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Quizzes > High School Quizzes > Mathematics

Compound Inequalities Word Problems Practice Quiz

Master challenging compound inequality concepts for success

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting the Compound Conundrum Challenge, a high school chemistry quiz.

Which of the following is the correct chemical formula for water?
H2O
HO2
H2O2
O2H
Water is composed of two hydrogen atoms and one oxygen atom. H2O is the universally accepted chemical formula for water.
Which type of bond is found in sodium chloride (NaCl)?
Ionic bond
Covalent bond
Metallic bond
Hydrogen bond
NaCl is formed by the transfer of electrons between sodium and chlorine, creating ions that are held together by ionic bonds. This type of bonding is typical for combinations of metals and nonmetals.
What is the smallest integer that satisfies the inequality x + 2 > 5?
4
3
2
5
The inequality x + 2 > 5 simplifies to x > 3, so the smallest integer greater than 3 is 4. This demonstrates a basic understanding of solving simple inequalities.
Which of the following is an example of an ionic compound?
Magnesium oxide (MgO)
Carbon dioxide (CO2)
Water (H2O)
Methane (CH4)
Magnesium oxide is composed of a metal and a nonmetal, which typically form ionic bonds. The other compounds listed are molecular compounds with covalent bonding.
What is a compound in chemistry?
A substance formed when two or more elements chemically combine in fixed proportions
A mixture of substances that are physically combined
An element that is found naturally in unified form
A substance only formed by physical blending of pure elements
A chemical compound is a pure substance formed when two or more different elements are chemically bonded in fixed ratios. This differentiates compounds from mixtures, where the elements are only physically combined.
What is the proper name for the compound CaCO3?
Calcium carbonate
Calcium bicarbonate
Calcium oxide
Calcium chlorate
CaCO3 is composed of calcium ions and the carbonate ion. It is commonly known as calcium carbonate, a compound often found in limestone.
Solve the compound inequality: 2x + 1 < 7 and x - 2 ≥ 0. What is the range of possible values for x?
2 ≤ x < 3
2 < x ≤ 3
0 ≤ x < 3
2 ≤ x ≤ 3
The first inequality simplifies to x < 3 and the second simplifies to x ≥ 2. The intersection of these conditions is 2 ≤ x < 3.
Which of the following compounds exhibits covalent bonding?
Carbon dioxide (CO2)
Sodium chloride (NaCl)
Magnesium oxide (MgO)
Potassium bromide (KBr)
Carbon dioxide is a molecular compound where atoms share electrons through covalent bonds. In contrast, the other compounds listed form ionic bonds.
Solve the compound inequality: -3 ≤ 2x + 1 < 5. What is the solution for x?
-2 ≤ x < 2
-1 ≤ x < 2
-2 < x ≤ 2
-2 < x < 2
Subtracting 1 from all parts of the inequality gives -4 ≤ 2x < 4, and dividing by 2 yields -2 ≤ x < 2. This step-by-step process demonstrates effective compound inequality solving.
What is the empirical formula of butane, given its molecular formula is C4H10?
CH2
C2H5
C4H10
C2H4
Dividing the subscripts in C4H10 by their greatest common divisor, 2, gives CH2. The empirical formula represents the simplest whole-number ratio of the elements in the compound.
If a 15 g sample of a compound contains 60% element A and 40% element B, what is the mass of element B in the sample?
6 g
9 g
5 g
7.5 g
Calculating 40% of 15 g results in 6 g. This problem requires the application of basic percentage calculations to determine the mass of one component in a compound.
A reaction requires that the temperature satisfies 25°C ≤ T < 50°C. Which of the following temperatures meets the condition?
25°C
50°C
24°C
55°C
25°C is at the inclusive lower bound and is less than 50°C, so it meets the condition. The other options either fall outside the required range or match the exclusive upper limit.
What is the correct name for the compound Fe2O3?
Iron(III) oxide
Iron(II) oxide
Ferric oxide
Ferrous oxide
Fe2O3 contains iron in a +3 oxidation state, indicated by the Roman numeral III in the name Iron(III) oxide. This precise nomenclature clarifies the oxidation state present in the compound.
Solve the compound inequality: 3(x - 1) > 6 and 2x + 5 ≤ 15. What is the solution for x?
3 < x ≤ 5
3 ≤ x < 5
3 ≤ x ≤ 5
3 < x < 5
The inequality 3(x - 1) > 6 simplifies to x > 3, and 2x + 5 ≤ 15 simplifies to x ≤ 5. The intersection of these conditions is represented by 3 < x ≤ 5.
Which of the following ions is a polyatomic ion?
NO3❻ (nitrate)
Na❺
Cl❻
K❺
NO3❻ is a polyatomic ion because it consists of multiple atoms bonded together. The other ions listed are monoatomic, consisting of a single atom.
A laboratory experiment requires that two conditions hold: the pH must be greater than 3 and less than or equal to 7, and the temperature T in °C must satisfy T > 15 and T < 30. Which of the following pairs (pH, T) meets both criteria?
(5, 20)
(3, 20)
(5, 30)
(7, 15)
The pair (5, 20) satisfies the conditions with a pH between 3 and 7 and a temperature between 15°C and 30°C. The other options violate at least one of the inequality conditions.
Solve the compound inequality: 2(x - 3) ≤ 5 and 4 - x > 0. What is the range of possible values for x?
x < 4
x ≤ 5.5
3 < x < 4
x ≤ 4
The inequality 2(x - 3) ≤ 5 simplifies to x ≤ 5.5, and 4 - x > 0 simplifies to x < 4. The more restrictive condition is x < 4, which is the proper solution set.
In forming a compound from magnesium (Mg²❺) and phosphate (PO4³❻), what is the correct formula to balance the charges?
Mg3(PO4)2
Mg2(PO4)3
Mg(PO4)
MgPO4
Balancing the charges requires three Mg²❺ ions (total charge +6) and two PO4³❻ ions (total charge -6), which yields the formula Mg3(PO4)2. This method ensures overall charge neutrality.
Determine the correct formula for aluminum sulfate. Given aluminum has a charge of +3 and sulfate has a charge of -2, what is the compound's formula?
Al2(SO4)3
Al(SO4)
Al3(SO4)2
Al2SO4
Two aluminum ions at +3 each give a total of +6, which balances with three sulfate ions at -2 each (totaling -6). The correct formula, Al2(SO4)3, reflects this charge balance.
A laboratory experiment requires that a compound's mass is strictly between 46 g and 58 g and its purity must be greater than 75%. Which of the following conditions does NOT satisfy both requirements?
Mass = 50 g, Purity = 80%
Mass = 45 g, Purity = 80%
Mass = 50 g, Purity = 76%
Mass = 57 g, Purity = 90%
Even though the purity in Option 2 is acceptable, the mass of 45 g falls below the required lower limit of 46 g. This option does not satisfy the mass condition, making it the correct choice.
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Study Outcomes

  1. Analyze the structure and properties of chemical compounds.
  2. Interpret compound inequalities within word problems accurately.
  3. Solve compound inequalities using systematic problem-solving strategies.
  4. Apply chemical compound concepts to cross-disciplinary math problems.
  5. Evaluate quiz results to identify areas for further review and practice.

Compound Inequalities Word Problems Cheat Sheet

  1. Grasp the Basics of Compound Inequalities - Compound inequalities combine two separate statements using "and" or "or," creating a new condition. "And" means both parts must be true simultaneously, while "or" requires only one to hold. For instance, "x > 2 and x < 5" confines x between 2 and 5. Dive into examples
  2. Solve "And" Compounds by Intersection - When you see "and," you're looking for where both ranges overlap. Solve each inequality separately, then find the intersection of those solutions. For example, "x > 1 and x < 4" gives the combined answer 1 < x < 4. Step-by-step guide
  3. Tackle "Or" Compounds via Union - "Or" means at least one condition holds, so you join all solutions together. Solve each piece independently and then unite their solution sets. For "x < -1 or x > 3," you get x in (-∞, -1) ∪ (3, ∞). Practice with problems
  4. Remember Sign Flips with Negatives - Multiplying or dividing by a negative number flips the inequality direction. If you divide -2x > 6 by -2, it becomes x < -3. Watching for that flip is crucial to avoid mistakes! Quick tips here
  5. Visualize on the Number Line - Graphing makes it easy to see where your solution lives. Use open circles for strict inequalities (>, <) and closed circles for inclusive ones (≥, ≤). Connecting the dots helps you double-check your answer at a glance. Number line examples
  6. Use Interval Notation - Interval notation is a compact way to express solution sets. You write [2, 5) to mean 2 ≤ x < 5, with brackets for inclusive and parentheses for exclusive endpoints. It's the universal math shorthand! Learn interval shorthand
  7. Translate Word Problems - Key phrases like "at least" translate to ≥, and "no more than" means ≤. Identify those clues to convert sentences into inequalities. It's like decoding a secret message! Word problem wizardry
  8. Apply to Real-World Scenarios - Think of acceptable temperature ranges or budget limits when solving these inequalities. Applying concepts to everyday life cements your understanding and makes math feel more relevant. Real-life examples
  9. Spy and Avoid Common Errors - Watch out for sign reversal slip-ups and mixing up "and" vs. "or." Always double-check each step and sanity-check your final solution. Catching these sneaky mistakes is half the battle! Error-busting guide
  10. Practice, Practice, Practice - Consistent drills with worksheets and online quizzes will sharpen your skills. The more problems you solve, the more confident - and faster - you'll become. Extra practice resources
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