DP Mathematical Studies Questionbank

• Syllabus

6.1

Sub sections and their related questions

Concept of a function, domain, range and graph.

• 10M.1.sl.TZ1.14a: Use the mapping diagram to write down two equations in terms of a and b.
• 10M.1.sl.TZ2.13d: The axis of symmetry is x = 2.5.x Write down the range of y.
• 10N.1.sl.TZ0.10d: The minimum value for y is – 4. Write down the range of f (x).
• 11N.1.sl.TZ0.13b: Sketch the graph of \(y = f(x)\) for the domain \( - 1 \leqslant x \leqslant 3\).
• 12N.1.sl.TZ0.10c: Write down the range of this quadratic function.
• 12N.2.sl.TZ0.5h: Write down the interval for which g(x) is increasing in the domain 0 < x < 5 .
• 12M.1.sl.TZ2.11b: The domain of f is  0 ≤ x ≤ 6. Find the range of f .
• 09N.1.sl.TZ0.11a: find the range of \(f\).
• 09M.1.sl.TZ1.7c: Write down the range of \(f (x)\).
• 11M.2.sl.TZ1.3a: Calculate \(f(2)\) .
• 11M.2.sl.TZ1.3f: Find the range of \(f\) .
• 13M.2.sl.TZ1.4d: Find the range of \(f\).
• 11M.2.sl.TZ2.5g: Using your sketch from (e), determine the range of the function \(f(x)\) for...
• SPM.1.sl.TZ0.7a: On the grid below sketch the graph of the function \(f(x) = 2{(1.6)^x}\) for the domain...
• SPM.1.sl.TZ0.7c: On the grid draw the graph of the function \(g(x) = 5 - 2x\) for the domain...
• SPM.2.sl.TZ0.4e: Some sea creatures have adapted so they can see in low intensity light and cannot tolerate too...
• 08M.1.sl.TZ1.11b: A function \(f\) is given by...
• 08M.1.sl.TZ2.10b: A function is defined as \(f(x) = 1 + {x^3}\) for...
• 15M.1.sl.TZ1.14c: The vertex of the function is \((3,{\text{ }}27)\). Write down the range of \(f\).
• 15M.1.sl.TZ2.15d: The range of \(A(x)\) is \(m \leqslant A(x) \leqslant n\). Hence write down the value of \(m\)...
• 15M.2.sl.TZ1.5f: The graph of \(y = f(x)\) has a local minimum point at \(x = 4\). Sketch the graph of...
• 16N.2.sl.TZ0.3f: Write down the length of MD correct to five significant figures.
• 259485: This is an example question for the example test. You can delete this question.
• 18M.2.sl.TZ1.4a: Find the value of k.
• 18M.2.sl.TZ1.4b: Using your value of k , find f ′(x).
• 18M.2.sl.TZ1.4c: Use your answer to part (b) to show that the minimum value of f(x) is −22 .
• 18M.2.sl.TZ1.4d: Write down the two values of x which satisfy f (x) = 0.
• 18M.2.sl.TZ1.4e: Sketch the graph of y = f (x) for 0 < x ≤ 6 and −30 ≤ y ≤ 60.Clearly indicate the minimum...
• 18M.2.sl.TZ2.6a: Sketch the curve for −1 < x < 3 and −2 < y < 12.
• 18M.2.sl.TZ2.6b: A teacher asks her students to make some observations about the curve. Three students...
• 18M.2.sl.TZ2.6c: Find the value of y when x = 1 .
• 18M.2.sl.TZ2.6d: Find \(\frac{{{\text{dy}}}}{{{\text{dx}}}}\).
• 18M.2.sl.TZ2.6e: Show that the stationary points of the curve are at x = 1 and x = 2.
• 18M.2.sl.TZ2.6f: Given that y = 2x3 − 9x2 + 12x + 2 = k has three solutions, find the possible values of k.

Function notation, eg \(f\left( x \right)\), \(v\left( t \right)\), \(C\left( n \right)\) .

• 10M.2.sl.TZ1.3a: Write down the values of x where the graph of f (x) intersects the x-axis.
• 12N.1.sl.TZ0.10a: It is given that f (2) = −5 . Find the value of a .
• 12M.1.sl.TZ1.14a: Find the value of (i) p ; (ii) q .
• 12M.1.sl.TZ1.14b: Write down the value of r .
• 12M.1.sl.TZ1.14c: Find the value of s .
• 12M.2.sl.TZ1.5b: Find the value of f (−1).
• 11M.2.sl.TZ1.3a: Calculate \(f(2)\) .
• 13M.2.sl.TZ1.4a: Calculate \(f (1)\).
• 13N.1.sl.TZ0.12a: Using the mapping diagram, write down two equations in terms of \(a\) and \(b\).
• 13N.2.sl.TZ0.4a: Find \(f( - 2)\).
• 14N.1.sl.TZ0.11b: Solve \(f(x) = g(x)\).
• 14N.1.sl.TZ0.11c: Write down the interval for the values of \(x\) for which \(f(x) > g(x)\).
• 15M.2.sl.TZ2.5a: Find \(f( - 2)\).
• 16N.2.sl.TZ0.3f: Write down the length of MD correct to five significant figures.
• 18M.2.sl.TZ1.4a: Find the value of k.
• 18M.2.sl.TZ1.4b: Using your value of k , find f ′(x).
• 18M.2.sl.TZ1.4c: Use your answer to part (b) to show that the minimum value of f(x) is −22 .
• 18M.2.sl.TZ1.4d: Write down the two values of x which satisfy f (x) = 0.
• 18M.2.sl.TZ1.4e: Sketch the graph of y = f (x) for 0 < x ≤ 6 and −30 ≤ y ≤ 60.Clearly indicate the minimum...
• 18M.2.sl.TZ2.6a: Sketch the curve for −1 < x < 3 and −2 < y < 12.
• 18M.2.sl.TZ2.6b: A teacher asks her students to make some observations about the curve. Three students...
• 18M.2.sl.TZ2.6c: Find the value of y when x = 1 .
• 18M.2.sl.TZ2.6d: Find \(\frac{{{\text{dy}}}}{{{\text{dx}}}}\).
• 18M.2.sl.TZ2.6e: Show that the stationary points of the curve are at x = 1 and x = 2.
• 18M.2.sl.TZ2.6f: Given that y = 2x3 − 9x2 + 12x + 2 = k has three solutions, find the possible values of k.

Concept of a function as a mathematical model.

• 12M.1.sl.TZ1.14a: Find the value of (i) p ; (ii) q .
• 12M.1.sl.TZ1.14b: Write down the value of r .
• 12M.1.sl.TZ1.14c: Find the value of s .
• 13M.2.sl.TZ1.4a: Calculate \(f (1)\).
• 13N.1.sl.TZ0.12a: Using the mapping diagram, write down two equations in terms of \(a\) and \(b\).
• 14N.1.sl.TZ0.11a: Write down (i)     the \(x\)-intercept of the graph of \(y = {\text{ }}f(x)\); (ii)     the...
• 16N.2.sl.TZ0.3f: Write down the length of MD correct to five significant figures.
• 18M.2.sl.TZ1.4a: Find the value of k.
• 18M.2.sl.TZ1.4b: Using your value of k , find f ′(x).
• 18M.2.sl.TZ1.4c: Use your answer to part (b) to show that the minimum value of f(x) is −22 .
• 18M.2.sl.TZ1.4d: Write down the two values of x which satisfy f (x) = 0.
• 18M.2.sl.TZ1.4e: Sketch the graph of y = f (x) for 0 < x ≤ 6 and −30 ≤ y ≤ 60.Clearly indicate the minimum...
• 18M.2.sl.TZ2.6a: Sketch the curve for −1 < x < 3 and −2 < y < 12.
• 18M.2.sl.TZ2.6b: A teacher asks her students to make some observations about the curve. Three students...
• 18M.2.sl.TZ2.6c: Find the value of y when x = 1 .
• 18M.2.sl.TZ2.6d: Find \(\frac{{{\text{dy}}}}{{{\text{dx}}}}\).
• 18M.2.sl.TZ2.6e: Show that the stationary points of the curve are at x = 1 and x = 2.
• 18M.2.sl.TZ2.6f: Given that y = 2x3 − 9x2 + 12x + 2 = k has three solutions, find the possible values of k.