|
INSTRUCTIONSUnless otherwise stated in the question all answers should: - be written WITHOUT spaces e.g. P=2l+2w- sets should be written with the SMALLEST number first e.g. {-3,-1,5,7}- be written with NUMBERS FIRST, followed by letters in ALPHABETICAL ordere.g. -2bcm, -3x2 - use ^ for powers e.g. xΛ2 squared is x2- be written in descending powers e.g. -3x3+x2-3x+1- use <= for less than or equals; >= for greater than or equals- use sqrt for square root- use cubert for cube root 1. The fifth term of an arithmetic sequence is 20 and the twelfth term is 41. The common difference is The first term of the sequence is The value of the 84th term is The sum of the first 200 terms is 2. The length of one side of a rectangle is 2 cm longer than its width. (d) Find the area of the square. The sum of the areas of the rectangle and the square is 2x2 + 4x +1 (cm2). (c) Given that this sum is 49 cm2, find x. (a) If the smaller side is x cm, find the perimeter of the rectangle in terms of x. The perimeter of a square is equal to the perimeter of the rectangle in part (a). (b) Determine the length of each side of the square in terms of x. cm2 cm cm 3. (a) Write down the following numbers in increasing order. 3.5, 1.6 ×10−19, 60730, 6.073×105, 0.006073×106, pi, 9.8×10−18 (b) Write down the median of the numbers. (c) State which of the numbers is irrational. 4. Consider the geometric sequence 8, a, 2,… for which the common ratio is 0.5. (b) The value of the eighth term, written as a decimal, is (a) Find the value of a. (d) The sum of the first twelve terms, to the nearest whole number, is 5. (a) Factorize the expression x2 − 25. (b) Factorize the expression x2 – 3x – 4. (c) Solve the equation x2 – 3x – 4 = 0. x = (Smallest) (Smallest) Smallest (Biggest) or x = (Biggest) e.g. (x-3)(x+6) NO spaces Biggest 6. The following table shows the monthly payments needed to repay a loan of $1000. This question continues on the next slide. (b) Find the exact total of the repayments she will make. (c) Find the rate of interest charged on the loan. (a) Calculate the exact monthly repayments she will make. Beryl took out a loan of $10000 for 18 months. The total she paid for the loan was $10837.80. Sarah takes out a personal loan of $24000 to buy a new car. Note: Money has 2 decimal numbers. $ $ % |