6th grade math

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Section 1: Ratios (12 points)

Part-to-Whole Ratios

  1. In a basket of 20 fruits, 12 are apples. Write the ratio of apples to total fruits in simplest form.
    Answer: ______
  2. A class has 18 students. If 10 are girls, what is the ratio of boys to the total class?
    Answer: ______

Ratios with Tape Diagrams & Word Problems

  1. 3. The ratio of red marbles to blue marbles in a bag is 3:5. If there are 24 blue marbles, how many red marbles are there?
    Answer: ______
  1. For every 4 pencils, there are 2 erasers. If there are 16 pencils, how many erasers are there?
    Answer: ______

Ratios and Measurements


5. A map scale is 1 inch : 10 miles. How many miles apart are two towns that are 4.5 inches apart on the map?
Answer: ______ miles

Ratios in Recipes (Word Problem)


6. A cookie recipe calls for 2 cups of flour for every 1 cup of sugar. If you use 5 cups of flour, how many cups of sugar do you need?
Answer: ______ cups

Section 2: Rates and Percentages (12 points)

Solving Unit Rate/Price Problems

  • 7. If 6 oranges cost $3.00, what is the cost per orange?
    Answer: $______
  1. A car travels 240 miles in 4 hours. What is the unit rate in miles per hour?
    Answer: ______ mph

Fraction, Decimal, and Percent Converting

  • 9. Write 3553​ as a decimal and a percent.
    Decimal: ______ Percent: ______
  1. Write 0.08 as a fraction in simplest form and as a percent.
    Fraction: ______ Percent: ______

Percent of a Number


11. Find 30% of 80.
Answer: ______

Finding Common Percentages


12. What is 50% of 200?
Answer: ______

Section 3: Negative Numbers (24 points)

Adding and Subtracting Negative Numbers
13. −5+8=−5+8= ______
14. 3−7=3−7= ______
15. −4+(−2)=−4+(−2)= ______
16. −9−(−3)=−9−(−3)= ______
17. 6+(−10)=6+(−10)= ______
18. −1−4=−1−4= ______
19. −7+12=−7+12= ______
20. 5−(−5)=5−(−5)= ______

Multiplying and Dividing Negative Numbers
21. −3×4=−3×4= ______
22. 5×(−2)=5×(−2)= ______
23. −6×(−3)=−6×(−3)= ______
24. −15÷3=−15÷3= ______
25. 20÷(−5)=20÷(−5)= ______
26. −24÷(−6)=−24÷(−6)= ______

Negative Numbers in Word Problems
27. The temperature at noon was 5°F. By midnight, it dropped 12 degrees. What was the temperature at midnight?
Answer: ______ °FA scuba diver is at –30 feet. She rises 15 feet. What is her new depth?
Answer: ______ feet

    Negative Fractions and Decimals
    29. −12+34=−21​+43​= ______
    30. −0.6−0.1=−0.6−0.1= ______
    31. −23×3=−32​×3= ______
    32. −1.5÷0.5=−1.5÷0.5= ______

    Section 4: Equations and Inequalities (30 points)

    Solving Equations
    33. x+8=15x+8=15
    x=x= ______

    1. 3y=273y=27
      y=y= ______
    2. z4=74z​=7
      z=z= ______
    3. 2m−5=112m−5=11
      m=m= ______

    Inequalities – Solve each inequality.
    37. x−3>4x−3>4
    Solution: xx ______

    1. 2n≤102n≤10
      Solution: nn ______
    2. −5<y+1−5<y+1
      Solution: yy ______

    Inequalities in Word Problems – Write the inequality only.
    40. Katie has at least $20. Write an inequality to represent the amount of money mm Katie has.
    Inequality: ______
    41.A number decreased by 7 is less than 15. Write an inequality.
    Inequality: ______

      Two-Step Inequalities – Solve.
      42. 3x+2≤143x+2≤14
      Solution: xx ______
      43.p2−1>32p​−1>3
      Solution: pp ______
      44.−4y+5≥17−4y+5≥17
      Solution: yy ______
      45.2(m−3)<102(m−3)<10
      Solution: mm ______

        Graphing Inequalities – Choose the correct description.
        46. Graph x≥2x≥2.
        Description: ______
        47.Graph n<−1n<−1.
        Description: ______

          Section 5: Plane Figures (22 points)

          Parallelogram Models
          48. Find the area of a parallelogram with a base of 9 cm and a height of 4 cm.
          Answer: ______ cm²
          49.A parallelogram has an area of 56 in² and a height of 7 in. What is the length of the base?
          Answer: ______ in

            Areas of Triangles (Missing Height or Base)
            50. A triangle has an area of 24 ft² and a base of 8 ft. What is its height?
            Answer: ______ ft
            51. A triangle has an area of 45 m² and a height of 10 m. What is the length of its base?
            Answer: ______ m

              Finding Areas of Quadrilaterals with Two Parallel Sides (Trapezoids)
              52. Find the area of a trapezoid with bases of 5 cm and 9 cm, and a height of 6 cm.
              Answer: ______ cm²
              53.A trapezoid has an area of 75 yd², a height of 5 yd, and one base of 10 yd. Find the length of the other base.
              Answer: ______ yd

                Challenge: Composite Figure
                54. Find the area of the figure made by attaching a triangle (base 6 in, height 4 in) to a rectangle (length 6 in, width 3 in).
                Answer: ______ in²
                55.A garden is shaped like a parallelogram with a base of 12 ft and height of 5 ft. Inside it, a triangular flower bed (base 6 ft, height 4 ft) is removed. Find the remaining area.
                Answer: ______ ft²

                  End of Test – Please check your work before submitting.

                  Answer Key for Teacher Use

                  Section 1: 1. 3:5, 2. 4:9, 3. 9, 4. 8, 5. 45, 6. 2.5
                  Section 2: 7. $0.50, 8. 60, 9. 0.6, 60%, 10. 2/25, 8%, 11. 24, 12. 100
                  Section 3: 13. 3, 14. –4, 15. –6, 16. –6, 17. –4, 18. –5, 19. 5, 20. 10, 21. –12, 22. –10, 23. 18, 24. –5, 25. –4, 26. 4, 27. –7, 28. –15, 29. 1/4, 30. –0.7, 31. –2, 32. –3
                  Section 4: 33. 7, 34. 9, 35. 28, 36. 8, 37. x>7x>7, 38. n≤5n≤5, 39. y>−6y>−6, 40. m≥20m≥20, 41. n−7<15n−7<15, 42. x≤4x≤4, 43. p>8p>8, 44. y≤−3y≤−3, 45. m<8m<8, 46. Closed circle at 2, shaded right, 47. Open circle at –1, shaded left
                  Section 5: 48. 36, 49. 8, 50. 6, 51. 9, 52. 42, 53. 20, 54. 30, 55. 48

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