Download Year 13 Mathematics with statistics

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