• Syllabus

5.1

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Sub sections and their related questions

Equation of a line in two dimensions: the forms \(y = mx + c\) and \(ax + by + d = 0\) .

• 10M.1.sl.TZ2.4d: The line L2 is perpendicular to L1 and passes through the point (3, 7). Find the equation of L2....
• 10M.2.sl.TZ1.2a.i: Find the coordinates of A.
• 11N.1.sl.TZ0.7c: Find the equation of the line parallel to AB that passes through M.
• 10N.1.sl.TZ0.4: The following diagrams show six lines with equations of the form y =mx +c. In the table below...
• 10N.2.sl.TZ0.2c: L2 passes through A and is perpendicular to AB. Write down the equation of L2. Give your answer...
• 12N.1.sl.TZ0.8a: Write down the gradient of L1 .
• 12N.1.sl.TZ0.8b: Line L2, is perpendicular to line L1, and passes through the point (4, 5) . (i) Write down the...
• 12M.1.sl.TZ1.9a: Explain why point P is not on the line L.
• 12M.1.sl.TZ1.9c: (i) Write down the gradient of a line perpendicular to line L. (ii) Find the equation of the...
• 09N.1.sl.TZ0.10c: Let M be the midpoint of the line segment AB. Find the equation of the line perpendicular to AB...
• 11N.2.sl.TZ0.4f: The line, \(L\) , passes through the point A and is perpendicular to the tangent at A. Find the...
• 09M.1.sl.TZ1.15a: Find the gradient of L.
• 11M.1.sl.TZ1.10a: Find(i)     the gradient of \({L_1}\) ;(ii)    the equation of \({L_1}\) .
• 11M.1.sl.TZ1.13a: Calculate the gradient of \({R_2}\) .
• 11M.1.sl.TZ1.13b: The point of intersection of \({R_1}\) and \({R_2}\) is \((4{\text{, }}k)\) .Find(i)     the...
• 09M.2.sl.TZ1.3c: Find the equation of line CD. Give your answer in the form \(ax + by = c\) where...
• 13M.1.sl.TZ1.10a: Give a reason why L1 does not pass through A.
• 11M.1.sl.TZ2.5b: Find the equation of \(L\) .
• 13M.1.sl.TZ1.10d: L2 does pass through A. Find the value of c.
• 13M.1.sl.TZ2.8a: Write down the gradient of the line L1.
• 13M.1.sl.TZ2.8b: A second line L2 is perpendicular to L1. Write down the gradient of L2.
• 13M.1.sl.TZ2.8c: The point (5, 3) is on L2. Determine the equation of L2.
• 13M.2.sl.TZ2.5e: Scott starts from a point C(0,150) . He hikes along a straight road towards the bicycle track,...
• 07N.1.sl.TZ0.13b: Find the equation of the straight line perpendicular to AB, passing through the point M.
• 08N.1.sl.TZ0.7a: Find the gradient of \({L_1}\) .
• 08N.1.sl.TZ0.7b: The equation of line \({L_2}\) is \(y = mx\) . \({L_2}\) is perpendicular to \({L_1}\) . Find...
• 08N.1.sl.TZ0.7c: The equation of line \({L_2}\) is \(y = mx\) . \({L_2}\) is perpendicular to \({L_1}\) . Find...
• 08M.1.sl.TZ2.6c: Find the equation of the line which is perpendicular to \(y = 3x + 4\) and which passes through...
• 08M.2.sl.TZ2.5a: Write down the coordinates of point \({\text{E}}\).
• 08M.2.sl.TZ2.5b: \({\text{C}}\) is a point on the line \({\text{DE}}\). \({\text{B}}\) is a point on the...
• 09M.1.sl.TZ2.9b, ii: Given that the line AC is perpendicular to the line AB find the value of p.
• 10M.2.sl.TZ1.2a.ii: Find the coordinates of B.
• 10M.2.sl.TZ1.2c.ii: N lies on the line AB. The line CN is perpendicular to the line AB. Find the equation of CN.  
• 14M.1.sl.TZ2.7c: The equation of a second wheelchair ramp, B, is \(2x + 24y - 1920 = 0\). (i)     Determine...
• 13N.2.sl.TZ0.4g: The line \(L\) passes through the point \((2, −12)\) and is perpendicular to \(T\). \(L\) has...
• 14M.1.sl.TZ1.10c: Point \({\text{P}}(2,16)\) lies on the graph of \(f\). Find the equation of the normal to the...
• 14N.1.sl.TZ0.7c: Find the value of \(n\).
• 14N.2.sl.TZ0.6a: The equation of the line BC is \(y = 4\). Write down the coordinates of point C.
• 14N.2.sl.TZ0.6b: The \(x\)-coordinate of point B is \(a\). (i)     Write down the coordinates of point B; (ii)  ...
• 14N.2.sl.TZ0.6c: Point A lies on the \(x\)-axis and the line AB is perpendicular to line OB. (i)     Write down...
• 14N.2.sl.TZ0.6d: The area of triangle AOB is three times the area of triangle OBC. Find an expression, in terms...
• 14N.2.sl.TZ0.6e: Calculate the value of \(a\).
• 15M.1.sl.TZ1.3c: The line \({L_2}\) is parallel to \({L_1}\) and passes through the point \((3,{\text{...
• 15M.1.sl.TZ2.3a: Write down (i)     the gradient of \({L_1}\); (ii)     the \(y\)-intercept of \({L_1}\).
• 15M.1.sl.TZ2.3b: The line \({L_2}\) is parallel to \({L_1}\) and passes through the point...
• 15M.1.sl.TZ2.3c: The line \({L_2}\) is parallel to \({L_1}\) and passes through the point...
• 15M.2.sl.TZ1.5e: The graph of \(y = f(x)\) has a local minimum point at \(x = 4\). Find the equation of the...
• 16N.2.sl.TZ0.3a: Show that A lies on \({L_1}\).
• 17N.1.sl.TZ0.2a: Find the coordinates of M.
• 17N.1.sl.TZ0.2b: Find the gradient of \({L_1}\).
• 17N.1.sl.TZ0.2c.i: Write down the gradient of \({L_2}\).
• 17N.1.sl.TZ0.2c.ii: Write down, in the form \(y = mx + c\), the equation of \({L_2}\).
• 18M.1.sl.TZ2.5a.i: Calculate the amount of money he has in the account after 5 years.
• 18M.1.sl.TZ2.5a.ii: Write down the amount of interest he earned after 5 years.
• 18M.1.sl.TZ2.5b: Karl decides to donate this interest to a charity in France. The charity receives 170 euros...

Gradient; intercepts.

• 10M.1.sl.TZ2.4a: Write down the y intercept of L1.
• 10M.1.sl.TZ2.4b: Write down the gradient of L1.
• 10M.2.sl.TZ1.2a.i: Find the coordinates of A.
• 11N.1.sl.TZ0.7b: Calculate the gradient of the line AB.
• 10N.1.sl.TZ0.4: The following diagrams show six lines with equations of the form y =mx +c. In the table below...
• 10N.2.sl.TZ0.2a: Find the gradient of AB.
• 10N.2.sl.TZ0.2b: L1 passes through C and is parallel to AB. Write down the y-intercept of L1.
• 12N.1.sl.TZ0.8a: Write down the gradient of L1 .
• 12N.1.sl.TZ0.8b: Line L2, is perpendicular to line L1, and passes through the point (4, 5) . (i) Write down the...
• 12M.1.sl.TZ1.9b: Find the gradient of line L.
• 09N.1.sl.TZ0.10a: Find the gradient of the line AB.
• 09M.1.sl.TZ1.4a: Write down the y-intercept of the line AB.
• 09M.1.sl.TZ1.4b: Calculate the gradient of the line AB.
• 09M.1.sl.TZ1.15a: Find the gradient of L.
• 11M.1.sl.TZ1.10a: Find(i)     the gradient of \({L_1}\) ;(ii)    the equation of \({L_1}\) .
• 09M.2.sl.TZ1.3a: Calculate the gradient of line CD.
• 11M.1.sl.TZ2.5a: Calculate the gradient of \(L\) .
• 09M.1.sl.TZ2.7a: Find the coordinates of P and of Q.
• 09M.1.sl.TZ2.9a: Calculate the gradient of the line AB.
• 09M.1.sl.TZ2.9b, i: Given that the line AC is perpendicular to the line AB write down the gradient of the line AC.
• 09M.1.sl.TZ2.11b: Let L be the line with equation y = 3x + 2. Write down the gradient of a line parallel to L.
• 13M.1.sl.TZ1.10b: Find the gradient of L1.
• 13M.2.sl.TZ1.4f: Points A and B lie on the graph of f . The x-coordinates of A and B are 1 and 7...
• 13M.1.sl.TZ2.8a: Write down the gradient of the line L1.
• 13M.2.sl.TZ2.5d: (i) Write down the midpoint of the line segment OB. (ii) Find the gradient of the line segment OB.
• 07M.1.sl.TZ0.10a: Determine the (i) coordinates of M, the midpoint of P and Q. (ii) gradient of the line drawn...
• 07M.1.sl.TZ0.10b: The perpendicular line drawn through M meets the y-axis at R (0, k). Find k.
• 07N.2.sl.TZ0.5a: Find the gradient of the line L.
• 08N.1.sl.TZ0.7a: Find the gradient of \({L_1}\) .
• 08N.2.sl.TZ0.5d: Let \({L_1}\) be the tangent to the curve at \(x = 2\). Let \({L_2}\) be a tangent to the curve,...
• 08M.2.sl.TZ1.1e: Write down the gradient of the line \(g(x) = x + 0.5\) .
• 08M.1.sl.TZ2.6a: Write down the gradient of the line \(y = 3x + 4\).
• 08M.2.sl.TZ2.5a: Write down the coordinates of point \({\text{E}}\).
• 08M.2.sl.TZ2.5b: \({\text{C}}\) is a point on the line \({\text{DE}}\). \({\text{B}}\) is a point on the...
• 10M.2.sl.TZ1.2a.ii: Find the coordinates of B.
• 14M.1.sl.TZ2.7a: Use the diagram above to calculate the gradient of the ramp.
• 14M.1.sl.TZ2.7b: The gradient for a safe descending wheelchair ramp is \( - \frac{1}{{12}}\). Using your answer...
• 14M.1.sl.TZ2.7c: The equation of a second wheelchair ramp, B, is \(2x + 24y - 1920 = 0\). (i)     Determine...
• 13N.2.sl.TZ0.4g: The line \(L\) passes through the point \((2, −12)\) and is perpendicular to \(T\). \(L\) has...
• 14M.1.sl.TZ1.9b: Find the gradient of the line AB.
• 14N.1.sl.TZ0.7c: Find the value of \(n\).
• 14N.2.sl.TZ0.6b: The \(x\)-coordinate of point B is \(a\). (i)     Write down the coordinates of point B; (ii)  ...
• 14N.2.sl.TZ0.6c: Point A lies on the \(x\)-axis and the line AB is perpendicular to line OB. (i)     Write down...
• 14N.2.sl.TZ0.6d: The area of triangle AOB is three times the area of triangle OBC. Find an expression, in terms...
• 15M.1.sl.TZ1.3b: Calculate the gradient of \({L_1}\).
• 15M.1.sl.TZ2.3a: Write down (i)     the gradient of \({L_1}\); (ii)     the \(y\)-intercept of \({L_1}\).
• 15M.1.sl.TZ2.3b: The line \({L_2}\) is parallel to \({L_1}\) and passes through the point...
• 15M.1.sl.TZ2.3c: The line \({L_2}\) is parallel to \({L_1}\) and passes through the point...
• 16N.2.sl.TZ0.3a: Show that A lies on \({L_1}\).
• 17N.1.sl.TZ0.2a: Find the coordinates of M.
• 17N.1.sl.TZ0.2b: Find the gradient of \({L_1}\).
• 17N.1.sl.TZ0.2c.i: Write down the gradient of \({L_2}\).
• 17N.1.sl.TZ0.2c.ii: Write down, in the form \(y = mx + c\), the equation of \({L_2}\).
• 18M.1.sl.TZ2.5a.i: Calculate the amount of money he has in the account after 5 years.
• 18M.1.sl.TZ2.5a.ii: Write down the amount of interest he earned after 5 years.
• 18M.1.sl.TZ2.5b: Karl decides to donate this interest to a charity in France. The charity receives 170 euros...

Points of intersection of lines.

• 10M.2.sl.TZ1.2d: N lies on the line AB. The line CN is perpendicular to the line AB. Calculate the coordinates of N.
• 10N.2.sl.TZ0.2d: Write down the coordinates of the point D, the intersection of L1 and L2.
• 10N.2.sl.TZ0.2e: There is a point R on L1 such that ABRD is a rectangle. Write down the coordinates of R.
• 12N.1.sl.TZ0.8c: Line L2, is perpendicular to line L1, and passes through the point (4, 5) . Write down the...
• 12M.1.sl.TZ1.9c: (i) Write down the gradient of a line perpendicular to line L. (ii) Find the equation of the...
• 11M.1.sl.TZ1.13b: The point of intersection of \({R_1}\) and \({R_2}\) is \((4{\text{, }}k)\) .Find(i)     the...
• 09M.2.sl.TZ1.3d: Lines AB and CD intersect at point E. The equation of line AB is \(x + 3y = 6\). Find the...
• 07M.1.sl.TZ0.12c: Draw a sketch, in the space provided, to show how the prices can be found graphically.
• 09M.1.sl.TZ2.7b: A second line with equation x − y = 3 intersects the line PQ at the point A. Find the coordinates...
• 08N.1.sl.TZ0.7c: The equation of line \({L_2}\) is \(y = mx\) . \({L_2}\) is perpendicular to \({L_1}\) . Find...
• 08M.1.sl.TZ2.6d: Find the coordinates of the point of intersection of these two lines.
• 15M.1.sl.TZ2.3c: The line \({L_2}\) is parallel to \({L_1}\) and passes through the point...
• 18M.1.sl.TZ2.5a.i: Calculate the amount of money he has in the account after 5 years.
• 18M.1.sl.TZ2.5a.ii: Write down the amount of interest he earned after 5 years.
• 18M.1.sl.TZ2.5b: Karl decides to donate this interest to a charity in France. The charity receives 170 euros...

Lines with gradients, \({m_1}\) and \({m_2}\) .

• 14N.2.sl.TZ0.6c: Point A lies on the \(x\)-axis and the line AB is perpendicular to line OB. (i)     Write down...
• 18M.1.sl.TZ2.5a.i: Calculate the amount of money he has in the account after 5 years.
• 18M.1.sl.TZ2.5a.ii: Write down the amount of interest he earned after 5 years.
• 18M.1.sl.TZ2.5b: Karl decides to donate this interest to a charity in France. The charity receives 170 euros...

Parallel lines \({m_1} = {m_2}\).

• 10M.2.sl.TZ1.3g: There is a second point, Q, on the curve at which the tangent to f (x) is parallel to L. Write...
• 11N.1.sl.TZ0.7c: Find the equation of the line parallel to AB that passes through M.
• 10N.2.sl.TZ0.2b: L1 passes through C and is parallel to AB. Write down the y-intercept of L1.
• 12M.1.sl.TZ2.13b: The equation of the line L is \(6x + 2y = -1\). Find the x-coordinate of the point on the curve...
• 11M.2.sl.TZ1.3h: There is a second point on the graph of \(f\) at which the tangent is parallel to the tangent at...
• 07N.2.sl.TZ0.5c: Find the coordinates of the point where the tangent to P is parallel to the line L.
• 08N.2.sl.TZ0.5d: Let \({L_1}\) be the tangent to the curve at \(x = 2\). Let \({L_2}\) be a tangent to the curve,...
• 15M.1.sl.TZ1.3c: The line \({L_2}\) is parallel to \({L_1}\) and passes through the point \((3,{\text{...
• 15M.1.sl.TZ2.3b: The line \({L_2}\) is parallel to \({L_1}\) and passes through the point...
• 15M.1.sl.TZ2.3c: The line \({L_2}\) is parallel to \({L_1}\) and passes through the point...
• 18M.1.sl.TZ2.5a.i: Calculate the amount of money he has in the account after 5 years.
• 18M.1.sl.TZ2.5a.ii: Write down the amount of interest he earned after 5 years.
• 18M.1.sl.TZ2.5b: Karl decides to donate this interest to a charity in France. The charity receives 170 euros...

Perpendicular lines, \({m_1} \times {m_2} = - 1\) .

• 10M.1.sl.TZ2.4c: The line L2 is perpendicular to L1 and passes through the point (3, 7). Write down the gradient...
• 10M.2.sl.TZ1.2c.i: N lies on the line AB. The line CN is perpendicular to the line AB. Find the gradient of CN.
• 10N.2.sl.TZ0.2c: L2 passes through A and is perpendicular to AB. Write down the equation of L2. Give your answer...
• 12N.1.sl.TZ0.8b: Line L2, is perpendicular to line L1, and passes through the point (4, 5) . (i) Write down the...
• 12M.1.sl.TZ1.9c: (i) Write down the gradient of a line perpendicular to line L. (ii) Find the equation of the...
• 09N.1.sl.TZ0.10c: Let M be the midpoint of the line segment AB. Find the equation of the line perpendicular to AB...
• 11N.2.sl.TZ0.4e: The line, \(L\), passes through the point A and is perpendicular to the tangent at A. Write...
• 11M.1.sl.TZ1.13a: Calculate the gradient of \({R_2}\) .
• 09M.2.sl.TZ1.3b: Show that line AD is perpendicular to line CD.
• 13M.1.sl.TZ1.10c: L2 is a line perpendicular to L1. The equation of L2 is \(y = mx + c\). Write down the value of m.
• 13M.1.sl.TZ2.8b: A second line L2 is perpendicular to L1. Write down the gradient of L2.
• 07M.1.sl.TZ0.10a: Determine the (i) coordinates of M, the midpoint of P and Q. (ii) gradient of the line drawn...
• 07M.1.sl.TZ0.10b: The perpendicular line drawn through M meets the y-axis at R (0, k). Find k.
• 07N.1.sl.TZ0.13b: Find the equation of the straight line perpendicular to AB, passing through the point M.
• 07N.2.sl.TZ0.5d: Find the coordinates of the point where the tangent to P is perpendicular to the line L.
• 08N.1.sl.TZ0.7b: The equation of line \({L_2}\) is \(y = mx\) . \({L_2}\) is perpendicular to \({L_1}\) . Find...
• 08M.2.sl.TZ1.1f: The line \(L\) passes through the point with coordinates \(( - 2{\text{, }} - 3)\) and is...
• 08M.1.sl.TZ2.6b: Find the gradient of the line which is perpendicular to the line \(y = 3x + 4\).
• 13N.2.sl.TZ0.4g: The line \(L\) passes through the point \((2, −12)\) and is perpendicular to \(T\). \(L\) has...
• 14M.1.sl.TZ1.9c: Decide whether triangle OAM is a right-angled triangle. Justify your answer.
• 14N.2.sl.TZ0.6c: Point A lies on the \(x\)-axis and the line AB is perpendicular to line OB. (i)     Write down...
• 15M.2.sl.TZ1.5e: The graph of \(y = f(x)\) has a local minimum point at \(x = 4\). Find the equation of the...
• 18M.1.sl.TZ2.5a.i: Calculate the amount of money he has in the account after 5 years.
• 18M.1.sl.TZ2.5a.ii: Write down the amount of interest he earned after 5 years.
• 18M.1.sl.TZ2.5b: Karl decides to donate this interest to a charity in France. The charity receives 170 euros...