Leaving Cert Mathematics Ordinary Paper 2 free practice questions with answers

Question 1 (30 marks) [The line]

(a) The line p has a slope of −2 and crosses the y-axis at the point (0, 6). Find the equation of p.

(a) Answer: y = −2x + 6

• The equation of a line with slope m and y-intercept c is y = mx + c.

• Here m = −2 and the line crosses the y-axis at (0, 6), so c = 6.

• The equation is y = −2x + 6.

(b) Find the area of the triangle formed by joining the following three points: O(0, 0), A(4, −6) and B(6, 6).

(b) Answer: 30 square units

• For a triangle with one vertex at the origin, Area = ½|x₁y₂ − x₂y₁|.

• Take A(4, −6) as (x₁, y₁) and B(6, 6) as (x₂, y₂): x₁y₂ − x₂y₁ = (4)(6) − (6)(−6) = 24 − (−36) = 60.

• Area = ½ × 60 = 30 square units.

(c) The diagram shows four lines, labelled p, q, r and s. The slope of each of the four lines is given in the table. Identify each of the lines in the diagram by writing the appropriate label (p, q, r or s) beside its slope. -2 -1 1 2 3 4 5 6 -2 -1 1 2 3 4 5 6 7 8 x y q p r s Four lines p, q, r and s

(c) Answer: slope 3 → q; slope −1 2 → s; slope 1 3 → p; slope −2 → r

• A line that rises from left to right has a positive slope; a line that falls has a negative slope. A steeper line has a slope of larger size.

• Check by reading two points on each line: slope = rise ÷ run. line q: slope 3; line p: slope slope −2; line s: slope

• Matching: slope 3 → q; slope 1 3 ; line r:

−1 2 . −1 2 → s; slope 1 3 → p; slope −2 → r.