Practice Maths

Gradient and Slope — Solutions

Click any answer to watch the solution video.

  1. Calculate the gradient from two points

    1. (0,0) and (3,6):
    2. (1,3) and (4,9):
    3. (2,5) and (6,13):
    4. (0,4) and (5,−1):
    5. (1,7) and (3,3):
    6. (−2,1) and (2,9):
    7. (3,3) and (7,3):
    8. (−1,−3) and (2,6):
    9. (0,10) and (4,2):
    10. (−3,5) and (1,−3):

  2. Classify gradient type

    1. m = 3:
    2. m = −5:
    3. m = 0:
    4. m = ½:
    5. m = −¾:
    6. Vertical line:
    7. m = −100:
    8. m = 0.01:

  3. Gradient from descriptions

    1. Road climbs 8 m per 100 m:
    2. Horizontal footpath:
    3. Ski slope drops 15 m per 30 m:
    4. Flagpole standing straight up:
    5. Ramp rises 1 m per 4 m:
    6. Line going down left to right:

  4. Steeper or gentler?

    1. m=3 vs m=5:
    2. m=−4 vs m=2:
    3. m=½ vs m=¼:
    4. m=−6 vs m=−2:
    5. m=1 vs m=−1:
    6. m=0.75 vs m=¾:

  5. Find the missing coordinate

    1. m=2; (1,3) and (4,?):
    2. m=−3; (0,5) and (2,?):
    3. m=4; (?,6) and (3,14):
    4. m=½; (2,1) and (6,?):
    5. m=−2; (1,8) and (?,2):
    6. m=3; (0,?) and (4,13):

  6. Real-world gradient problems

    1. Wheelchair ramp:
    2. Collinear points:
    3. Road gradient:
    4. Compare two lines:

  7. Ramp design

    1. (i) Ramp A gradient:
    2. (ii) Ramp B horizontal run:
    3. (iii) Compliance:

  8. Gradient from marked points on graph (y = 2x − 1)

    1. Marked points:
    2. Rise and run:
    3. Gradient:
    4. Verify with another pair:

  9. Two lines with different gradients (Line A: y = 3x; Line B: y = 12x)

    1. Steeper line:
    2. Gradient of Line A:
    3. Gradient of Line B:
    4. Why larger gradient = steeper:

  10. Negative gradient from graph (points (0, 1) and (2, −3))

    1. Gradient:
    2. Meaning of negative gradient:
    3. Compare to gradient −3: