Free Grade 3 Working with Gradient Common Errors Quizzes
Free Grade 3 quizzes for Working with Gradient Common Errors: 12 real questions with a full answer key and worked solutions. A coordinate (x, y) gives a position: across first, then up. The gradient of a line is rise over run, and y = mx + c describes a straight line.
Free
Stretch
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with gradient common errors
Identify working with gradient common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with gradient common errors
Explain working with gradient common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with gradient common errors
Calculate working with gradient common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with gradient common errors
Compare working with gradient common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
Prerequisites
Close these gaps first — each has its own free lesson, worksheet and quiz.
How Working with Gradient Common Errors works
A coordinate (x, y) gives a position: across first, then up. The gradient of a line is rise over run, and y = mx + c describes a straight line.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.Which quadrant is the point (5, 3) in?[1]
- 2.Which quadrant is the point (4, 5) in?[1]
- 3.Which quadrant is the point (2, -6) in?[1]
- 4.Which quadrant is the point (-2, -5) in?[1]
- 5.Find the midpoint of (-3, -1) and (5, -5).[2]
- 6.Find the midpoint of (-2, -4) and (0, -8).[2]
- 7.Find the midpoint of (-4, -3) and (0, -9).[2]
- 8.Find the midpoint of (-6, 3) and (-4, 1).[2]
- 9.Find the equation of the line through (4, -1) and (12, -7).[3]
- 10.Find the equation of the line through (-4, -1) and (2, -5).[3]
- 11.Find the equation of the line through (0, -2) and (10, 6).[3]
- 12.Find the equation of the line through (-6, 2) and (-2, -6).[3]
Show answers and working
1. First quadrant
x is positive, y is positive. Quadrants go anticlockwise from top-right.
2. First quadrant
x is positive, y is positive. Quadrants go anticlockwise from top-right.
3. Fourth quadrant
x is positive, y is negative. Quadrants go anticlockwise from top-right.
4. Third quadrant
x is negative, y is negative. Quadrants go anticlockwise from top-right.
5. (1, -3)
Average the x values: (-3 + 5) ÷ 2 = 1. Average the y values: (-1 + -5) ÷ 2 = -3.
6. (-1, -6)
Average the x values: (-2 + 0) ÷ 2 = -1. Average the y values: (-4 + -8) ÷ 2 = -6.
7. (-2, -6)
Average the x values: (-4 + 0) ÷ 2 = -2. Average the y values: (-3 + -9) ÷ 2 = -6.
8. (-5, 2)
Average the x values: (-6 + -4) ÷ 2 = -5. Average the y values: (3 + 1) ÷ 2 = 2.
9. y = -0.75x + 2
Gradient m = (-7 − -1) / (12 − 4) = -0.75. Substitute (4, -1): c = -1 − -0.75 × 4 = 2.
10. y = -0.67x − 3.67
Gradient m = (-5 − -1) / (2 − -4) = -0.67. Substitute (-4, -1): c = -1 − -0.67 × (-4) = -3.67.
11. y = 0.8x − 2
Gradient m = (6 − -2) / (10 − 0) = 0.8. Substitute (0, -2): c = -2 − 0.8 × 0 = -2.
12. y = -2x − 10
Gradient m = (-6 − 2) / (-2 − -6) = -2. Substitute (-6, 2): c = 2 − -2 × (-6) = -10.
Worked examples
Which quadrant is the point (1, -4) in?
- x is positive, y is negative.
- Quadrants go anticlockwise from top-right.
- Answer: Fourth quadrant
Find the midpoint of (-5, -3) and (3, -3).
- Average the x values: (-5 + 3) ÷ 2 = -1.
- Average the y values: (-3 + -3) ÷ 2 = -3.
- Answer: (-1, -3)
Find the equation of the line through (-3, 6) and (1, 12).
- Gradient m = (12 − 6) / (1 − -3) = 1.5.
- Substitute (-3, 6): c = 6 − 1.5 × (-3) = 10.5.
- Answer: y = 1.5x + 10.5
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Plots (y, x) instead of (x, y).
Correction: Along the corridor, then up the stairs.
Calculates gradient as run over rise.
Correction: Gradient = change in y ÷ change in x.
Teacher tips
- · Play coordinate battleships.
Parent tips
- · Find places on a map using grid references.
Real-life applications
- · Maps, game boards, GPS.
Assessment objectives
How mastery is evidenced, and which standards it maps to.
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Frequently asked
- Is this Grade 3 Working with Gradient Common Errors quiz really free?
- Yes. Every quizzes on FreeMathWorksheet is free to use, print and share — no account, no paywall and no watermark.
- What should a learner already know before this?
- Start with Working with Gradient Word Problems, Working with Gradient Techniques, Introducing Gradient. Each one has its own free lesson, worksheet and quiz.
- How is the quiz sequenced?
- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- What comes next after Working with Gradient Common Errors?
- Move on to Introducing Gradient, Gradient in Context, which build directly on this idea.
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