Before you start to practice Graphs topically,


Do you Know
  • Gradient of a straight line, 
  • The equation of a straight line, 
  • Distance between the two points, 
  • Midpoint of a line segment, 
  • Parallel and perpendicular lines, 
  • Interpracting graph, 
  • y intercept, x intercept.
If YES, you may continue,
    1(Edexcel/Math B/2014/jan/paper01/q11)

    The equation of a straight line is \( y = mx + 2 \).
    The straight line passes through the point \((2, -8)\).
     Calculate the value of \( m \).------[2]
    2(Edexcel/Math B/2014/jan/paper01/q22)

    The coordinates of point \( A \) are \((2, 4)\) and the coordinates of point \( B \) are \((6, 1)\).

    (a) Express \( AB \) as a column vector.------[2]
    (b) Calculate the modulus of \( AB \).------[2]
    3(Edexcel/Math B/2014/jan/paper01R/q9)

    The point \( Q \) with coordinates \((5, p)\) is a point on the line with equation \( 2x - 3y = 4 \).
    Find the value of \( p \).------[2]
    4(Edexcel/Math B/2014/jan/paper01R/q15)

    The equation of a straight line is given by \( 2x + 3y = 12 \).

    (a) Find the gradient of the line.------[2]
    (b) Write down the coordinates of the point of intersection of the line with the \(y\)-axis.------[1]
    5(Edexcel/Math B/2014/june/paper02R/q1)

    The point \( A \) has coordinates \((-3, 7)\) and the point \( B \) has coordinates \((5, -8)\).
     Calculate
    (a) the length of \( AB \),------[2]
    (b) the gradient of \( AB \).------[2]
    6(Edexcel/Math B/2015/jan/paper01/q6)

    A straight line passes through the points with coordinates \((1, 3)\) and \((-5, -2)\). Calculate the gradient of the line.------[2]
    7(Edexcel/Math B/2015/jan/paper01R/q2)

    Find the gradient of the straight line whose equation is: \[ 3x - 2y = 12 \]------[2]
    8(Edexcel/Math B/2015/june/paper01/q10)

    The straight line joining the points with coordinates \((1, -2a)\) and \((a, 1)\) has gradient \(5\).
    Find the value of \( a \).------[3]
    9(Edexcel/Math B/2015/june/paper01R/q5)

    Find the gradient of the line with equation \( 3y = x - 4 \).    ------[2]
    10(Edexcel/Math B/2016/jan/paper01/q5)

    Here are the equations of four straight lines.
    \[ \begin{cases} y = 1 - x \\ 2y = 5x + 3 \end{cases} \qquad \begin{cases} 3y = 6x + 1 \\ y = 2x + 1 \end{cases} \]

    (a) Write down the equations of the two lines that have the same gradient.------[1]
    (b) Write down the equations of the two lines that pass through the point \((0, 1)\).------[1]

To be continued....

Answer Key of Graph (2014-2016)

  1. $m=-5$
  2.  (a) $ \overrightarrow{A B}=\left(\begin{array}{c}4 \\ -3\end{array}\right),$ (b) $|\overrightarrow{A B}|=5$
  3.  (a) $ p=2 \quad $ 
  4.  (a) $-\frac{2}{3} $ OR $ 0.667 $ (b) $(0,4) \quad$ 
  5.  (a) $17$ (b) $-\frac {15}{8}$
  6.  $\frac{5}{6}$
  7.  gradient $=\frac{3}{2}$
  8.  $a=2 \quad $
  9.  $m=\frac{1}{3} \quad$
  10.  (a) $3 y=6 x+1, y=2 x+1$ (b) $y=1-x, y=2 x+1$
  11.  (a) $\quad(3,4)$ (b) $5 \quad $
  12.  $ \frac{1}{3} $ 
  13.  (a)(i)  Draw  (ii) Draw (b) $B(0,-3), C(-3,-1)$
  14.  (a) show (b) show (c) show (d) $ 63.3,66.6,80.1 $ (e) curve (f) $1.4 \leqslant x \leqslant 4.5 $ 
  15.  (a) $23.9,-5,-2$ (b) graph (c) Accept ans in range -22 to -29 (d) $y=-15$ drawn , 2.4 (e) correct straight line (f)graph
  16.  (a) $-2.75,0.25,1.25$ (b) curve (c) $x=1.65( \pm 0.05)$ $x=4.85( \pm 0.05)$; Accept $(165,-2.18)$ and $(4.85,-0.57)$ (d) gradient $=0.5 ( \pm 0.05$ allowing $\pm \frac{1}{2} \mathrm{ss})\quad$
  17.  (a) 8,8.3,18.2 (b) Draw (c) $5 (\pm 0.3)$ (d) Draw (e) show (f) $0.9( \pm 0.1), 2.9( \pm 0.1)$
  18.  (a) $-2.8,-4.6,-0.4$ (b) curve (c) $-5.5 \pm 1$ small square (d) gradient $3.8-4.4$ (e) $1.1 \pm 1$ small square, $2.9 \pm 1$ small square (f) Explain 
  19.  (a) $ \frac{1}{2} \times 3 x \times 4 x$ (b) $3 x+4 x+5 x$ (c) $y=\frac{60-12 x}{6}(10-2 x)$ (d) show (e) 134,86 (f) curve (g) $ x=4.4 / 4.5$; accept $116-122$
  20.  (a) $-10,-22,-9.4$ (b) Curve (c) $y=5 x-8$ draw (d) $0.32\langle x, 2.89\rangle x$ (e) $y=-25$ draw
  21.  (a) $h-20 \quad$ (b) $V=\frac{1}{3} \pi r^2(h-20)$ (c) show (d) $43,85,67$ (e) Curve (f) $6.8 , 9.1\left( \pm \frac{1}{2}\right)$ small square (g) $2300 \mathrm{~cm}^3(1900-2500)$
  22.  (a) $-0.28,3.28 \quad$ (b) Grid (c) $-0.3,1.3 \quad$ (d) $x<-0.7, x>0.4, x<1.9$ (e) $-0.8,0.8,1.6$
  23.  (a) $(5,0)$ (b) $x \geqslant 0$  
  24.  $y \leqslant 2, y \geqslant x-2, y \geqslant 4-2 x \quad$ 
  25.  $ 2 y =x+4 ; y=5-2 x ; y=0 $ 
  26.  $x+y\leqslant6,x\geqslant 0, x+4y \geqslant6$
  27.  (a) The particle is stationary. (b) $80 \mathrm{~km}$  
  28.  (a) $ \$ 2.40$ (b) $ \$1.80 \quad$ 
  29.  (a) I hour $30 \mathrm{~min}(90 \mathrm{~min}) \quad$ (b) $87.5 \mathrm{~km} / \mathrm{h} \quad$ (c) $1212( \pm 3 \mathrm{3mins})$
  30.  (a) $75 \mathrm{~km} \quad$ (b) $25 \mathrm{~km} / \mathrm{h} \quad$ (c) 1.5 hours
  31.  (a) graph (b) $70 \mathrm{~km} / \mathrm{h}$ (c) draw (d) (i) $10: 33( \pm 2 \mathrm{~min})$ (ii) $28 \mathrm{~km}( \pm 1 \mathrm{~km}) \quad$ 
  32.  (a) Graph (b) $10350 \mathrm{~m}$ (c) $27 \mathrm{~m} / \mathrm{s}$ (d) $\frac{1}{2} \mathrm{~m} / \mathrm{s}^2$
  33.  (a) Graph (b) Graph (c) $72 \mathrm{~km} / \mathrm{h}$ (d) $44 \mathrm{~km}( \pm 2 \mathrm{~km}= \pm 1 \mathrm{ss})$