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Year 13 Mathematics with statistics Baseline Data Gathering. Factorise Name…………………………………… /42 /5 1. x 2 6 x 9 2. 18ab 2 12a 2 b 2 4. r 2 5r 6 3. 16 p 2 4 x 2 5. If x 2 12 x k Is a perfect square then find k k = /5 Indices x (a) If 4 20 then x is closest to?(i) 0.8 (ii) 2.15 Solve for x (b) 9 x 27 (c) 4 x 1 64 x= Simplify (d) x 3 x 5 x 4 Solving (iv) log20 log4 (iii) 3.2 x= (e) (3ab 2 ) 4 /5 (a) Find the solution set to (3x 4)(5 x ) 0 x= or (b) Solve the equation 3x 2 2 x 4 (use the formula) give your answers to 4sf. x= (c) Solve the simultaneous equations (d) Solve x 2 4 x 0 3x 4 y 0 x 2 y 5 x= x= or or x= y= (e) Solve x 3 2.8 x= x= or x= /10 Statistics (a) Explain the difference between continuous and discrete data. (b) Explain the word “random” as it is used in sampling. 1 (c) Length of longest finger of adults (in cm). length 5.0 5.5 6.0 – 6.5 freq 4 6 11 13 (i) 7.0 – 12 7.59 8.5 – 9.0 3 8.0 6 Find the mode, median and mean Mode Median Mean Prob = (ii) Find probability that a longest finger is between 6.0 and 7.5cm (ii) Draw a cumulative frequency graph and on it show the upper quartile. 70 60 50 40 30 20 10 0 /5 Sequences and Series 3 (a) Evaluate (2 n n) (b) List the first 4 terms of a GP with S 6 and the n 2 first term is 3. Sum = T1 = T2 = T3 = (c) Find the sum of the first 20 terms of the GP 8, 6, 4.5, …………. (d) Find T30 in the following AP 4, 4.2, 4.4, 4.6, …….. (e) The first term of a AP is 20. If the eighth term is 48 then find the common difference. T4 = Sum = T30 = Common difference = Calculus Differentiate (a) f ( x ) 3x 8 f (x ) /7 (b) f ( x ) 43 x 8 f (x ) (c) f ( x ) (3x 2) 2 f (x ) (d) f ( x) f (x ) (e) 4 2x 5 f ( x) 3 5 x f (x ) 2 (f) Find the gradient of the tangent to the curve y 3x 2 2 x 4 at the point where x = 2 Gradient = (g) Find the stationery points for the function f ( x ) First point = ( Probability , ) Second point = ( ) Totals What is the probability of: (i) A person chosen at random is a smoker? Prob = Prob = (ii) A male person chosen at random is a smoker (c) , /5 (a) Complete the table below Female Male Smokers 13 15 Non smokers 10 9 Totals (b) 4x 3 2 x 2 8x 7 3 If two dice are thrown then find the probability that: (i) The sum is a prime number. Prob = (ii) At least one of the numbers is divisible by 3. Prob = 3