Grade 12 Mathematics practice

What is on the worksheet

1. Find the sum of the first 5 terms of a geometric sequence with first term 2 and ratio 4.

2. f(t) = 8t + (-7); g(t) = 2t + (-1). Find f(g(6)).

3. Evaluate log base 3 of (243 × 9).

4. f(t) = 9t + (8); g(t) = 6t + (1). Find f(g(4)).

5. An arithmetic sequence has first term 16 and common difference 13. Find term 14.

6. f(t) = 3t + (4); g(t) = 4t + (-5). Find f(g(-1)).

7. Evaluate log base 2 of (2 × 2).

8. Evaluate log base 3 of (3 × 27).

9. In a right triangle, the legs opposite and adjacent to θ are 22 cm and 29 cm. Find tan θ as a fraction.

10. A cone has radius 2 cm and height 24 cm. Use π = 3.14. Find its volume in cm³.

11. Evaluate the definite integral of (6x + 7) from x = 1 to x = 5.

12. f(x) = 2x³ + 4x² + (-8)x. Find f′(0).

13. 270° equals kπ radians. Find k as a fraction or integer.

14. Find the discriminant of 5x² + 20x + 12 = 0.

15. Data: 3, 6, 9, 12, 15, 18, 21, 24. Using medians of the lower four and upper four values, find the interquartile range.

16. Find the sum of the first 10 terms of an arithmetic sequence with first term 12 and common difference 7.

17. A score of 5 occurs 3 times; a score of 13 occurs 5 times. Find the mean as a fraction or decimal.

18. Find the limit of 3x² + 4 as x approaches 2.

19. For f(x) = 12x^3, find f′(3).

20. Find the population variance of 61, 66, 71, 76, 81. Divide by 5.