QUESTION ONE (30 MARKS)
a) Solve the following equations for x. i. 3 ?? + 5 = 2 -6 – ?? – 2?? (2 Marks) ii. ??-2 ?? + 1 = 2?? 7 (3 Marks) iii. 2?? ??+3 = 3 ??-10 + 2 (3 Marks) b) Factorise and solve 4??2 – 20?? + 9 = 0. (5 Marks) c) Find the 40th term and the sum of the first 40 terms of the arithmetic sequence 10, 8, 6,… (5 Marks) d) The following marks scored by 10 students in a maths test. 50, 54, 60, 70, 73, 61, 68, 50, 40, 52 Find: i. The mode mark (1 Mark) ii. The mean mark (3 Marks) iii. The media mark (2 Marks) e) i) Define a set. (2 Marks) ii) Let ?? = ??,??,?? ,?? = ??,??,?? . Find ?? ? ??,?? n ?? ?????? ?? n ?? n (?? ? ??). (7 Marks)
QUESTION TWO (20 MARKS)
a) the following are marks of 20 students in a mathematics exam
2
Class Frequency 0-9 3 10-19 3 20-29 4 30-39 2 40-49 3 50-59 5
Use the data to compute i. Arithmetic mean. (2 Marks) ii. Median (4 Marks) iii. Modal class (1 Mark) iv. Variance (4 Marks) v. Standard deviation (1 Mark) b) given the sequence 4, 20, 100,…. Evaluate T9 and S9. (4 Marks) c) solve 2?? + 3?? = 5 3?? + 5?? = 7 by substitution. (4 Marks)
QUESTION THREE (20 MARKS)
a) Solve for y in 5 2??-6
=
10-?? ??2-6??+9 . (6 Marks) b) Given that 20 = 60 1 – ??-?? 2 determine the value of t, correct to 3 significant figures. (3 Marks) c) Factorise the expression ??2 – 42?? + 320 and solve for x. (4 Marks) d) John deposits ksh. 100,000 which earns simple interest at a rate of 10% p.a. Determine i. The interest after 3 years. (3 Marks) ii. The total amount in the bank after 3 years. (1 Mark) e) The 6th term of an AP is 17 and the 13th term is 38. Determine the 19th term. (3Marks)
QUESTION FOUR (20 MARKS)
a) Solve for each of the following and check your answer i. 4?? ??2-2?? = 1 5-?? (4 Marks) ii. 3??+4 ??-1 = 2 + 7 ??-1 (4 Marks) b) A widget is being sold in a store for $13540 and has been marked up 7%. How much did the store pay for the widget? (3 Marks) c) Solve the equation ??2 – 10?? + 34 = 0. (5 Marks) d) Solve 3?? + 2?? = 12 5?? – 4?? = -2 by elimination method.
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