Basic Trigonometry: WJEC GCSE Numeracy Intermediate November 2022 Unit 2 Q7

Numeracy Intermediate November 2022 Unit 2 Q7

WJECIntermediateCurrent spec13 marksBasic Trigonometry Percentages Upper & Lower Bounds

(a)

10 years ago, Matteo bought a car for £4500.
His car depreciated in value by 20% in the first year.
In each of the following years, his car depreciated by 14% of its previous year’s value.

Show that the value of Matteo’s car is now less than £950.

You must show all your working. [3]

(b)

Matteo’s car insurance has increased by 25% from the amount he paid last year.
His car insurance is £750 this year.

Calculate the amount Matteo paid for his car insurance last year. [2]

Matteo paid £ ………………………… for his car insurance last year.

(c)

The diagram below shows the front of Matteo’s garage.

Front of garage: a rectangle with right angles at each corner, height 240 cm at the side, below an isosceles triangle (two equal sloping sides marked) with base angle 33° and a dashed perpendicular height; total height 320 cm; the bottom edge is labelled Width

Diagram not drawn to scale

Calculate the width of Matteo’s garage. [5]

(d)

The length of Matteo’s car is 400 cm, correct to the nearest 10 cm.
The length of his garage is 550 cm, correct to the nearest 10 cm.

When Matteo parks his car, he leaves exactly 70 cm between the car and the back wall of the garage.

Calculate the maximum length of the space between Matteo’s car and the garage door. [3]

Plan view of a car inside the garage: Length of garage shown across the top, Back wall on the left with a 70 cm gap to the front of the car, Garage door on the right

Diagram not drawn to scale

Mark scheme (a)

Scheme	Marks	Comments
4500 × (1 - 0.2(0)) × (1 - 0.14)⁹ or 4500 × 0.8(0) × 0.86⁹ or equivalent	M2	For M2, do not ignore any additional years considered, unless 10 years selected or implied in later working M1 for equivalent of one of the following (which may be embedded in other working): 4500 × (1 - 0.2(0)) (= 3600) 4500 × 0.8(0) (= 3600) 4500 × (1 - 0.14)⁹ (= 1157.97...) 4500 × 0.86⁹ (= 1157.97...)
An answer in the range (£)926.35 to (£)926.40	A1	An answer for 10 years (not beyond) must be selected Allow an answer of (£)926 provided not from rounding an amount outside the range given Award M1, SC1 for an answer (4500 × 0.8 × 0.86¹⁰ =) (£)796.68(5.... ) or (£)796.69 or (£)796.70 or (£)797

Scheme	Marks	Comments
100 × 750 ÷ 125 or 100 × \(\dfrac{750}{125}\) or equivalent	M1
(£) 600	A1	Answer space takes precedence

Mark scheme (c)

Scheme	Marks	Comments
		Accept equivalents using the sine rule throughout ‘½ width’ may be referred to by any unknown
Sight of appropriate 80 (cm) (height of triangle)	B1	Check if indicated on the diagram
(½ width =) \(\dfrac{80}{\tan 33^\circ}\) or (½ width =) 80 × tan (90° – 33°)	M2	(= 123.189... cm or 123.2 cm) FT ‘their 80’ provided ≤ 120 and ≠ 90 M1 for sight of tan 33° = \(\dfrac{80}{\tfrac{1}{2}\text{ width}}\) or tan (90° – 33°) = \(\dfrac{\tfrac{1}{2}\text{width}}{80}\)
× 2	m1	FT provided at least M1 previously awarded, i.e. for intention to double ‘their ½ width’
(Width of garage is) 246(cm) to 246.4(cm)	A1	CAO. ISW

Mark scheme (d)

Scheme	Marks	Comments
(Maximum space =) 555 – 395 – 70 or 550 – 400 + 2 × 5 – 70 or equivalent	M2	Check the diagram M1 for any of the following: use of 550 < ‘their 555’ ≤ 560 AND 390 ≤ ‘their 395’ < 400 for sight of 555 and 395 for sight of 550 – 400 + 2 × 5
90 (cm)	A1	CAO Award M1 and SC1 for an answer of (555 – 395 =) 160 (cm)