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Graphs of Functions and Graphical Solution

Secondary 3 practice

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Graphs of Functions and Graphical Solution practice questions

Secondary 3 topics from the O-Level Mathematics 4052 syllabus. Every question below has a full worked solution.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

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What this topic covers

Worked examples

Example 1

Given y=6x+1y = \dfrac{6}{x} + 1, find the value of yy when x=−3x = -3.
Show the worked solution
  • y=6x+1y = \dfrac{6}{x} + 1
  • Substitute x=−3x = -3:
  • y=6(−3)+1substitutey = \dfrac{6}{(-3)} + 1 \quad \scriptsize\textit{substitute}
  • y=−2+1y = -2 + 1
  • y=−1y = -1

Answer: −1-1

Example 2

The graph of y=x3+5xy = x^3 + 5x has been drawn. Using the graph, a horizontal line y=ky = k is drawn to solve x3+5x−2=0x^3 + 5x - 2 = 0. Find the value of kk.
xyy = x3 + 5x-60-40-20204060-3-2-1123O
Show the worked solution
  • We need to solve x3+5x−2=0x^3 + 5x - 2 = 0.
  • Rearrange so that the left-hand side matches the drawn graph y=x3+5xy = x^3 + 5x:
  • x3+5x=2rearrangex^3 + 5x = 2 \quad \scriptsize\textit{rearrange}
  • The graph of y=x3+5xy = x^3 + 5x intersects the horizontal line y=2y = 2 at the solution.
  • k=2k = 2

Answer: 22

Example 3

An object accelerates uniformly from rest to 1010 m/s in 66 seconds, travels at 1010 m/s for 1010 seconds, then decelerates uniformly to rest in 66 seconds. Find the total distance travelled, in metres.
Show the worked solution
  • Distance == area under the speed-time graph
  • The graph is a trapezium. Split into three regions:
  • Triangle (acceleration phase): 12×6×10=30\dfrac{1}{2} \times 6 \times 10 = 30 m
  • Rectangle (constant speed): 10×10=10010 \times 10 = 100 m
  • Triangle (deceleration phase): 12×6×10=30\dfrac{1}{2} \times 6 \times 10 = 30 m
  • Total distance=30+100+30\text{Total distance} = 30 + 100 + 30
  • =160= 160 m

Answer: 160160

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Which syllabus does this follow?

O-Level Mathematics (4052), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.

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