Pure Maths Item Bank 1

UACE MATHEMATICS SAMPLE ITEMS PURE MATHEMATI CS ITEM 1 A community group in Gulu is managing the costs for drilling three boreholes (A, B, and C). The total cost was UGX 25,000,000. The cost of Borehole B was UGX 1,000,000 less than Borehole A. The combined cost of Boreholes A and C was three times the cost of Borehole B. Let the costs of drilling boreholes A, B and C be a, b, and c in UGX respectively. Tasks: a) Formulate a system of three linear simultaneous equations representing the information given. b) By Using Row reduction, calculate the individual cost of drilling each borehole (a, b and c) If the cost per meter drilled was UGX 250,000 for all boreholes, determine the depth of Borehole A. ITEM 2 A certain city is experiencing social challenges with two distinct population groups having different experiences of urban life, the city planners are trying to understand if there is a common problem affecting both groups, they are modelling the wellbeing of two groups using two separate quadratic equations. 𝒙𝟐 + 𝒑𝒙 + 𝒒 = 𝟎 p represents acc ess to social services and q represents employment opportunities. and 𝒙𝟐 + 𝒎𝒙 + 𝒌 = 𝟎. The collective wellbeing is given by, where 𝑚 represents educational attainment and healthcare access, k represents safety quality. The social challenge exists if (𝒒 − 𝒌)2 = (𝒎 − 𝒑)(𝒑𝒌 − 𝒎𝒒). Task. As a data analyst identify whether the common social challenge exist or not. ITEM 3 A certain city in Uganda is investing in a new smart traffic management system designed to optimize traffic flow and reduce congestion especially during the rush hours. The system caters road density, vehicle capacity and pedestrian movement, the engineers have developed some indicator related to the efficiency of the …