Two 20-mark Module 3 questions with CK, AK and R marks — grouped delivery-time data with a cumulative frequency curve, and a surveyor’s plot using the sine and cosine rules, area, bearings and scale.
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.
“Which delivery company is more reliable?” “Is the landowner’s area claim right?” Module 3 turns grouped data and non-right-angled triangles into evidence you can argue from.
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 2, RFG 2, geometry and trigonometry 2, vectors and matrices 2.
Midpoints for the estimated mean; ogive at upper boundaries; read n/2, n/4, 3n/4.
(n − cf at the value) ÷ n × 100.
a² = b² + c² − 2bc cos A for two sides and the included angle.
sin B ÷ b = sin A ÷ a.
½ab sin C.
Length factor k; area factor k².
Compare, check claims against calculated values, recommend, state limits.
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 delivery company recorded the times, in minutes, taken to deliver 80 parcels: 0 < t ≤ 10 (6), 10 < t ≤ 20 (18), 20 < t ≤ 30 (30), 30 < t ≤ 40 (20), 40 < t ≤ 50 (6).
(a) (a) Complete a cumulative frequency table. [2]
(b) (b) State the modal class and the class width. [2]
(c) (c) Calculate an estimate of the mean delivery time. [3]
(d) (d) Draw the cumulative frequency curve and plot the points (upper boundary, cumulative frequency). (Check: (0, 0), (10, 6), (20, 24), (30, 54), (40, 74), (50, 80); smooth curve; scales 2 cm to 10 min and 2 cm to 20 parcels.) [2]
(e) (e) Use your graph to estimate the median and the interquartile range. [3]
(f) (f) Estimate the percentage of parcels that took more than 35 minutes. [2]
(g) (g) A rival company has a median of 23 minutes and an interquartile range of 9 minutes. Compare the two companies and say which is more reliable. Give a reason. [3]
(h) (h) State TWO limitations of using this data to compare the companies. [3]
Question 2 [20 marks]
A surveyor measures a triangular plot of land ABC. AB = 80 m, AC = 65 m and angle BAC = 58°. The bearing of B from A is 072°.
(a) (a) Write down the cosine rule for BC and calculate BC, correct to 3 significant figures. [3]
(b) (b) State the formula for the area of a triangle given two sides and the included angle, and calculate the area of the plot. [3]
(c) (c) Calculate angle ABC, correct to 1 decimal place. [3]
(d) (d) C is on the clockwise side of AB. Write down the bearing of C from A, and the bearing of A from C. [2]
(e) (e) The plot is drawn on a plan with a scale of 1 : 500. Calculate the length of AB on the plan and the area of the plot on the plan, in cm². [3]
(f) (f) The owner claims the area of the plot is 2 500 m². Use your answer to (b) to comment on the claim. [3]
(g) (g) Fencing costs $45 per metre and the budget is $9 000. Calculate the cost of fencing the boundary and advise whether the budget is enough. [3]
Everything in this lesson is based on these parts of the CXC syllabus and papers.