Maths non calculator Flashcards
Kevin is y years old his sister is 11 and his brother is twice his age all 3 siblings have a total age of 26,wite an equation to find kevins age
y+11+2y=26
3y+11=26 -11
3y=15 /3
y=5
xn+1=3sq root 60-2x to the power of 2 over n use this formula to work out an aproximate value of x starting with x1=3
x1=3=ans
replace xn with ans
3sq root(60-2 X ans sq)=19.4
x2=19.4422
Does a cumaltitive frequency graph plot a midpoint
no only frequency polygons do
How do you find the coefficinet of 2 sq
second difference /2
complete the nth term for this sequence
1 2 3 4 5
5 12 21 32 45
For equation
+7,+9 second difference =+2
then subtract n2(2) from the sequence
5-1=4
12-4=8 difference is +4=
4n
A purple square is in the middle of 4 shapes the measurments around it are 8cm and 3cm work out the area of the purple square
3 + w=8 -3
w=5
5 x 5=25
what is the equation for the area of a square
width x width
factorise f sq+4f+3
(f+1)(f+3)
what is the equation to find the area of one square
length sq
what is the percentage change from 7905 to 8331.87
8331.87-7905=426.87
426.87/7905=0.054 x 100
=5.4
Ruby and thomas played 80 games of rock paper scissors Ruby won 35% of the games and thomas won 20% how many did they draw
80 x 0.35=28
80 x 0.2=16
28+16=44
80-44=36
Vinnie invests 2800 in two accounts for 11 years how much will he make out of account a(simple interest at a rate of 8% per year b(compound interest at a rate of 6% per year)
a)0.08 x 2800=244 x 11
2684
b)2800 x 1.06 to the power 11=ans-2800
=2214.37
when transforming graphs how do you know if it’s to the whole function or not
if a single number comes after a squaring in an equation than it’s to the whole function
What is 0.7% of 13,250
0.7 x100=0.007
0.007 X 13250=92.75
what is the answer to q1 in book
10.6
y=f(x) is mapped onto 0,-3 from 0,0 write the function for this
y=f(x)-3
Expand and simplify (2+ root 3)(8-root 3)
expand brackets
(2 x 8)+ (2 x -root 3)+(root 3 x 8)+(root 3 x -root3)
16+(-2 root 3)+(8 root 3)+(-3)
(16-3)=13
(-2 root 3 +8 root 3)=6 root 3
13+ 6 root 3
A student draws a triangle and labels an angle as x,the hypotenuse has a length of 12.4cm and the adjacent has a side length of 9.8cm calculate the size of x
to find an angle use cos-1
we use cos because we only have hyp and adj
cos-1(9.8/12.4)=37.78
Blue and yellow paint are mixed in a dye to make a ratio of 8:3 to make 44 litres of a green-coloured dye.A further of 8 litres yellow dye is added to the mixture.What is the new ratio
8:3 x4=44
12+8=20
32:20
find hcf
/4=
8:5
Angle d and f sit on a straight line their ratios are
2:3 calculate the size of them
2+3=5
180/5=36
2 x 36=72
3 x 36=108
what is the equation for relative frequency
frequency of event/number of trials
500 people played a game the relative frequency of winning was 0.34,how many times was the game won
0.34 x 500=170
74 is then decreased by 6.3g calculate the upper and lower bound of this
74.5 and 73.5
6.25 an 6.35 for each of them you have to separate the lower bound from the upper bound and vica verca
73.5-6.35=67.15
74.5-6.25=68.25
lower bound=67.15
upper bound=68.25
the distance around the edge of a circular swimming pool is 26m,calculate the distance from the edge of the pool to the centre
circumference=26m
circumference =2pi r /2pi
26/2 pi=4.1
r=radius
Harvey has a ring size circumference of 57.3mm what would his ring size be if it was measured in a dimaeter
circumference=pi d
57.3=pi d /pi
57.3/pi=d
=18.2
A circle fits exactly within a square the area of the square is 25mm work out the circumference of the circle
diameter=side length of square
sq root of 25=5=side length
5 x pi=5pi
How do we find the side length of a square
area of a square=side length sq
Alex rode a bike making 7 complete rotations the diamtetr of the wheel was 1.7m how far did he ride
pi x 1.7 x 7=37.4
kite a and kite b are similar kite a has one length which is 18mm and it’s area is 250mm sq kite b area is x and it’s area is 10mm sq work out x
10 x k sq=250 /10
25=k sq
k=5
X x 5=18 /5
18/5=x
x=3.6
I think of a number that has 2 decimal places,when i round my number to 1 decimal place i get 16.8 as my answer what is the smallest number I could b thinking of
16.75
What is the largest whole number that rounds to 800 when rounded to the nearest 100
849
If (x+6):3 is equivalent to 7x:12 then what is the value of x
you have to get both sides of the ratio equal
3 x 4=12 then times other side by 4 and it is equal to the other ratio
4(x+6)=7x
4x+24=7x -7x
-3x+24=0 -24
-3x=-24
x=-24/-3
=8
what number has the prime decomposition 5 sq x 41
25 x 41=1025
Eastwood writes down the prime decomposition of 224 as 2 to the power of a X b find a and b
write a factor tree down and keep on dividing by 2 until you come across a prime number this is your answe
2 to the power of 5(how many times we have divided by 2) X 7(the number left)
solve the following inequality r/2+15>45
r/2+15>45 -15
r/2>30 x2
r>60 answer
A pair of simeltanous equations are shown 6x+7y=41 and 8x+11y=63 the coeficcinets of x are 6 and 8 find the lcm of this then multiply it into the equation
lcm=24
6x+7y=41 x4
8x+11y=63 x3 this is to get x as 24
24x+28y=164
24x+33y=189 then subtract to find y
make sure you have a positive coefficient
5y=25/5
5=y
sub y into an original equation to solve x
6x+35=41 -35
6x=6 /6
1=x
ABC is a triangle AB=a+5b,AC=9b express CB in terms of ab ab is in an opposite direction
CB=-AB+AC
CB=-a+5b+9b collect like terms
-a+14b
What is -1 3/7(vector)+ 14 1/-2(vector)=
times them
-3/-7+14/-28 add top and bottom together
11/-35
AB is a straight line where AB=6a-8b
M is the midpoint of AB
Express AM in the terms of a and b
AM=0.5 AB
0.5AB=3a-4b
how do we find the class width
upper end of class-lower end of class
how do we find frequecy density
frequency/class width
For every orange counter there are 8 green counters.For every 2 green counters there are 3 purple counters.What is the ratio of orange counters to purple counters
1:8 2:3 green counters are common so we find the lcm to get them equal
2:3 x4
8:12
1:12
