IB Maths SL Past Paper PDF
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This IB Maths SL past paper covers topics such as logarithms, arithmetic sequences, and problems involving series and sequences. It includes problems with clear instructions, sample questions and answers to practice for future exams.
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# IB Questionbank Maths SL ## 1. **(a) Find log2 32.** **(b) Given that log2 (32^x / 8^y) can be written as px + qy, find the value of p and of q.** (Total 5 marks) ## 2. Consider the arithmetic sequence 2, 5, 8, 11, .... **(a) Find u101.** **(b) Find the value of n so that un = 152.** (...
# IB Questionbank Maths SL ## 1. **(a) Find log2 32.** **(b) Given that log2 (32^x / 8^y) can be written as px + qy, find the value of p and of q.** (Total 5 marks) ## 2. Consider the arithmetic sequence 2, 5, 8, 11, .... **(a) Find u101.** **(b) Find the value of n so that un = 152.** (Total 6 marks) ## 3. Given that log5 x = y, express each of the following in terms of y. **(a) log5 x^2** **(b) log5 (x/2)** **(c) log25 x** **Working** **Answers** **(a)** **(b)** **(c)** (Total 6 marks) ## 4. In an arithmetic sequence u21 = -37 and u4 = -3. **(a) Find** **(i) The common difference;** **(ii) The first term.** **(b) Find S10.** **Answers** **(a)** **(b)** (Total 7 marks) ## 5. Let ln a = p, ln b = q. Write the following expressions in terms of p and q. **(a) ln a^3b** **(b) ln (sqrt(a) / b)** (Total 6 marks) ## 6. Solve the equation log9 81 + log9 9 + log9 3 = log9 x. **Working:** **Answer:** (Total 4 marks) ## 7. **(a) Write down the first three terms of the sequence un = 3n, for n ≥ 1.** **(b) Find** **(i) Σ (3n) for n=1 to 20 ** **(ii) Σ (3n) for n=21 to 100** (Total 6 marks) ## 8. Find the sum of the arithmetic series 17 + 27 + 37 +...+ 417. **Working:** **Answer:** (Total 4 marks) ## 9. A theatre has 20 rows of seats. There are 15 seats in the first row, 17 seats in the second row, and each successive row of seats has two more seats in it than the previous row. **(a) Calculate the number of seats in the 20th row.** **(b) Calculate the total number of seats.** (Total 6 marks) ## 10. In an arithmetic sequence, S40 = 1900 and u40 = 106. Find the value of u1 and of d. (Total 6 marks) ## 11. An arithmetic sequence, u1, u2, u3, ..., has d = 11 and u27 = 263. **(a) Find u1.** **(b) (i) Given that un = 516, find the value of n.** **(ii) For this value of n, find Sn.** (Total 6 marks)
