Unit 1 · Checkpoint quiz

Unit 1 checkpoint: Number skills

12 questions · about 25-30 minutes · no time limit

Answer every question, then press Grade my answers at the bottom. You'll see what you got right, a worked solution for each question, and links to the lessons worth revisiting. Pencil and paper are encouraged.

This is practice, not a test of you. A low score just shows where to look next.

Compute \(-8 + 3 - (-6)\).

Subtracting \(-6\) is the same as adding 6: \(-8 + 3 + 6\).

\(-8 + 3 = -5\), then \(-5 + 6 = 1\).

Answer: \(1\).

Multiply and simplify: \(\dfrac{4}{9} \cdot \dfrac{15}{8}\).

Cancel first: 4 and 8 share a 4 (leaving 1 and 2); 15 and 9 share a 3 (leaving 5 and 3).

\(\dfrac{1}{3} \cdot \dfrac{5}{2} = \dfrac{5}{6}\).

Answer: \(\dfrac{5}{6}\).

Divide: \(-\dfrac{5}{6} \div \dfrac{10}{9}\).

Multiply by the reciprocal: \(-\dfrac{5}{6} \cdot \dfrac{9}{10}\).

Cancel: 5 and 10 share a 5 (leaving 1 and 2); 9 and 6 share a 3 (leaving 3 and 2).

\(-\dfrac{1 \cdot 3}{2 \cdot 2} = -\dfrac{3}{4}\). Answer: \(-\dfrac{3}{4}\).

Add: \(\dfrac{3}{8} + \dfrac{5}{12}\).

The LCD of 8 and 12 is 24.

\(\dfrac{3}{8} = \dfrac{9}{24}\) and \(\dfrac{5}{12} = \dfrac{10}{24}\).

\(\dfrac{9}{24} + \dfrac{10}{24} = \dfrac{19}{24}\). Answer: \(\dfrac{19}{24}\).

Subtract: \(3\tfrac{1}{2} - \dfrac{5}{6}\).

Mixed number to improper fraction: \(3\tfrac{1}{2} = \dfrac{7}{2}\).

LCD is 6: \(\dfrac{7}{2} = \dfrac{21}{6}\). Then \(\dfrac{21}{6} - \dfrac{5}{6} = \dfrac{16}{6}\).

Simplify: \(\dfrac{16}{6} = \dfrac{8}{3}\). Answer: \(\dfrac{8}{3}\), which is \(2\tfrac{2}{3}\).

Compute \(20 - 3(4 - 6)^2 \div 6\).

Parentheses: \(4 - 6 = -2\). Exponent: \((-2)^2 = 4\).

Multiply and divide, left to right: \(3 \cdot 4 = 12\), then \(12 \div 6 = 2\).

Subtract: \(20 - 2 = 18\). Answer: \(18\).

Which expression is equal to \(9\)?

  1. \(-3^2\)
  2. \(-(3^2)\)
  3. \((-3)^2\)
  4. \(-3 \cdot 3\)

In \(-3^2\) the exponent applies only to the 3: \(-3^2 = -(3 \cdot 3) = -9\). Choice b is the same thing, and d is also \(-9\).

In \((-3)^2\) the parentheses square the whole \(-3\): \((-3)(-3) = 9\).

Answer: c.

Compute \(\dfrac{12 - 2^3}{\sqrt{16} + 4}\).

The fraction bar groups the top and the bottom. Top: \(12 - 8 = 4\).

Bottom: \(\sqrt{16} + 4 = 4 + 4 = 8\).

\(\dfrac{4}{8} = \dfrac{1}{2}\). Answer: \(\dfrac{1}{2}\).

Evaluate \(b^2 - 4ac\) when \(a = 2\), \(b = -3\), and \(c = -5\).

Substitute with parentheses: \((-3)^2 - 4(2)(-5)\).

\((-3)^2 = 9\) and \(4(2)(-5) = -40\).

\(9 - (-40) = 9 + 40 = 49\). Answer: \(49\).

Evaluate \(-2x^2 + x\) when \(x = -3\).

Substitute with parentheses: \(-2(-3)^2 + (-3)\).

Exponent first: \((-3)^2 = 9\), so \(-2 \cdot 9 = -18\).

\(-18 + (-3) = -21\). Answer: \(-21\).

Simplify \(4(3x - 2) - 2(5x - 7)\).

Distribute the 4 and the \(-2\): \(12x - 8 - 10x + 14\). (The \(-2\) times \(-7\) gives \(+14\).)

Combine like terms: \(12x - 10x = 2x\) and \(-8 + 14 = 6\).

Answer: \(2x + 6\).

Which expression is equivalent to \(5 - 2(x - 3)\)?

  1. \(3x - 9\)
  2. \(-2x - 1\)
  3. \(-2x + 8\)
  4. \(-2x + 11\)

Multiplication comes before subtraction, so distribute the \(-2\) first: \(-2(x - 3) = -2x + 6\).

Then \(5 - 2x + 6 = -2x + 11\).

Answer: d. (Choice a comes from doing \(5 - 2\) first; b from forgetting that \(-2 \cdot -3 = +6\).)

Want to look something up first? Number skills cheat sheet · Glossary

Confused by a solution? Ask your teacher bot to walk through that exact question with you.