Condensed Exam Assessment
Third Quarter Exam
Mathematics: Inequalities & Geometry Mastery
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Instructions
Select the best answer for each of the following 50 multiple-choice questions. For geometric problems, use properties of angles, triangles, and quadrilaterals.
Section I: Inequalities Mastery
1. Which inequality represents the sentence: "A number \( w \) is greater than \(-3\)"?
a) \( w < -3 \) b) \( w > -3 \) c) \( w \leq -3 \) d) \( w \geq -3 \)
2. "A number \( y \) minus \( \frac{1}{2} \) is no more than \( -\frac{3}{2} \)." Which is the correct inequality?
a) \( y - \frac{1}{2} \leq -\frac{3}{2} \)
b) \( y - \frac{1}{2} < -\frac{3}{2} \)
c) \( y - \frac{1}{2} \geq -\frac{3}{2} \)
d) \( y - \frac{1}{2} > -\frac{3}{2} \)
3. To ride a bumper car, you must be at least 42 inches tall. Which inequality represents this?
a) \( h < 42 \) b) \( h \leq 42 \) c) \( h > 42 \) d) \( h \geq 42 \)
4. Is \( j = 7 \) a solution for \( 5 + j > 8 \)?
a) Yes, because \( 12 > 8 \)
b) No, because \( 12 < 8 \)
c) Yes, because \( 7 > 5 \)
d) No, because 7 is not greater than 8
5. For the inequality \( q > -1.3 \), what type of circle should be used on the number line?
a) Closed circle at \(-1.3\)
b) Open circle at \(-1.3\)
c) Closed circle at \( 0 \)
d) Open circle at \( 1.3 \)
6. In which direction should the number line be shaded for \( s < 1\frac{3}{4} \)?
a) To the right
b) To the left
c) Both directions
d) No shading needed
7. Solve: \( d + 12 < 19 \)
a) \( d < 31 \) b) \( d > 7 \) c) \( d < 7 \) d) \( d > 31 \)
8. Solve: \( t - 4 \leq -14 \)
a) \( t \leq -10 \) b) \( t \leq -18 \) c) \( t \geq -10 \) d) \( t \geq -18 \)
9. Solve: \( -8 \leq z + 6.4 \)
a) \( z \leq -1.6 \) b) \( z \geq -14.4 \) c) \( z \leq -14.4 \) d) \( z \geq -1.6 \)
10. When solving \( -3x > 12 \), what must you do to the inequality symbol?
a) Keep it the same
b) Change it to an equals sign
c) Reverse the symbol
d) Remove it completely
11. Solve: \( 6q < -18 \)
a) \( q < -3 \) b) \( q > -3 \) c) \( q < 3 \) d) \( q > 3 \)
12. Solve: \( -\frac{r}{3} \leq 6 \)
a) \( r \leq -18 \) b) \( r \geq -18 \) c) \( r \leq 18 \) d) \( r \geq 18 \)
13. Solve: \( -4 > -\frac{4}{3}s \)
a) \( s > 3 \) b) \( s < 3 \) c) \( s > -3 \) d) \( s < -3 \)
14. Solve the two-step inequality: \( 3x + 4 > 16 \)
a) \( x > 4 \) b) \( x < 4 \) c) \( x > 6.6 \) d) \( x < 6.6 \)
15. Solve: \( \frac{z}{-2} - 6 \leq -2 \)
a) \( z \leq -8 \) b) \( z \geq -8 \) c) \( z \leq 8 \) d) \( z \geq 8 \)
16. Solve: \( -2t - 5 < 9 \)
a) \( t < -7 \) b) \( t > -7 \) c) \( t < 7 \) d) \( t > 7 \)
17. Solve: \( 7(q + 2) < -77 \)
a) \( q < -13 \)
b) \( q < -11 \)
c) \( q < -9 \)
d) \( q > -13 \)
18. Solve: \( -\frac{1}{3}(p + 9) \leq 4 \)
a) \( p \leq -21 \) b) \( p \geq -21 \) c) \( p \leq 3 \) d) \( p \geq 3 \)
19. Solve: \( 1.2(j + 3.5) \geq 4.8 \)
a) \( j \geq 0.5 \) b) \( j \leq 0.5 \) c) \( j \geq 4 \) d) \( j \leq 4 \)
20. Which is a solution for \( -2.4m > -6.8 \) when \( m = -3 \)?
a) True, \( 7.2 > -6.8 \)
b) False, \( 7.2 < -6.8 \)
c) True, \( -7.2 > -6.8 \)
d) False, \( -7.2 < -6.8 \)
21. Solve: \( -6z \geq 36 \)
a) \( z \leq -6 \) b) \( z \geq -6 \) c) \( z \leq 6 \) d) \( z \geq 6 \)
22. If \( m > 3 \), which of the following is NOT a solution?
a) 3 b) 4 c) 5 d) 100
23. Each gumball costs $0.25. You have $2.50. Which inequality represents the number of gumballs \( g \) you can buy?
a) \( 0.25g \geq 2.50 \)
b) \( 0.25g \leq 2.50 \)
c) \( 2.50g \leq 0.25 \)
d) \( 0.25 + g \leq 2.50 \)
24. You have $100 for a party. Each guest costs $8. What is the maximum number of guests you can invite?
a) 12 guests
b) 13 guests
c) 8 guests
d) 10 guests
25. You have $30. Each pack of cards costs $5. You want at least $10 left. Solve \( 30 - 5x \geq 10 \).
a) \( x \leq 4 \) b) \( x \geq 4 \) c) \( x \leq 8 \) d) \( x \geq 8 \)
Section II: Angle Relationships
26. Which describes vertical angles?
a) They sum to \( 90^\circ \)
b) They sum to \( 180^\circ \)
c) They are congruent (equal in measure)
d) They are always right angles
27. If two angles are supplementary, their sum is:
a) \( 45^\circ \) b) \( 90^\circ \) c) \( 180^\circ \) d) \( 360^\circ \)
28. If two angles are complementary, their sum is:
a) \( 45^\circ \) b) \( 90^\circ \) c) \( 180^\circ \) d) \( 360^\circ \)
29. Two angles are vertical. One measures \( 123^\circ \). What is the measure of the other?
a) \( 57^\circ \) b) \( 123^\circ \) c) \( 90^\circ \) d) \( 180^\circ \)
30. Angle A is \( 69^\circ \). Angle B is adjacent to Angle A and they form a right angle. What is the measure of Angle B?
a) \( 21^\circ \) b) \( 31^\circ \) c) \( 111^\circ \) d) \( 69^\circ \)
31. Vertical angles are formed by:
a) Parallel lines
b) Intersecting lines
c) A single ray
d) A triangle
32. Solve for \( x \) if vertical angles measure \( (x + 3)^\circ \) and \( 84^\circ \).
a) \( x = 81 \) b) \( x = 87 \) c) \( x = 93 \) d) \( x = 177 \)
33. Solve for \( x \) if complementary angles measure \( (2x - 8)^\circ \) and \( 42^\circ \).
a) \( x = 28 \) b) \( x = 34 \) c) \( x = 56 \) d) \( x = 25 \)
34. Complementary angles form what type of angle?
a) Acute angle
b) Obtuse angle
c) Right angle
d) Straight angle
35. Supplementary angles form what type of angle?
a) Right angle
b) Straight angle
c) Acute angle
d) Congruent angle
36. Angle X and Angle Y are supplementary. Angle X is \( 110^\circ \). Find the measure of Angle Y.
a) \( 70^\circ \) b) \( 80^\circ \) c) \( 90^\circ \) d) \( 180^\circ \)
37. Solve for \( x \) if complementary angles measure \( (3x + 1)^\circ \) and \( 44^\circ \).
a) \( x = 15 \) b) \( x = 12 \) c) \( x = 45 \) d) \( x = 5 \)
38. If Angle 1 and Angle 2 are vertical angles and Angle 1 is \( 42^\circ \), what is the sum of Angle 1 and Angle 2?
a) \( 42^\circ \) b) \( 84^\circ \) c) \( 90^\circ \) d) \( 180^\circ \)
39. Which of the following best describes supplementary angles?
a) They share a vertex and form a right angle
b) They are across from each other at intersection
c) They form a straight line and sum to \( 180^\circ \)
d) They are always \( 45^\circ \) each
40. If two angles are adjacent and form a right angle, they are:
a) Vertical angles
b) Supplementary angles
c) Complementary angles
d) Obtuse angles
Section III: Triangles & Quadrilaterals
41. What is the sum of the angle measures in any triangle?
a) \( 90^\circ \) b) \( 180^\circ \) c) \( 360^\circ \) d) Depends
42. Find the value of \( x \) in a right triangle where one acute angle measures \( 49^\circ \).
a) \( 41^\circ \) b) \( 49^\circ \) c) \( 51^\circ \) d) \( 90^\circ \)
43. A triangle has angle measures of \( 40^\circ, 50^\circ, \) and \( 90^\circ \). How is it classified?
a) Acute scalene
b) Right scalene
c) Obtuse isosceles
d) Right isosceles
44. Find \( x \) for a triangle with angles \( 110^\circ, 35^\circ, \) and \( (x + 12)^\circ \).
a) \( x = 23 \) b) \( x = 35 \) c) \( x = 47 \) d) \( x = 70 \)
45. A triangle has sides of 3.5 cm, 4 cm, and an angle of \( 125^\circ \). This triangle is:
a) Acute b) Right c) Obtuse d) Straight
46. What is the sum of the angle measures in any quadrilateral?
a) \( 180^\circ \) b) \( 270^\circ \) c) \( 360^\circ \) d) \( 540^\circ \)
47. Find the missing angle \( x \) in a quadrilateral with angles of \( 90^\circ, 90^\circ, \) and \( 128^\circ \).
a) \( 52^\circ \) b) \( 62^\circ \) c) \( 90^\circ \) d) \( 128^\circ \)
48. A trapezoid has angles of \( 80^\circ, 95^\circ, 38^\circ, \) and \( x^\circ \). What is the value of \( x \)?
a) \( 147^\circ \) b) \( 157^\circ \) c) \( 137^\circ \) d) \( 127^\circ \)
49. A parallelogram has a \( 50^\circ \) angle. What is the measure of the opposite angle?
a) \( 50^\circ \) b) \( 130^\circ \) c) \( 180^\circ \) d) \( 90^\circ \)
50. In a rhombus with two \( 120^\circ \) angles, what are the measures of the other two angles?
a) \( 120^\circ \) and \( 120^\circ \)
b) \( 60^\circ \) and \( 60^\circ \)
c) \( 30^\circ \) and \( 30^\circ \)
d) \( 90^\circ \) and \( 90^\circ \)
End of Examination • Please check your answers
