 243

9. A geometric sequence has a first term of 2 and a common ratio of 3. What is the 6th term?

a) 162 b) 486 c) 1458 d) 3645

10. What is the formula to find the sum of a finite geometric series?

a) Sn = a1(1-r^n)/(1-r)

b) Sn = a1(1-r^n)/(r-1)

c) Sn = a1(n/2)(a1 + an)

d) Sn = n/2(2a1 + (n-1)d

11. Which property of logarithms is expressed as logb(mn) = logb(m) + logb(n)?

a) Product Rule b) Quotient Rule c) Power Rule d) Inverse Property

12. Simplify the expression: log2(8) - log2(4)

a) 1 b) 2 c) 4 d) 32

13. Rewrite the expression using the power rule: log5(x3)

a) 3log5(x) b) log5(3x) c) log5(x/3) d) log5(x3)

14. Which property of logarithms is expressed as logb(m/n) = logb(m) - logb(n)?

a) Product Rule b) Quotient Rule c) Power Rule d) Inverse Property

15. Simplify the expression: 2log3(x) + log3(y)

a) log3(x2y) b) log3(2xy) c) log3(x2 + y) d) log3(x + y2)

16. Expand the logarithm: log (xy2/z)

a) log x + 2 log y - log z

b) log x + log 2y - log z

c) log x + 2 log y + log z

 d) log x + log y2 –z

17. Which expression is equivalent to log2(16)

a) log2(8) + log2(2) b) log2(20) - log2(4) c) 4log2(4) d) 8log2(2)

Solving Equations with Logarithms

18. Solve for x: log3(x) = 2

a) 5 b) 6 c) 8 d) 9

19. Solve for x: log(x + 1) = 0

a) 0 b) 1 c) -1 d) e

20. Solve for x: log2(x) + log2(x - 2) = 3

a) 4 b) -2 c) 2, 4 d) -2, 4

21. Solve for x: 2log5(x) = log5(9)

a) 3 b) -3 c) ±3 d) 9

22. Solve for x: log4(x) + log4(x-6) = 2

a) 8 b) -2 c) 8, -2 d) 10

23. Solve for x: log(3x + 2) = log(x + 8)

a) 3 b) 6 c) 8 d) 10

24. Solve for x: log2(x + 5) = 4

a) 9 b) 11 c) 16 d) 21

25. Solve the equation for x: 2 log3x - log3 4 = 2

a) x = 6 b) x = 8 c) x = 12 d) x = 18

31. Convert 120 degrees to radians.

a) 2π/3 b) 3π/2 c) π/6 d) 5π/6

32. Convert π/4 radians to degrees.

a) 45° b) 60° c) 90° d) 180°

33. What is the measure of the angle in standard position that passes through the point (1, 0)?
 a) 0° b) 90° c) 180° d) 270°

34. An angle of 270° is in which quadrant?

a) Quadrant I b) Quadrant II c) Quadrant III d) Quadrant IV

35. Find the complementary angle of 30°.

a) 60° b) 150° c) 210° d) 330°

36. If θ is an angle in standard position and P(-3, 4) is a point on the terminal side of θ, find sin θ.

a) 3/5 b) -3/5 c) 4/5 d) -4/5

37. If cos θ = -1/2 and θ is in Quadrant II, find tan θ.

a) √3 b) -√3 c) 1/√3 d) -1/√3

38. Evaluate: sin(2π/3)

a) 1/2 b) -1/2 c) √3/2 d) -√3/2

39. Evaluate: cos(150°)

a) √3/2 b) -√3/2 c) 1/2 d) -1/2

40. Find the reference angle for 300°.

a) 30° b) 60° c) 120° d) 240°

41. In triangle ABC, if a = 8, A = 30°, and B = 60°, find b.

a) 8√3 b) 8/√3 c) 16 d) 4

42. Given a triangle where A = 45°, B = 60°, and a = 10, find the length of side b.

a) 10√2 b) 10√3 c) (10√6)/2 d) 5√6

43. Find the area of triangle ABC if a = 10, b = 12, and C = 30°.

a) 30 b) 60 c) 30√3 d) 60√3

44. The area of a triangle is 50 ft2. If two sides are 10 and 20, and the included angle is θ, find sin θ.

a) ½ b) 2 c) √3/2 d) 1

45. In triangle ABC, if a = 5, b = 7, and C = 60°, find c.

a) √39 b) 39 c) √109 d) 109

46. In triangle ABC, if a = 8, b = 5, and c = 10, find angle A.

a) 49.5° b) 55.8° c) 60° d) 65.2°

 47. Given a triangle with sides a = 9, b = 12, and included angle C = 75°, find the length of the third side, c.

a) 14.7 b) 15 c) 20 d) 8

48. In triangle ABC, a = 6, b = 8, and c = 10. Find the measure of angle C.

a) 30° b) 60° c) 90° d) 120°

49. Solve for x: log3(x - 4) = 2

a) 5 b) 7 c) 11 d) 13

50. In triangle ABC, A = 60°, B = 45°, and a = 20. Find the length of side b.
a) 10√6 b) 20√2 c) (20√6)/3 d) 10

51. Find the area of a triangle with sides of length 8 and 10 and an included angle of 120°.

a) 20√3 b) 40 c) 40√3 d) 80

52. What is the sum of the geometric series 2 + 6 + 18 + 54 + ... + 486?

a) 728 b) 242 c) 1456 d) 1094

53. Convert 2 radians to degrees.

a) 90° b) 114.6° c) 120° d) 360°

54. Identify the y-intercept and the axis of symmetry for the function of f(x) = 10𝑥2 + 40x + 42.

A 42; x = 4 B 0; x = –4 C 42; x = –2 D –42; x = 2

55. Write an equation in standard form for the line that is parallel to the graph of –8x = 5 – 4y and has y-intercept –0.5.
A x – 0.5y = 0.25 B 10x – 5y = 2.5 C 4x – 2y = 1 D 2x – y = 1

56. Find the slope of the line that passes through (−4.5,72) and (3, 3.5).
F – 16 G –6 H undefined J0