Mathematics · Practice test
SS 1 practice test
17 questions + 2 written tasks. Answers and your score show when you submit the whole test.
1. Express 0.00562 in standard form.
2. Express 0.0027981 in standard form, correct to 2 significant figures.
3. Express the product of 0.06 and 0.09 in standard form.
4. Evaluate (3.2 × 10⁴) × (2.5 × 10⁻⁶), giving the answer in standard form.
5. Evaluate 27^(2/3) × 16^(-1/4).
6. Solve 2^(x + 1) = 32.
7. Simplify √50 − √18 + √8.
8. Without tables, evaluate log₁₀ 8 + log₁₀ 125.
9. Given log 2 = 0.3010 and log 3 = 0.4771, find log 18.
10. Find the number whose logarithm to base 10 is 2.6025.
11. Use tables or a calculator to evaluate (53.75)².
12. If sin x = cos 50°, then x equals
13. cos 57° has the same value as
14. Evaluate cos 40° − sin 30° to 4 decimal places.
15. If sin θ = 5/13 and θ is acute, find cos θ and tan θ.
16. In triangle ABC, angle B = 90°, BC = 4 cm and angle BAC = 60°. Find AB to one decimal place.
17. A student writes: log(a + b) = log a + log b. Test this with a = b = 10 and explain the error.
Written tasks
Not part of the score above. Write your answer here or on paper, then you, a parent or a teacher can mark it with the marking guide.
1. Two fair dice are thrown. (a) Draw the sample space. (b) Find the probability that the total is (i) 8 (ii) at least 10 (iii) a prime number. (c) Explain whether a total of 7 or a total of 10 is more likely. (9 marks)
2. Marks of 60 students: 0–9: 4; 10–19: 6; 20–29: 10; 30–39: 14; 40–49: 12; 50–59: 8; 60–69: 6. (a) Draw a cumulative frequency curve. (b) Estimate the median and interquartile range. (c) If the pass mark is 40, estimate the percentage who passed and comment on the result. (9 marks)
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