DP Mathematical Studies Questionbank

• Syllabus

6.2

Sub sections and their related questions

Linear models.

• 12M.1.sl.TZ2.6b: Use the model to calculate the boiling point of water at a height of 1.37 km above sea level.
• 12M.1.sl.TZ2.6c: Water boils at the top of Mt. Everest at 70 °C. Use the model to calculate the height above sea...
• 07M.1.sl.TZ0.12c: Draw a sketch, in the space provided, to show how the prices can be found graphically.
• 09M.1.sl.TZ2.2a: Write down the fixed cost.
• 09M.1.sl.TZ2.2b: It takes \(3 \frac{1}{2}\) hours to complete a job for Paula. Find the total cost.
• 09M.1.sl.TZ2.2c: Steve received a bill for 510 AUD. Calculate the time it took the plumber to complete the job.
• SPM.1.sl.TZ0.13a: Using the model, write down a second equation in \(a\) and \(b\) .
• SPM.1.sl.TZ0.13b: Using your graphic display calculator or otherwise, find the value of \(a\) and of \(b\) .
• SPM.1.sl.TZ0.13c: Use the model to predict the temperature of the liquid \(60{\text{ seconds}}\) after the start of...
• 07N.2.sl.TZ0.1ii.b: On the same diagram, sketch the line \(y = 7 − 2x\) and find the coordinates of the point of...
• 14N.1.sl.TZ0.11a: Write down (i)     the \(x\)-intercept of the graph of \(y = {\text{ }}f(x)\); (ii)     the...
• 14N.1.sl.TZ0.11b: Solve \(f(x) = g(x)\).
• 14N.2.sl.TZ0.1g: A forest ranger uses her own formula for estimating the air temperature. She counts the number of...
• 14N.2.sl.TZ0.1h: A cricket makes 20 chirps in 15 seconds. For this chirp rate (i)     calculate an estimate for...
• 15M.1.sl.TZ1.12a: At 150°C the length of the iron bar is 180 mm. Write down an equation that shows this information.
• 15M.1.sl.TZ1.12b: At 210°C the length of the iron bar is 181.5 mm. Write down an equation that shows this second...
• 15M.2.sl.TZ2.6d: All the bicycles that are produced are sold. The bicycles are sold for 304 USD each. Explain why...
• 16N.2.sl.TZ0.1b: (i)     \({\bar x}\), the mean number of hours spent on social media; (ii)     \({\bar y}\), the...
• 16N.2.sl.TZ0.1c: Plot the point \((\bar x,{\text{ }}\bar y)\) on your scatter diagram and label this point M.
• 16N.2.sl.TZ0.1d: Write down the value of \(r\), the Pearson’s product–moment correlation coefficient, for these data.
• 16N.2.sl.TZ0.1h: Write down a reason why this estimate is not reliable.
• 16N.2.sl.TZ0.3f: Write down the length of MD correct to five significant figures.
• 17M.1.sl.TZ2.14c: Calculate how much extra money Jashanti needs.
• 17N.1.sl.TZ0.6a: Use this information to write down an equation involving \(x\) and \(y\).
• 17N.1.sl.TZ0.6b: Use this ratio to write down \(y\) in terms of \(x\).
• 17N.1.sl.TZ0.6c: Find the value of \(x\) and of \(y\).
• 18M.1.sl.TZ2.6a: Find the value of a.
• 18M.1.sl.TZ2.6b: Find the coordinates of R.
• 18M.1.sl.TZ2.6c: Line L3 is parallel to line L2 and passes through the point (2, 3). Find the equation of line...

Linear functions and their graphs, \(f\left( x \right) = mx + c\) .

• 10M.1.sl.TZ1.15b: Draw the line y = 5 on your sketch.
• 12N.2.sl.TZ0.5f: (i) Sketch the graph of y = g(x) for −2 ≤ x ≤ 5 and −15 ≤ y ≤ 25, indicating clearly your answer...
• 07M.1.sl.TZ0.12c: Draw a sketch, in the space provided, to show how the prices can be found graphically.
• SPM.1.sl.TZ0.7c: On the grid draw the graph of the function \(g(x) = 5 - 2x\) for the domain...
• 07N.2.sl.TZ0.1ii.b: On the same diagram, sketch the line \(y = 7 − 2x\) and find the coordinates of the point of...
• 08M.2.sl.TZ1.1c: On the same diagram as part (a) sketch the graph of \(g(x) = x + 0.5\) .
• 08M.2.sl.TZ1.4i.d: (i)     Sketch the graphs of the two equations from parts (a) and (b). (ii)    Write down the...
• 08M.2.sl.TZ2.4i.f: (i) Draw and label the line \( y = 1\) on your graph. (ii) The equation \(f(x) = 1\) has two...
• 14N.1.sl.TZ0.11a: Write down (i)     the \(x\)-intercept of the graph of \(y = {\text{ }}f(x)\); (ii)     the...
• 14N.1.sl.TZ0.11c: Write down the interval for the values of \(x\) for which \(f(x) > g(x)\).
• 14N.2.sl.TZ0.1g: A forest ranger uses her own formula for estimating the air temperature. She counts the number of...
• 14N.2.sl.TZ0.1h: A cricket makes 20 chirps in 15 seconds. For this chirp rate (i)     calculate an estimate for...
• 15M.1.sl.TZ1.12a: At 150°C the length of the iron bar is 180 mm. Write down an equation that shows this information.
• 15M.1.sl.TZ1.12b: At 210°C the length of the iron bar is 181.5 mm. Write down an equation that shows this second...
• 16N.2.sl.TZ0.1a: On graph paper, draw a scatter diagram for these data. Use a scale of 2 cm to represent 5 hours...
• 16N.2.sl.TZ0.1b: (i)     \({\bar x}\), the mean number of hours spent on social media; (ii)     \({\bar y}\), the...
• 16N.2.sl.TZ0.1c: Plot the point \((\bar x,{\text{ }}\bar y)\) on your scatter diagram and label this point M.
• 16N.2.sl.TZ0.1d: Write down the value of \(r\), the Pearson’s product–moment correlation coefficient, for these data.
• 16N.2.sl.TZ0.1h: Write down a reason why this estimate is not reliable.
• 16N.2.sl.TZ0.3f: Write down the length of MD correct to five significant figures.
• 17M.1.sl.TZ2.14c: Calculate how much extra money Jashanti needs.
• 17N.1.sl.TZ0.6a: Use this information to write down an equation involving \(x\) and \(y\).
• 17N.1.sl.TZ0.6b: Use this ratio to write down \(y\) in terms of \(x\).
• 17N.1.sl.TZ0.6c: Find the value of \(x\) and of \(y\).
• 18M.1.sl.TZ2.6a: Find the value of a.
• 18M.1.sl.TZ2.6b: Find the coordinates of R.
• 18M.1.sl.TZ2.6c: Line L3 is parallel to line L2 and passes through the point (2, 3). Find the equation of line...