iGCSE Mathematics (0580) : C3.5 Equations of linear graphs iGCSE Style Questions Paper 3

Question

(a) (i) Find the equation of line L.

Give your answer in the form y = mx + c.

(ii) On the grid, draw the line y = 1.

(iii) Write down the coordinates of the point where the two lines intersect.

(b) (i) Complete the table of values for y = x² + x – 8.

(ii) On the grid, draw the graph of y = x² + x – 8 for -4 ≤ x ≤ 4.

(iii) Write down the equation of the line of symmetry of the graph.

(iv) Use your graph to solve the equation x² + x – 8 = 0.

▶️ Answer/Explanation

Solution

(a)(i) Ans: y = 1.5x – 2

Line $ L $ passes through $(0, -2)$ and $(2, 1)$. Slope $ m = \frac{1 – (-2)}{2 – 0} = 1.5 $. Using $ y = mx + c $, the equation is $ y = 1.5x – 2 $.

(a)(ii)

Draw a horizontal line at $ y = 1 $ on the grid.

(a)(iii) Ans: (2, 1)

Solve $ 1.5x – 2 = 1 $ to find $ x = 2 $. The intersection point is $(2, 1)$.

(b)(i) Ans: -6, -6, 12

Substitute $ x = -2, 1, 4 $ into $ y = x^2 + x – 8 $ to get $ y = -6, -6, 12 $.

(b)(ii)

Plot the points and draw a smooth curve through them.

(b)(iii) Ans: x = -0.5

The line of symmetry for $ y = ax^2 + bx + c $ is $ x = \frac{-b}{2a} $. Here, $ x = \frac{-1}{2} = -0.5 $.

(b)(iv) Ans: x ≈ -3.4, 2.4

The solutions to $ x^2 + x – 8 = 0 $ are the x-intercepts of the graph, approximately $ x = -3.4 $ and $ x = 2.4 $.

Question

(a) Find the equation of line $L$ in the form $y=mx+c.$

(b) Write down the coordinates of the point where line $L$ crosses the x-axis.

(c) (i) Complete the table of values for $y=x^2+5x+3.$

(ii) On the grid, draw the graph of $y= x^2+ 5x+ 3$ for $-6\leqslant x\leqslant1.$

(d) (i) On the grid, draw the line $y=6.$

(ii) Use your graphs to solve the equation $x^2+5x+3=6.$

▶️ Answer/Explanation

Solution

(a) Ans: y = -2x + 7

Using the points (3.5, 0) and (0, 7), the gradient is $ m = \frac{7 – 0}{0 – 3.5} = -2 $. The y-intercept is 7, so the equation is $ y = -2x + 7 $.

(b) Ans: (3.5, 0)

Set $ y = 0 $ in the equation $ y = -2x + 7 $. Solving gives $ x = 3.5 $, so the x-intercept is (3.5, 0).

(c)(i) Ans: 3, -3, -3, 3, 9

Substitute the given x-values into $ y = x^2 + 5x + 3 $. For example, for $ x = -5 $, $ y = (-5)^2 + 5(-5) + 3 = 3 $. Repeat for other x-values.

(c)(ii)

Plot the points from the table and draw a smooth curve through them.

(d)(i)

Draw a horizontal line at $ y = 6 $ on the grid.

(d)(ii) Ans: 0.4 to 0.7, -5.7 to -5.4

The solutions are the x-coordinates where the curve $ y = x^2 + 5x + 3 $ intersects the line $ y = 6 $. From the graph, these are approximately $ x \approx 0.55 $ and $ x \approx -5.55 $.

iGCSE Mathematics (0580) : C3.5 Equations of linear graphs iGCSE Style Questions Paper 3

Resources

Members

Company