Penstripe Student Planner Catalogue 24-25 - Flipbook - Page 174
6
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NUMERACY - SHAPE & SPACE
NUMERACY - ALGEBRA
Mathematics - algebra
Mathematics - shape & space
A straight line is 180°
1100
600
300
A reflex angle is
more than 180°
850
750
Around a point
is 360°
The angles in a triangle
add up to 180°
Angles in a quadrilateral
add up to 360°
Parallel lines
Parallel lines
Parallel lines
a
z
f
b
b
Corresponding angles (f)
are the same
4b
Supplementary angles (a & b)
add up to 180°
k/2
means “k divided by 2”
v2
means “v x v”
or “v squared”
c
H
c
u
ten
po
A
O
a
θ
b
Pythagoras’ theorem
c2 = a 2 + b 2
sin θ =
Ο
H
=
cos θ =
A
H
=
tan θ =
Ο
A
=
Sine law
a
=
sinA
A
opposite
SOH
hypotenuse
TOA
Remember! SOH CAH TOA
ax ÷ ay = ax-y
Simplifying expressions
p0 = 1
p-n means 1/pn
E.g. 3-2 = 1/32 = 1/9
E.g. 3a + 4b - 2a + b - 3c
p1/n means n√p
E.g. 271/3 = 3√27 = 3
Circle the first type of like
terms. Collect them together.
DEAL WITH THE DIGITS AND
THEN WITH THE INDICES!!!
E.g. 6a2b x 3ab3
= 6x3 x a2x a x b x b3
= 18 x a(2+1) x b(1+3)
Remember
– common mistake!
Underline the next set of like
terms. Collect them together.
a
(ax)y = axy
p1 = p
= 18a3b4
a2 = a x a and 2a = 2 x a
E.g. 6a2b ÷ 3ab3
so
= 6÷3 x a2 ÷ a x b ÷ b3
a2 + 2a cannot be simplified
further as a2 is not LIKE 2a !!!
+ 5b -3c
a
= 2
b
Multiplying brackets grid method
c
b
=
sinC
sinB
Multiplying brackets
grid method
a(b+c)
Multiplying brackets
grid method
a(b-c)
x
b
c
x
b
-c
x
a
b
ab
ac
a
ab
-ac
a
a2
ab
c
ac
cb
= ab - ac
An example of
multiplying to get a
quadratic equation
(a+2)(a-3)
Multiplying double
brackets
(a+b)(a+c)
a
= ab + ac
b
x
w
l
h
a
h
l
Quadratic formula
For solving ax +bx+c = 0
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2016Penstripe
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Rectangle
Perimeter = 2 (l+w)
Area = l x w
a
c
h
Parallelogram
Perimeter = 2 (a+b)
Area = b x h
r
b
Triangle
Perimeter = a+b+c
bxh
Area = 2
Circle
Circumference = 2πr
Area = πr2
Description
Numeracy - shape & space
174
Design Right and Copyright © 2023 Penstripe
Cuboid
Volume = l x w x h
Prism
Volume = cross section area x l
REMEMBER!
x = –b+
– b2–4ac
2a
Other useful websites:
Perimeter is the 1-D length around a shape: m, cm
Area is the 2-D space inside a shape: m2, cm2
Volume is the 3-D space inside a solid: m3, cm3
Capacity is the amount something can hold: l, ml
Remember to start with the same UNITS!
Page Ref.
Y5-5
Description
Numeracy - algebra
a
-3
a
a2
-3a
2
2a
-6
= a2 - 3a + 2a - 6
= a2 - a - 6
= a2 + ab + ac + bc
w
x a(2-1) x b(1-3)
= 2ab-2
= a +5b -3c
C
Perimeter, area & volume
l
ax x ay = ax+y
means p x p x p
pn means p x p x … x p
(n times)
Continue and tidy up!
Cosine law
a2 = b2+c2–2bc cosA
b2 = a2+c2–2ac cosB
c2 = a2+b2–2ab cosC
1
Area of a triangle = 2 ab sinC
adjacent
CAH
hypotenuse
opposite
adjacent
B
Rules of indices
Simplifying by collecting
like terms
=
hy
p
means “4 multiplied
by b” or “4 lots of b”
= 3a -2a +4b +b -3c
Trigonometry
se
3
= 3a -2a +4b +b -3c
f
Alternate angles (z)
are the same
Vertically opposite angles
are equal
p2 means p x p
= 3a + 4b -2a + b -3c
a
b
z
a
Indices (powers)
a – 5 means “take 5 from a”
or “5 less than a”
Useful web addresses
www.mathsnet.net
www.countonus.org.uk
www.nrich.maths.org
www.bbc.co.uk/bitesize/subjects
www.emaths.co.uk
www.mathsisfun.com
Page Ref.
Y5-6
DesignRight
Rightand
andCopyright
Copyright©©1997,
1997,2016
2016Penstripe
PenstripeY1Y5
Design
An obtuse angle is more
than 90° and less than 180°
A right angle is 90°
An acute angle is less
than 90°
3 + s means “3 plus s”
or “s more than 3”
