Two 20-mark Module 2 questions with CK, AK and R marks — a quadratic model for a fenced enclosure and a trigonometry problem on a wheelchair ramp — with advice on how to approach each.
4 narrated scenes. Press play, listen and read along — the points appear as they are explained. Use ‹ Prev / Next › or the scene bar to jump to any scene.
A farmer has 40 m of fencing. What is the largest pen he can build? A school has a steep ramp. Is it safe, and what would a safe one cost? Module 2 questions turn algebra and trigonometry into decisions.
Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.
Copy these into your notebook in your own words — that is how they stick.
Statistics 1, algebra 2, RFG 1, geometry and trigonometry 1, vectors and matrices 1.
A = x(P/2 − x); complete the square for the maximum; solve inequality by factorising.
Pythagoras for lengths; tan θ = O/A for slope; tan θ for horizontal length.
Cross-section area × length (width).
(new − old) ÷ old × 100.
Compare with a standard; weigh benefits against costs; recommend.
CK 6, AK 8, R 6 — label your work so each type is visible.
Units, rounding to 3 s.f., sensible answers.
8 items modelled on real CSEC Paper 1 questions. Choose one answer for each, then check. Aim for 80% or better. Work each item on paper first.
Write full answers, then reveal the mark scheme and tick the points you earned (40 marks in total). Show all your working — method marks count. Your answers are saved on this device.
Question 1 [20 marks]
A farmer has 40 m of fencing to make a rectangular pen. One side is x metres long.
(a) (a) Show that the other side is (20 − x) metres and that the area is A = 20x − x². [2]
(b) (b) Complete the table for A = 20x − x² when x = 0, 5, 10, 15 and 20. [2]
(c) (c) Write A in the form a − (x − h)². [2]
(d) (d) Hence state the maximum area and the dimensions that give it. [3]
(e) (e) The farmer needs an area of at least 96 m². Solve 20x − x² ≥ 96. [3]
(f) (f) Sketch the graph of A against x for 0 ≤ x ≤ 20, marking the maximum point and the points where A = 96. Describe its symmetry. [3]
(g) (g) Fencing costs $15 per metre. Calculate the cost of the fencing. [2]
(h) (h) The farmer says “a square pen always gives the greatest area for a fixed length of fence.” Use your results to justify or challenge this for a rectangle. [3]
Question 2 [20 marks]
A school has a wheelchair ramp that rises 1.2 m over a horizontal distance of 5 m. The ramp is 2 m wide. A safety guideline says the angle of a ramp must not be more than 4.8°.
(a) (a) Calculate the length of the sloping surface of the ramp, correct to 3 significant figures. [2]
(b) (b) Write down a trigonometric ratio for the angle of slope θ and calculate θ, correct to 1 decimal place. [2]
(c) (c) Calculate the horizontal distance needed for a ramp of height 1.2 m at an angle of 4.8°. [3]
(d) (d) Show that the present ramp does not meet the guideline. [2]
(e) (e) The ramp is a triangular prism. Calculate the volume of concrete for the present ramp, and its cost at $380 per cubic metre. [3]
(f) (f) A new ramp has a horizontal length of 14.3 m. Calculate the volume of concrete, the cost, and the percentage increase in cost compared with the present ramp. [4]
(g) (g) The principal must decide between keeping the present ramp and building the new one. Advise her, giving TWO reasons and one thing she should check. [4]
Everything in this lesson is based on these parts of the CXC syllabus and papers.