WorksheetsEA-Algebra: Equations and Inequalities
Total questions: 24
Worksheet time: 12mins
Solve for x: |2x − 3| = 5
x = 2, x = −3
x = 1, x = −4
x = 4, x = 1
x = 4, x = −1
Solve the inequality: (3x + 1)/(x − 2) > 0. Which interval describes the solution set?
(−∞, −1/3) ∪ (2, ∞)
(−∞, 2) ∪ (−1/3, ∞)
(−1/3, 2) only
(−∞, −1/3) ∪ (−1/3, 2)
Solve the system of equations: 2x + 3y = 7 and 4x − y = 5
x = 1, y = 5
x = 3, y = −1
x = 2, y = −1
x = 2, y = 1
A company sells two types of concert tickets: standard at 50andVIPat 80. The total revenue is $4,200 from 70 tickets. How many standard and VIP tickets were sold?
55 standard and 15 VIP
45 standard and 25 VIP
50 standard and 20 VIP
44 standard and 26 VIP
40 standard and 30 VIP
A rectangle has length three times its width. The perimeter is 96 units. What are the rectangle’s width and length?
8 units and 24 units
10 units and 30 units
16 units and 48 units
12 units and 36 units
14 units and 42 units
In triangle ABC, AB = AC and ∠BAC = 40°. What are the measures of ∠B and ∠C?
∠B = 70°, ∠C = 70°
∠B = 40°, ∠C = 40°
∠B = 50°, ∠C = 90°
∠B = 70°, ∠C = 40°
∠B = 20°, ∠C = 20°
In a circle of radius 10 units, two parallel chords AB and CD are 12 units apart. If AB = 16 units, what is the length of CD?
CD = 22 units
CD = 20 units
CD = 24 units
CD = 18 units
CD = 12 units
An inscribed angle in a circle subtends an arc measuring 80°. What is the measure of the inscribed angle?
35°
60°
30°
40°
50°
A circle has center at (4,5) and passes through the point (3,4). Which equation represents this circle?
(x−4)2+(y−5)2=3
(x−4)2+(y−5)2=2
(x−4)2+(y−5)2=4
(x−4)2+(y−5)2=1
Find the area of the triangle with vertices A(1,2), B(4,6), and C(5,3).
11 square units
10 square units
9 square units
8 square units
A square pyramid has base side length 10 units and slant height 13 units. What is its volume?
1000 cubic units
1200 cubic units
650.0 cubic units
433.0 cubic units
866.0 cubic units
A cylinder has radius 4 units and height 10 units. What is its total surface area?
112π square units
128π square units
96π square units
88π square units
104π square units
Solve for θ in degrees if 2sinθ + 1 = 0 with 0° ≤ θ ≤ 360°.
θ = 270° and 90°
θ = 30° and 150°
θ = 210° and 330°
θ = 270° only
θ = 90° only
In right triangle ABC with ∠C = 90°, sides a = 7 and b = 24 adjacent to ∠C, find the hypotenuse c.
c = 17
c = 24 − 7
c = 7 + 24
c = √(7·24)
c = 25
In △ABC with ∠C = 90°, a = 7 and b = 24, which is the measure of ∠A to the nearest tenth of a degree?
∠A ≈ 16.3°
∠A ≈ 73.7°
∠A ≈ 45.0°
∠A ≈ 61.9°
∠A ≈ 28.1°
For y = 3 sin(2x) − 1, what is the amplitude?
Amplitude is 3
Amplitude is −1
Amplitude is 2
Amplitude is 1
Amplitude is 1/2
For y = 3 sin(2x) − 1, what is the period?
π
4π
2π
π/2
3π
For y = 3 sin(2x) − 1, which statement correctly describes the shifts?
Shifted down three units, right π/2
Shifted up one unit, no phase shift
Shifted down one unit, left π units
Shifted down one unit, no phase shift
Shifted up one unit, right π/2
How many subsets are in the power set of an 8‑element set, including the empty set and the full set?
256 subsets total
240 subsets total
128 subsets total
64 subsets total
In a complete simple graph with 10 vertices, how many undirected edges are present?
100 edges in total
90 edges in total
40 edges in total
45 edges in total
How many ways can 7 identical candies be distributed to 3 children if each child must receive at least one candy?
15 distributions possible
28 distributions possible
21 distributions possible
10 distributions possible
From the graph of the line through A(2,3) and B(6,7), what is the slope-intercept form of the line?
y = 1.5x – 0.5
y = 2.0x – 1.0
y = 0.5x + 2.0
y = 1.0x + 1.0
A bike rental costs follow a linear pattern shown in the table: 1 hour → 7,2hours→ 12, 3 hours → 17,4hours→ 22, 5 hours → $27. Which equation gives total cost C in dollars as a function of hours h?
C = 5h + 1
C = 4h + 3
C = 6h + 1
C = 5h + 2
A cylinder has radius 5 cm and height 10 cm. Using π ≈ 3.14, what is its total surface area? Use S=2πr2+2πrh .
628.0 square centimeters
314.0 square centimeters
392.5 square centimeters
471.0 square centimeters
