These are fully worked solutions to the November 2024 ZIMSEC O-Level Mathematics (4028/1) Paper 1. Study each solution carefully, paying attention to the method marks — examiners award marks for correct working even if the final answer is wrong.

Section A — Short Answer Questions

Question 1 [3 marks]

Evaluate ( 3frac{1}{2} div 1frac{3}{4} + 2frac{1}{4} )

Solution:

[ 3frac{1}{2} div 1frac{3}{4} = frac{7}{2} div frac{7}{4} = frac{7}{2} imes frac{4}{7} = 2 ]

[ 2 + 2frac{1}{4} = 4frac{1}{4} ]

Answer: ( 4frac{1}{4} )  ? M1 A1 A1

Question 2 [4 marks]

Factorise completely: ( 3x^2 - 12 )

Solution:

Take out the common factor first: ( 3(x^2 - 4) )

Recognise difference of two squares: ( 3(x+2)(x-2) )

Answer: ( 3(x+2)(x-2) )  ? M1 M1 A2

Question 3 [4 marks]

A map has a scale of ( 1 : 50,000 ). Two towns are 8.4 cm apart on the map. Find the actual distance in kilometres.

Solution:

[ ext{Actual distance} = 8.4 imes 50,000 = 420,000 ext{ cm} ]

[ = frac{420,000}{100,000} = 4.2 ext{ km} ]

Answer: ( 4.2 ) km  ? M1 M1 A2

Section B — Structured Questions

Question 9 [10 marks] — Quadratics and Graphs

Given ( y = x^2 - 2x - 3 ):

(a) Complete the table of values for ( -2 leq x leq 4 )

(b) Draw the graph (on graph paper — see attached PDF)

(c) Use the graph to solve ( x^2 - 2x - 3 = 0 )

Solution (c): The parabola crosses the x-axis at ( x = -1 ) and ( x = 3 ). Therefore the roots are ( oxed{x = -1 ext{ or } x = 3} )

Verify by factorisation: ( (x+1)(x-3) = 0 Rightarrow x = -1 ext{ or } x = 3 ) ?

Question 12 [12 marks] — Trigonometry

In triangle ABC, ( AB = 7 ) cm, ( BC = 9 ) cm and ( angle ABC = 64° ).

Find: (a) AC    (b) The area of triangle ABC

Solution (a) — Cosine Rule:

[ AC^2 = AB^2 + BC^2 - 2 cdot AB cdot BC cdot cos(angle ABC) ]

[ = 49 + 81 - 2(7)(9)cos 64° ]

[ = 130 - 126 imes 0.4384 = 130 - 55.24 = 74.76 ]

[ AC = sqrt{74.76} approx 8.65 ext{ cm} ]

Solution (b) — Area:

[ ext{Area} = frac{1}{2} cdot AB cdot BC cdot sin(angle ABC) = frac{1}{2}(7)(9)sin 64° ]

[ = 31.5 imes 0.8988 approx 28.3 ext{ cm}^2 ]

Download the full paper with all 15 questions + complete marking scheme in the attachment below.