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Math Challenge: Exponents, Roots, and Percentages

Test your math skills with questions on exponents, roots, percentages, and more. From solving equations to simplifying expressions, this quiz covers a variety of mathematical concepts.

nicholas-sherman
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Math Challenge: Exponents, Roots, and Percentages

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  1. This and That

  2. Exponents & Roots

  3. What’s the Answer?

  4. Solve This

  5. Percents

  6. A Little Bit of Everything

  7. Solve This This & That What’s the Answer? Percents A Little Bit of Everything Exponents & Roots $100 $100 $100 $100 $100 $100 $200 $200 $200 $200 $200 $200 $300 $300 $300 $300 $300 $300 $400 $400 $400 $400 $400 $400 $500 $500 $500 $500 $500 $500

  8. $100 Question This & That • Explain why | 4 | = | -4 | . • Then show how to solve | -5 + 10 |.

  9. $100 Answer This & That They are both 4 units away from zero. -5 + 10 = 5 The absolute value of 5 is 5

  10. $200 Question This & That Simplify the following expressions:

  11. $200 Answer This & That A.) 4 B.) -6

  12. $300 Question This & That Is (-3, 16) is a solution to y = 3x + 25? Explain or show how you know.

  13. $300 Answer This & That (-3, 16) 16= 3(-3) + 25 16= -9 + 25 16= 16 Yes, (-3, 16) a solution

  14. $400 Question This & That Explain what the difference is between rational and irrational numbers. Give 3 examples of each type (Give at least one as a square root).

  15. $400 Answer This & That A rational number can always be written as a fraction. The decimals end or repeat. Examples: any fraction, whole #, integer, Square roots that have a perfect square Irrational numbers go on and on without repeating Example: Pi or square roots that don’t have a perfect square

  16. $500 Question This & That Evaluate the expression below. Show your steps 10 - (3 + 2)0 + 2-3

  17. $500 Answer This & That

  18. $100 Question Exponents& Roots Write the following problems into scientific notation: a.) 3080 b.) 0.000708

  19. $100 Answer Exponents & Roots A.) 3.08 ×103 B.) 7.08 ×10-4

  20. $200 Question Exponents & Roots Multiply. Leave your answer in scientific notation. (4.5 x 102) x (3 x 10-4)

  21. $200 Answer Exponents & Roots To keep the numbers in scientific notation, group the factors together and the powers of 10 together: (4.5 x 3) x (102 x 10-4) Then use the laws of exponents (add the exponents when bases are the same): 13.5 x 10-2. This is not in scientific notation, so 1.35 x 10-1

  22. $300 Question Exponents & Roots Show how to multiply exponents with the same base x9 • x8 Show how to divide exponents with the same base (-9)18 (-9)9 Show how to raise a power to a power? (32)-4

  23. $300 Answer Exponents & Roots Multiplying exponents with the same base x9 • x8 add the exponents x17 Dividing exponents with the same base (-9)18subtract the exponents (-9)9 (-9)9 Raising a power to a power? (32)-4 multiply the exponents 3-8

  24. $400 Question Exponents & Roots 15cm ? 9 cm Find the missing side.

  25. $400 Answer Exponents & Roots Use the Pythagorean Theorem c = 12 cm

  26. $500 Question Exponents & Roots For safety reasons, the base of a 24 foot ladder must be at least 8 feet from the base of the wall. To the nearest, tenth of a foot, how high can the 24 foot ladder reach?

  27. $500 Answer Exponents & Roots Use the Pythagorean Theorem. The ladder can safely reach about 22.6 ft. 24 ft. ? ft 8 ft.

  28. $100 Question What’s the Answer? Solve:

  29. $100 Answer What’s the Answer?

  30. $200 Question What’s the Answer? Solve: (-7)(-3.9) =

  31. $200 Answer What’s the Answer? 27.3

  32. $300 Question What’s the Answer?

  33. $300 Answer What’s the Answer?

  34. $400 Question What’s the Answer? Solve: 2.1 ÷ 0.07 =

  35. $400 Answer What’s the Answer? 30

  36. $500 Question What’s the Answer?

  37. $500 Answer What’s the Answer?

  38. $100 Question Solve This Solve for x: 9 = x – (-5)

  39. $100 Solve This First add the opposite to simplify the right side: 9 = x + (+5) Then use the -5 -5 Subtraction ------------------------ Property of Equality: 4 = x

  40. $200 Question Solve This Solve the equation: 20 – 4x = 40

  41. $200 Answer Solve This 20 – 4x = 40 -20 -20 -4x = 20 -4 -4 x = -5

  42. $300 Question Solve This Solve and graph the inequality: -5 + x < 25

  43. $300 Answer Solve This X < 30 Graph: open to the left

  44. $400 Question Solve This Connor works at a car dealership where he makes 15% commission on his sales. He sold a car and made $3,300. What was the price of the car he sold?

  45. $400 Answer Solve This 15% of Price of car = Commission 0.15 (p) = 3,300 p = $22,000 The car costs $22,000 You can also set up a proportion.

  46. $500 Question Solve This Jerry borrowed $16,000 to buy a new car. At the end of 5 years, he had repaid a total of $22,200. At what simple interest rate did he borrow the money?

  47. $500 Answer Solve This 22,200 – 16,000 = 6,200 (Int. paid) I = Prt 6,200 = 16,000 (r) 5 6,200 = 80,000(r) 0.0775 = r, so 7.75%

  48. $100 Question Percents 115 is what percent of 40?

  49. $100 Answer Percents 287.5%

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