🎉 Final Graphs Checkpoint
You have reached the end of the Graphs topic. This checkpoint tests whether you can combine skills from across the complete journey.
Work without looking back at the lessons first. Then use the lesson
pages to correct and understand any mistakes.
Confidence Checklist
- I can use coordinates and quadrants.
- I can choose and use scales.
- I can complete tables and plot graphs.
- I can use function notation.
- I can find gradient and intercepts.
- I can interpret linear, quadratic, cubic and inverse graphs.
- I can interpret distance–time, speed–time, displacement–time and velocity–time graphs.
- I can distinguish when gradient or area is needed.
Section A: Core Skills
- Write the coordinates of a point 4 units left and 3 units down from the origin.
- State the quadrant containing (6, −2).
- For f(x) = x² − 3x, find f(−2).
- Find the gradient through (1, −2) and (5, 10).
- State the y-intercept of y = −3x + 8.
- Find the x-intercept of y = 5x − 15.
Section B: Drawing and Interpretation
- Complete a table and draw y = 2x − 1 for −3 ≤ x ≤ 3.
- Use the graph to estimate x when y = 4.
- Draw y = x² − 2x − 3 for −2 ≤ x ≤ 4.
- Estimate the roots and turning point.
- Describe two differences between a quadratic graph and an inverse graph.
Section C: Exam-Style Travel Questions
- A cyclist travels 8 km in 20 minutes, rests for 10 minutes and then travels another 12 km in 30 minutes. Draw a distance–time graph and compare the speeds of the two moving sections.
- A car accelerates uniformly from 5 m/s to 25 m/s in 10 seconds. Find its acceleration.
- The car then travels at 25 m/s for 16 seconds. Find the distance travelled during this section.
- It decelerates uniformly to rest in 5 seconds. Find the distance during braking and the total distance for all three stages.
- A velocity–time graph contains an area of 75 m above the axis and 20 m below it. Find displacement and total distance.
Section D: Extension Thinking
- A straight line has equation y = mx + c and passes through (0, −3) and (4, 9). Find m and c.
- Explain how a graph can solve two equations simultaneously.
- Explain why the graph of y = 1/x approaches but never reaches either axis.
- Create a real-life situation that could be represented by a negative gradient.
✅ Check Your Work
Attempt the questions before opening the solutions.
Show answers and working
Section A
- (−4,−3)
- Quadrant IV.
- f(−2)=4+6=10.
- Gradient=(10−(−2))/(5−1)=3.
- 8.
- x=3.
Section B
- For x=−3,−2,−1,0,1,2,3, y=−7,−5,−3,−1,1,3,5.
- x=2.5.
- For x=−2 to 4, y=5,0,−3,−4,−3,0,5.
- Roots −1 and 3; turning point (1,−4).
- A quadratic is a continuous parabola and may cross an axis; an inverse graph has two separate branches and approaches axes as asymptotes.
Section C
- First speed=8÷(1/3)=24 km/h. Second speed=12÷0.5=24 km/h, so the moving speeds are equal. Plot (0,0), (20,8), (30,8), (60,20).
- a=(25−5)÷10=2 m/s².
- d=25×16=400 m.
- Braking distance=½×5×25=62.5 m. First stage distance=½(5+25)×10=150 m. Total=150+400+62.5=612.5 m.
- Displacement=75−20=55 m. Total distance=75+20=95 m.
Section D
- c=−3 and m=(9−(−3))/4=3, so y=3x−3.
- Plot both equations on the same axes; their intersection gives values satisfying both.
- x=0 is forbidden, and 1/x becomes arbitrarily small but never equals zero for finite x.
- Example: the value of a car decreases as its age increases.
Celebration Message
Graphs are not merely pictures. They are a mathematical language for
position, change, movement and relationships. You now have the tools to
read that language.
Where to Go Next
Revisit any lesson where your confidence is low, complete the mixed review again and then move to the Graphs worksheet and question bank when they are added.
Revision Guidance and Readiness
- Attempt the questions without notes first.
- Use the answers or worked solutions to identify the exact step that needs attention.
- Return to the relevant lesson, then retry missed questions.
- You are ready to move on when you can explain your method and check your result independently.