Question
(a) (i) Complete the table of values for \(y = x^2 + x\).
(ii) On the grid, draw the graph of \( y = x^2 + x\) for \(-3 \leq x \leq 3\).
(iii) On the grid, draw the line y = 10.
(iv) Use both your graphs to solve
\(x^2 + x = 10\) for \(-3 \leq x \leq 3\).
(b) Another line, L, has the equation \(y = \frac{2}{3}x -5\).
(i) Write down the gradient of L.
(ii) Write down the equation of a straight line that is parallel to L.
(c) 
Write the equation of the line, K, in the form y = mx + c .
Answer/Explanation
Answer:
(a) (i) 2 and 2
12
(ii) 7 points correctly plotted
correct curve through the 7points
(iii) correct line
(iv) 2.6 – 2.8
(b) (i) \(\frac{2}{3}\)
(ii) \(y = \frac{2}{3}x + c\)
(c) [y=]2x – 3
Question
(a) Complete the table of values for \(y = x^2 + 2x – 1\).
| x | -5 | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
| y | 14 | 2 | -1 | -1 | 2 |
(b) On the grid, draw the graph of \(y = x^2 + 2x – 1\). for \(-5 \leq x \leq 3\).
(c) (i) On the grid, draw the line of symmetry.
(ii) Write down the equation of the line of symmetry.
(d) (i) On the grid, plot the points (-5, 7) and (0, -3) and join them with a straight line, L.
(ii) Write down the x co-ordinate of each point where the line L crosses the graph of \(y = x^2 + 2x -1\).
x = …………………… and x = ……………………
(iii) Work out the gradient of the line L.
Answer/Explanation
Answer:
(a) 7 -2 7 14
(b) Correct smooth curve
(c) (i) Ruled line, x = –1, drawn
(ii) x = –1 oe
(d) (i) Ruled line L drawn, joining
(–5, 7) and (0, −3)
(ii) −3.3 to −3.5, −0.5 to −0.7
(iii) −2
Question
The diagram shows a point P, a shape S and lines A and B on a \(1cm^{2}\) grid.
(a) Line A is parallel to line B.
Explain what parallel means.
…………………………………………………………………………………………………………………………………..
(b) Write down the coordinates of point P.
( ………………….. , ………………….)
(c) (i) Write down the mathematical name for shape S.
………………………………………….
(ii) Work out the area of shape S.
…………………………………..\( cm^{2}\)
(d) (i) Find the gradient of line A.
………………………………………….
(ii) Write down the equation of line A.
………………………………………….
Answer/Explanation
(a) Correct explanation
(b) (5,8)
(c)(i) Parallelogram
(ii)15
d(i)\(\frac{2}{5}\)
(ii)\(y=\frac{2}{5}x+6\)