General Chemistry II: Mathematics Diagnostic

IntoChemistry | General Chemistry II Math Readiness

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Initial math diagnostic

Take this at the beginning of the course. The 24 questions sample six foundational skills. This is a learning check, not a placement test.

Suggested: review any skill area below 75%; this cutoff is an instructional choice, not a validated prediction threshold. Scores are not automatically sent to Talon.

Choose one response for each question, then select “Check my answers.” No timer. Hints are optional. You can retry freely. Questions are formative, not proctored.

Question 1. Solve x² -4x + 3 = 0. What is the smaller root?

0 4 3 1

Hint for question 1

Two algebraic roots may exist; compare them.

Question 2. Solve x² -6x + 8 = 0. What is the smaller root?

4 1 5 2

Hint for question 2

Two algebraic roots may exist; compare them.

Question 3. Find pH when [H₃O⁺] = 1.0 × 10^-2 M.

1.00 4.00 2.00 3.00

Hint for question 3

The negative sign makes pH positive for concentrations below 1 M.

Question 4. Find pH when [H₃O⁺] = 1.0 × 10^-3 M.

3.00 4.00 5.00 2.00

Hint for question 4

The negative sign makes pH positive for concentrations below 1 M.

Question 5. A first-order quantity halves with k = 0.1 min⁻¹. Calculate half-life.

3.47 min 13.9 min 3.01 min 6.93 min

Hint for question 5

Use natural logarithm for exponential decay.

Question 6. A first-order quantity halves with k = 0.2 min⁻¹. Calculate half-life.

1.73 min 1.51 min 6.93 min 3.47 min

Hint for question 6

Use natural logarithm for exponential decay.

Question 7. A graph of ln[A] versus time has slope -0.1 s⁻¹. What is first-order k?

0.20 s⁻¹ 0.10 s⁻¹ 0.05 s⁻¹ 0.17 s⁻¹

Hint for question 7

The slope is negative but k is positive.

Question 8. A graph of ln[A] versus time has slope -0.2 s⁻¹. What is first-order k?

0.20 s⁻¹ 0.10 s⁻¹ 0.27 s⁻¹ 0.40 s⁻¹

Hint for question 8

The slope is negative but k is positive.

Question 9. 0.2 mol solute is dissolved in 0.5 kg of solvent. Find molality.

0.4 mol/kg 4 mol/kg 0.8 mol/kg 0.2 mol/kg

Hint for question 9

Molality has kilograms of solvent in the denominator.

Question 10. 0.3 mol solute is dissolved in 1 kg of solvent. Find molality.

0.15 mol/kg 0.3 mol/kg 3 mol/kg 0.6 mol/kg

Hint for question 10

Molality has kilograms of solvent in the denominator.

Question 11. An ICE-table approximation neglects x=0.004 M relative to C=0.2 M. What is 100x/C?

2.80 % 1.60 % 2.40 % 2.00 %

Hint for question 11

Compute change divided by initial concentration.

Question 12. An ICE-table approximation neglects x=0.005 M relative to C=0.25 M. What is 100x/C?

2.80 % 1.60 % 2.00 % 2.40 %

Hint for question 12

Compute change divided by initial concentration.

Question 13. Which values solve x²−9=0?

x=−3 and x=3 x=0 and x=9 x=−9 and x=9 x=3 only

Hint for question 13

Squaring either of two opposite numbers can yield the same positive value.

Question 14. For x²−4x+3=0, which root lies between 0 and 2?

4 1 3 −1

Hint for question 14

Try factoring into two binomials.

Question 15. What is log₁₀(1000)?

10 −3 3 2

Hint for question 15

Ask what exponent of ten produces the input.

Question 16. At 25 °C, a strong monoprotic acid has [H₃O⁺]=1.0×10⁻⁵ M. What is pH?

−5.00 9.00 4.00 5.00

Hint for question 16

The pH definition includes a negative sign.

Question 17. What is ln(e²)?

0.301 10² 2 e²

Hint for question 17

ln and eˣ are inverse operations.

Question 18. Which operation isolates t from e^(−kt)=0.5?

Take a square root Square both sides Multiply both sides by e Take ln of both sides

Hint for question 18

Remove an exponential by its inverse function.

Question 19. On a first-order plot of ln[A] versus time, what does the negative slope equal?

k² −k [A]₀ 1/k

Hint for question 19

Match terms to y=mx+b.

Question 20. An Arrhenius plot has ln k on y and 1/T on x. Which quantity is associated with the slope?

Ea/T −Ea/R ln A Ea×R

Hint for question 20

Identify the coefficient multiplying x.

Question 21. What is the denominator in molality?

moles of solution kilograms of solution kilograms of solvent liters of solution

Hint for question 21

Distinguish solvent mass from final solution volume.

Question 22. A solution contains 0.50 mol solute in 250 mL final solution. What is molarity?

2.0 M 0.50 M 0.0020 M 0.125 M

Hint for question 22

Convert milliliters to liters.

Question 23. An approximate ICE change x=0.010 M from C=0.50 M is what percent?

2.0% 0.2% 20% 5.0%

Hint for question 23

Divide the magnitude of change by the initial amount.

Question 24. Which is the exact expression for remaining reactant concentration when initial C decreases by x?

C−x Cx C+x C/x

Hint for question 24

Translate a decrease into subtraction.

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