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) (i) Complete the table of values for\( y=x^{2}-5x.\)
(ii) On the grid, draw the graph of \(y=x^{2}-5x for -1\leq x\leq 6.\)
(iii) Write down the co-ordinates of the lowest point of your graph.
(………………… , …………………)
(iv) Use your graph to solve the equation x^{2}-5x=3.
x = ………………. or x = ……………….
(b)
Line L is drawn on the grid.
(i) Find the equation of line L in the form y = mx + c.
y = …………………………………………
(ii) Line P is parallel to line L and passes through the point (0, -1).
On the grid above, draw line P for \(-5\leq x\leq 5.\)
Answer/Explanation
(a)(i) 6, 0, 6
(ii) Correct curve
(iii) (2.5, –6.4 to –6.1)
(iv) –0.7 to –0.4, 5.4 to 5.7
(b)(i) y=-\frac{1}{2}x+2
(b)(ii) Correct ruled line for -5\leq x\leq 5.
Question
(a) (i) Write down the gradient of the line y=-4x+7.
…………………………………………
(ii) Write down the equation of a line parallel to y=2x+3
y = ………………………………………..
(iii) Write down the co-ordinates of the point where the graph of y=6x-5 crosses the y-axis.
(……………. , …………….)
(iv) The point (k, 7) lies on the line y=4x-3.
Find the value of k.
k = ………………………………………..
(b) (i) Complete the table of values for \(y=x^{2}-x-5.\)
(ii) On the grid, draw the graph of \(y=x^{2}-x-5 for -3\leq x\leq 4.\)
(iii) Write down the co-ordinates of the lowest point on the graph.
(……………. , …………….)
(iv) (a) On the grid, draw the line of symmetry of the graph.
(b) Write down the equation of this line.
…………………………………………
Answer/Explanation
(a)(i) – 4
(ii) 2x + k k ≠ 3
(iii) (0, –5)
(iv) 2.5
(b)(i) 1, –5, –3, 1, 7
(ii) Correct smooth curve
(iii) (0.5, h )
where –5.5 ⩽ h < –5
(iv)(a) Correct line of symmetry drawn
(b) x = 0.5