IGCSE 0580 — Practice Paper 4 (Questions)
IGCSE 0580 — Practice Paper 4 (Topics: Algebra 1,2,3 and Number 1,2)
Instructions:
• Answer all questions.
• Show all working clearly. This question paper has 10 questions.
• Calculators allowed where appropriate (adapt to your normal practice).
Questions
1. (Number 1) Simplify the fraction 84/126 to its lowest terms. Hence find the highest common factor (HCF)
of 84 and 126.
2. (Number 2) Calculate 0.000456 × 3.2. Write your answer in standard form.
3. (Algebra 1) Solve for x: (3x + 2)/4 − (x − 1)/6 = 5/12.
4. (Algebra 1) (a) Expand and simplify (2x − 3)(x + 4).
(b) Factorise fully 2x^2 + 5x − 3.
5. (Algebra 2) Solve the quadratic equation 2x^2 − 3x − 5 = 0. Give exact values for x.
6. (Algebra 2) Solve the simultaneous equations:
3x + 2y = 16
x−y=2
7. (Algebra 3) Solve the inequality 2(3x − 1) ≤ 5x + 4. Give the solution in interval notation.
8. (Algebra 3) Find the equation of the line through the points A(2, −1) and B(−3, 4) in the form y = mx + c.
9. (Algebra 3) A geometric sequence has its 4th term equal to 8 and its 7th term equal to 64.
(a) Find the common ratio r.
(b) Find the first term a.
10. (Number 2 / Algebra) A quantity P is increased by 20% and then decreased by 15%. The result is 408.
Find the original quantity P.