Download Copy of Module 3 part II

MODULE 3 HIGHER
objective
long division and multiplication
division with decimals
round to significant figures
identify factors and multiples of a number
be able to identify a prime number
use prime factor decompostion to calculate LCM and HCF
multiply and divide negative numbers
follow heirarchy of operations (BIDMAS)
write one quantity as a fraction of another
add and subtract fractions
235 x 24 = 5640; 636 ÷ 53 = 12
42 ÷ 0.2 = 210; 19.8 ÷ 0.55 = 36
45 281 ≈ 45 300 (to 3 s.f.), 7.3782 ≈ 7.38 (to 3 s.f.)
factors of 24 are 1,2,3,4,6,8,12,24; first 5 multiples of 6 are 6, 12, 18, 24, 30
list all prime numbers between 40 and 50
60 = 22 x 3 x 5
3 x -4 = -12; -24 ÷ -6 = 4
(-3 x 5) x -2 = 30
12 out of 30 days = 2/5
5
/6 - 3/4 = 1/12; 2 1/3 + 3 5/7 = 6 1/21
multiply fractions
4
divide fractions
percentage change
write one quantity as a percentage of another
repeated percentage change
reverse percentage change
dividing amounts into given ratio
finding missing amounts using ratios
speed, time and distance
unitary method
best buys
density, mass and volume
use index laws to simplify or evaluate expressions
Understand fractional and negative powers
5
Convert to and from standard form
Calculations with standard form without calculators
Calculations with standard form with calculators
Convert recuring decimals to fractions
3.6 million = 3.6 x 106; 0.004 = 4 x 10-3, 2.5 x 104 = 2500
(2 x 104) x (6 x 107) = 2 x 6 x 104 x 107 = 12 x 1011 = 1.2 x 1012
(1.8 x 1015) ÷ (1.86 x 105) = 9.7 x 109
0.777777… = 7/9
Use rules to simplify surds
plot gradratic graphs and use graphs to solve equation
use method of intersection to solve equations
find constant of proportionality given relationship
direct proportion with squares, cubes and roots
inverse proportion
limits of accuracy
problems involving limits of accuracy
√a x √b = √ab; √a ÷ √b = √(a/b); C√a x D√b = CD√ab; C√a ÷ D√b = C/D√(a/b)
/9 x 3/10 = 2/15; 2 2/5 x 1 7/8 = 4 1/2
/6 ÷ 3/4 = 5/6 x 4/3 = 1 1/9; 2 1/2 ÷ 3 1/3 = 5/2 ÷ 10/3 = 5/2 x 3/10 = 15/20 = ¾
to calculate 4% increase x 1.04; to calculate 23% decrease x 0.77
12 out of 30 days = (12 ÷ 30) x 100 = 40%
tree grows 5% each year, starts at 10cm, how tall after 3 days; 10 x (1.05)3= 11.6
after 20% decrease cost is 70. What was original price? c x 0.8 = 70, c = 70 ÷ 0.8 = 87.50
share £40 in the ratio 2:3; £16 and £24
An amount is shared in ratio 3:5, 1st amount is 210, what is 2nd amount? 350
Calculate one value given 2 of the others. How far traveled if go at 60 mph for 3.5 hours? 210 miles
If 8 pens cost £2.64, how much do 5 pens cost? 1 pen is 33p so 5 pens cost £1.65
Which is best: 800g for £1.60 or 2.5kg for £4.75? 1st is 5g for 1p, 2nd is 5.26g for 1p
Calculate one value given 2 of the others.
2a2 x 3a4 = 6a6; (2a2)3 = 8a6
251/2 = √25 = 5; 64-2/3 = 4-2 = 1/16
T is proportional to M. If T = 20 when M = 4, find an equation to link the two; T = 5M
g is proportional to v2. If g = 36 when v = 3, find an equation to link the two; g = 4v2
R is inversely proportional to F. If R = 9 when F = 4, find an equation to link the two; R = 36/F
What is min/max length if given as 220m measured to 3 s.f.? Min is 219.5, max is 220.5
If length and width to 1cm are 7 and 5, what is max area? 7.5 x 5.5 = 41.25