IGCSE Mathematics - International (0607) — May–June 2024, Paper 61
13 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.
Start with Question 1 →A: INVESTIGATION — SUMS OF POWERS (30 marks). This investigation looks at connections between the sum of the positive integers, 1 + 2 + 3 + …, the sum of their squares, the sum of…
Answer this question and get it marked →Use the method to calculate the sum of the first 128 positive integers. That is 1 + 2 + 3 + … + 128.
Answer this question and get it marked →Complete the table. Use Question 1, Question 2 and any patterns you notice. Number of positive integers, starting at 1 Multiplication Sum --- --- --- 12 6 × 13 78 26 13 × 27 351…
Answer this question and get it marked →1 + 2 + 3 + … + n has n positive integers and its sum is T. Find a formula for T in terms of n.
Answer this question and get it marked →Complete the table. n Sum of first n positive integers (Calc) Sum (T) Sum of first n square numbers (Calc) Sum (S) S/T as fraction with denominator 3 --- --- --- --- --- --- 1 1 1…
Answer this question and get it marked →Complete the table. Sum of first n positive integers (Calc) Sum (T) Sum of first n cube numbers (Calc) Sum (C) --- --- --- --- 1+2 3 1³+2³ 9 1+2+3 6 1³+2³+3³ 36 1+2+3+4 10…
Answer this question and get it marked →Complete the table. Use Question 6(a) to help you. n Sum of first n cube numbers (Calc) Sum (C) Sum of first n 5th powers (Calc) Sum (F) F/C as fraction with denominator 3 --- ---…
Answer this question and get it marked →B: MODELLING — INCOME INEQUALITY (30 marks). This task looks at a model to measure the spread of income within the population of a country. x is the decimal fraction of the…
Answer this question and get it marked →In reality, the total income of a country is not shared equally, so there is income inequality. In 1905 Max Lorenz invented the Lorenz curve to show income inequality. A Lorenz…
Answer this question and get it marked →In 1912 Corrado Gini invented the Gini coefficient, which measures how much income inequality there is in a country. The Gini coefficient is two times the shaded area between the…
Answer this question and get it marked →Mei uses these steps to model the Gini coefficient for the curve in Question 9. Step 1: Plot point F from Question 9 on the Lorenz curve. Step 2: Approximate the area below the…
Answer this question and get it marked →Mei decides to use a point P(x, y) in Step 1 of her model. Find the area in Step 3 of her model as an expression without brackets in terms of x and y.
Answer this question and get it marked →Mei knows that her approximation, G = x − y, is always smaller than the actual Gini coefficient. So, to make her model as accurate as possible, she takes the maximum value of G =…
Answer this question and get it marked →