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Higher November 2017 Paper 2 Q6

EduqasHigherCurrent spec10 marksBasic TrigonometryFactorisingSolving Quadratics

6.

(a) The area of the trapezium shown below is 15 cm2.
Trapezium with parallel sides (7 - w) cm and 2w cm, and perpendicular height w cm

Diagram not drawn to scale

(i) Claire is trying to find a value for \(w\) to calculate the lengths of the parallel sides.
She has started her work by using the formula for the area of the trapezium.

Claire then plans to
  • collect like terms within the brackets, and
  • multiply by 2 throughout.
Complete the next step in Claire’s work in the box below. [1]

Area of the trapezium:   \(\dfrac{w \times (7 - w + 2w)}{2} = 15\)

\(w \times (\ \ldots\ldots\ +\ \ldots\ldots\ ) = \ldots\ldots\)

(ii) From your answer in (a)(i) show that \(w^2 + 7w - 30 = 0\).
You must show all your working. [1]
(iii) Factorise \(w^2 + 7w - 30\) and hence solve \(w^2 + 7w - 30 = 0\).
You must give both possible solutions to the equation. [3]
(iv) Hence find the length of each of the parallel sides. [1]
(b) The diagram below shows a different trapezium.
Right-angled trapezium with parallel sides 14.2 cm (top) and 18.6 cm (bottom), height 3.3 cm, and angle y between the sloping side and the 18.6 cm side

Diagram not drawn to scale

Calculate the size of the angle \(y\). [4]
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