Download Pre-GCSE Maths for Year 9

Pre-GCSE Skills List June 2016
Heart of England
Mathematics
Pre-GCSE Skills List
Pre-GCSE Skills List June 2016
M1
Use mathematical notation/symbols correctly & show working out
N1
Know & use times-tables up to 12
N2
Add, subtract, multiply & divide with integers, including negative numbers
N3
Add, subtract, multiply & divide with decimals
N4
Add subtract, multiply & divide with fractions
N5
Know and use the order of operations (BIDMAS)
N6
Find factors & multiples of numbers
N7
Convert between and compare fractions, decimals & percentages.
N8
Know square numbers up to 15 and cube numbers up to 5, plus powers of 10
N9
Understand indices including √ 𝑎𝑛𝑑 ∛
N10
Use inequality symbols between pairs of numbers
N11
Increase & decrease an amount by a given percentage
N12
Share in a given ratio and link ratio to fractions
A1
Read & plot co-ordinates in 4 quadrants
A2
Simplify algebraic expressions by collecting like terms
A3
Expand & factorise expressions with a single bracket
A4
Substitute values into an expression or formula
A5
Use & find the nth term of a linear sequence
A6
Plot straight line graphs
A7
Solve 1-, 2- & 3-step linear equations
G1
Scale axes accurately for co-ordinate & data presentation purposes
G2
Name 2D & 3D shapes
G3
Find the area & perimeter of rectangle, triangle, parallelogram, trapezium & circle.
G4
Know angle rules, including angles in parallel lines.
G5
Find interior & exterior angles of polygons
G6
Identify reflection & rotational symmetry in 2D shapes
G7
Calculate volume & surface area of cuboids
D1
Draw bar charts, line graphs & pie charts
D2
Calculate mean, median, mode & range for a small data set
D3
Determine probability for single and multiple events
Pre-GCSE Skills List June 2016
M1: Use mathematical notation/symbols correctly & show working out
Key Points:
In this part look at the mistakes students made and think how to
improve your own working.
No
MathsWatch
Rewrite the calculations using mathematical symbols and fill the gaps:
□ is 100
c) 0.4 increased by □ is 1
e) 1.0 take away □ is 0.6
g) 583 subtract □ is 343
a) 47 added to
b)
□ plus 61
d) The sum of
is 134
□ and 360 is 630
□ subtract 61 is 774
h) □ is 49 more than 533
f)
What is wrong with these statements? Find and correct the mistakes.
a) 22 – 16 = 6 ÷ 2 = 3 + 4 = 7
b) 5 ÷ 75 = 15
c) Mia had £10.37. She spent £4.89 on a gift for her mother. How much
money does Mia have left?
Answer: £6.48
d) Factors of 14 are 2 and 7.
e) 3² = 6
f) 1, 2, 3, 4, 5, 7, 11, 13, 17, 19 are first 10 prime numbers
g) 52 is a multiple of 3 and 4.
Rewrite these numbers properly underneath
Pre-GCSE Skills List June 2016
N1: Know & use times-tables up to 12
Key Points:
No
MathsWatch
In this part you need to learn times tables up to 12 and use that to
answer these questions.
Work out:
12 x 4 =
10 x 12 =
3x6=
9x8=
12 x 9 =
3 x 11 =
7 x 12 =
11 x 6 =
8x4=
11 x 8 =
10 x 10 =
9x7=
11 x 4 =
11 x 2 =
7x4=
4x9=
7 x 10 =
3x9=
9x5=
11 x 10 =
7x6=
8x7=
10 x 12 =
11 x 8 =
7x2=
4x3=
6x8=
2x9=
11 x 12 =
9x8=
There are 8 chairs in each row. How many chairs are there in 12 rows?
One colour box costs $12. How much will 4 such colour boxes cost?
How many days are in 12 weeks?
An airport holds 12 cars per row. The car park has 8 rows but only 6 of the rows
are filled. How many more cars can it hold?
Pre-GCSE Skills List June 2016
N2: Add, subtract, multiply & divide with integers, including negative numbers
Key Points:
o
o
o
When you are adding or subtracting numbers make sure you line up
the units with units, tens with tens, hundreds with hundreds and so
on.
When you are multiplying by 10, 100 and 1000 put as many extra
zeros as you have in multiplier.
When you are multiplying or dividing remember that
 Odd number of minuses will give you negative answer
 Even number of minuses will give you positive answer
MathsWatch
N13a, N14a
N15a, N16
N19
Work out, without a calculator
a) 847 + 325 =
b) 7140 + 396 =
c) 294 – 157 =
d) 6293 – 1734 =
e) 35 x 4 =
f) 73 x 6 =
g) 214 x 8 =
h) 315 x 7 =
i) 315 x 10 =
j) 17 x 1000 =
k) 43 x 20 =
l) 26 x 300 =
m) 56000 ÷ 20 =
n) 868 ÷ 7=
o) 1128 ÷ 24 =
p) 4464 ÷ 36 =
An astronaut spends 67 hours on the moon. How many minutes did the astronaut
spend on the moon?
A factory has made 4416 basketball caps. An equal number of caps are to be
delivered to 12 stores. How many caps does each store receive?
Work out, without a calculator
a) 3 - 4 =
b) -3 + 5 =
c) -2 + 7 =
d) -3 - 1 =
e) -3 - 2=
f) -4 + 6 =
g) 3 - 8 =
h) -5 + 9 =
i) 6 + (-3) =
j) 3 + (-4) =
k) 5 + (-5) =
l) -5 + (-3) =
m) 2 – (-4)=
n) 5 – (-1)=
o) 8 – (+3) =
p) 10 – (+7) =
r) 7 x (-3) =
s) -2 x (-6) =
t) 12 x (-7) =
u) – 8 x (- 4) =
v) -72 ÷ (-12) =
w) -80 ÷ 4 =
x) -100 ÷(-10) =
y) 144 ÷ (-12) =
Pre-GCSE Skills List June 2016
N3: Add, subtract, multiply & divide with decimals
Key Points:
When you want to add or subtract two decimals make sure the decimal points line
up.
MathsWatch
Use the bus stop method for division, but remember to keep decimal point in the
same place.
N14b, N15b
N2b, N13b
N17b
Arrange the following groups of numbers in order, smallest first:
a) 0.98, 0.099, 1.001, 0.9, 1.090, 0.899, 0.009.
b) 0.076, 0.067, 0.008, 0.090, 0.077, 0.007, 0.107.
Work out, without a calculator
a) 6.5 + 8.3 =
b) 4.5 +5.4 =
c) 0.54 + 0.36 =
d) 0.22 + 0.88 =
e) 5.3 + 0.24 =
f) 7.1 + 0.65 =
g) 38.19 + 27.4 = h) 62.95 + 38.77 =
i) 6.9 – 3.5 =
j) 8.7 – 1.6 =
k) 9.2 – 0.8 =
m) 0.72 – 0.08 =
n) 0.63 – 0.29 =
o) 50.46 – 29.84 = p) 60.46 – 29.9 =
l) 7.5 – 0.7 =
Jenny weighs 61.83 kilograms and Francis weighs 56.49 kilograms.
a) What is their combined weight? (show your working)
b) By how much is Jenny heavier than Francis? (show your working)
Work out, without a calculator
a) 2.8 x 10 =
b) 5.6 x 100 =
c) 10 x 3.09 =
d) 100 x 0.063 =
e) 4.32 x 4=
f) 5.98 x 2=
g) 42.64 x 7 =
h) 112.83 x 6 =
i) 18.2 ÷10 =
j) 865.12 ÷ 100 = k) 9.6 ÷ 100 =
l) 17 ÷ 1000 =
m) 7.8 ÷ 6 =
n) 16.8 ÷ 3 =
p) 526.8 ÷ 4 =
o) 91.02 ÷ 6 =
A packet of crisps weighs 26.7 grams. What is the weight of 6 packets?
Charles pays £153.30 for 6 months of Broadband on his computer. What is the
cost for each month?
Pre-GCSE Skills List June 2016
N4: Add subtract, multiply & divide with fractions
Key Points:
MathsWatch
When you are add or subtract two fractions remember to have the same
denominator.
N36
When possible, simplify your answer at the end.
N37
When you are multiplying or dividing change any mixed numbers into improper
fractions first.
Find:
a)
e)
1
2
2
3
1
of 22
b) of 700
of 18
f) of 30
1
c)
5
3
g)
5
6
of 1920
7
100
of 300
d)
1
15
of 4500
3
h) of 32
8
Work out; simplify your answer if possible:
a)
1 1
 =
3 3
3
4
2
3
b)
2 3
 =
7 7
c)
3 1
 =
4 5
d)
3 4
 =
7 9
3
8
g)
8 4
 =
9 9
h)
9
3
 =
10 10
e) 1  2 =
f) 6  2
3 2
 =
4 7
m) 1  4 =
3 5
1 1
r)  =
3 5
j)
j)
4
=
5
11 2
 =
15 3
9 7
n)  =
10 8
5 2
s)  =
8 3
3
2
=
5
7
2
7
o)  3 =
11
15
1
t) 7  =
2
k) 2  1
A theme park makes £300 profit each day. If
1
2
1
3
6
9
=
7
10
2
2
p) 4  1 =
3
5
8
u) 1  5 =
9
l) 10  4
of the profit comes from entry
fees, comes from selling food and comes from selling gifts how much money
6
5
is made from everything else each day?
1
1
1
Susie has £150 wages. She spends on her rent, on her bills, on lots of shoes.
3
5
4
How much does she have left to spend on clothes shopping?
2
3
Angie gets £125 pocket money per week. If he spends of it on sweets and of
5
10
it on toys and saves the rest, how much will he have saved after 4 weeks?
Pre-GCSE Skills List June 2016
N5: Know and use the order of operations (BIDMAS)
Key Points:
In the world of mathematics, everyone has agreed to work out problems in the same
order so that there is only one correct answer:
B (brackets) I (indices) D (division) M (multiplication) A (addition) and S (subtraction).
Makes BIDMAS.
1)
N20
Work out:
aa) 7+ 6 x 2=
b) 9 ÷ 3 + 5=
c) 14 + 30 ÷ 5=
dd) 22 – 6 x 3=
e) (24 – 9) ÷ 3=
f) 40 ÷(12 – 4)=
gg) 4 + 32 =
h) (14 ÷ 2)² =
i) 20 ÷ 22 =
jjj) 33 – 7=
k) 4 x 52 =
l) 2+ (4 + 3)2 =
n) 2² + 3 x 7=
o) 3 x (52 − 42 )=
m) 7 + 5 x (2 + 5)²=
2)
MathsWatch
Put the brackets into equations to make it work:
aa) 4 x 5 – 3 = 8
b) 18 + 3 x 5 = 105
dd) 16 - 4² + 3 = -3
Put symbols to make it work:
7 5 3 = 6
Fill the missing number in each problem
a)
□–3x8
= - 13
b) 39 ÷ □ +9 x 3 = 30
c) 7 + 4 ÷ □ – 5 = 4
d)
□ ÷ 6 + 4 x 2 – 18 = - 8
e) 22 ÷ 11 + 4 – 8 x □ = - 18
c) 32 – 5 x 2 + 4 = 2
Pre-GCSE Skills List June 2016
N6: Find Factors and Multiples of Pairs of Numbers
Key Points:
Factor – is a number which divides exactly into another number (there will be no
remainder)
Multiples – are the numbers in a multiplication table.
HCF – Highest Common Factor
Find the factors of:
a) 8
b) 26
c) 33
d) 50
e) 63
f) 64
g) 65
h) 100
Find the first 5 multiples of:
a) 2
b) 5
c) 7
d) 11
e) 20
Find the product of prime factors for:
a)
b)
c)
d)
e)
f)
8
36
63
84
99
100
Determine the HCF of:
a)
b)
c)
d)
e)
4 and 22
6 and 15
30 and 12
28 and 42
45 and 63
Determine the LCM of:
a)
b)
c)
d)
e)
4 and 22
6 and 15
30 and 12
7 and 9
20 and 100
N10, N11
N31
6, 12, 18, 24, 30, … are multiples of 6.
LCM – Lowest Common Multiple
MathsWatch
f) 31
g) 50
h) 100
Pre-GCSE Skills List June 2016
N7: Convert between and compare fractions, decimals & percentages.
Key Points:
67
Per cent means “out of 100”, so 67% means 100.
To change a fraction into a percentage, convert the denominator into 100
eg
4
5
MathsWatch
N32
80
= 100 = 80%
Complete the tables
a)
b)
Put these fractions, decimals and percentages in order, smallest to largest.
Pre-GCSE Skills List June 2016
N8: Know square numbers up to 15 and cube numbers up to 5, plus powers of 10
Key Points:
When a whole number is multiplied by itself, we get a square number.
MathsWatch
2
A calculator has a button for squaring 𝑥 .
N25
When a whole number is multiplied by itself three times, we get a cube number.
A calculator has a button for cubing 𝑥 3 .
Evaluate the following:
aa) 42 =
b) 102 =
c) 82 =
dd) 122 =
e) 12 =
f) 62 =
gg) 72 =
h) 52 =
i) 152 =
jjj) 142 =
k) 112 =
l) 92 =
m) 32 =
n) 22 =
o) 132 =
aa) 53 =
b) 23 =
c) 43 =
dd) 13 =
e) 33 =
f) 03 =
Evaluate the following:
For each of the following numbers, write YES if it is a perfect square or NO if it is not.
aa) 31
b) 49
c) 46
dd) 14
e) 1
f) 114
gg) 121
h) 9
i) 10
jjj) 199
k) 81
l) 64
n) 212
o) 100
m) 144
The area of one face of a cube equals 16. Calculate the volume of the cube.
The volume of a cube is equal to 125. Calculate the total surface area of the cube.
Pre-GCSE Skills List June 2016
N9: Understand indices including √ 𝒂𝒏𝒅 ∛
Key Points:
The square root of a number n is the number which is multiplied by itself to give that
number n. The square root of 36 is 6, because 6 x 6 = 36.
MathsWatch
N25
3
The symbol for square root is √ and for cube root is √
A calculator has a button for finding square roots √
3
and √
Work out
a) √16
b) √9
3
h) √64
b) √81
e) √1
3
i) √8
c) √36
f) √196
3
j) √1
d) √100
3
g) √125
3
k) √27
Circle number which has a whole number as a square root.
30
32
34
36
Circle number which doesn’t have a whole number as a square root.
25
35
49
64
What is the quickest way to find the square root of 8
-
divide 8 by 2
multiply 8 by 2
take 2 away from 8
use a calculator
You are given the two numbers “9 squared” and “81”. How do they relate to each
other?
-
81 is the larger number
9 squared is the larger number
they are both the same
they are in no way related
Add together the square root of 81 with the cube root of 216. Now, square the
result. What is your final answer?
Pre-GCSE Skills List June 2016
N10: Use inequality symbols between pairs of numbers
Key Points:
- > means greater than
o 5>2
o -1 > -4
- < means less than
o 4<9
o -2 < 3
- ≥ means greater than or equal to
o 6≥2
o 3≥3
- ≤ means less than or equal to
o 3≤5
o 2≤2
1) If
Mathswatch
A20a/b
< 125, write a possible number for
2) If
> 62, write a possible number for
3) If
≤ 21, write a possible number for
4) If
≥ 30, write a possible number for
5) If
< - 8, write a possible number for
6) If
> -3, write a possible number for
7) If 2 <
8) If -7 ≤
≤ 8, write a possible number for
< -1, write a possible number for
9) Fill in either < or > for each of the following
a) 4
8
b) -1
-5
c) -1
4
d) 6
-5
10) Write whether each of the following are true or false
a) 5 < 6
b) 3 ≥ 3
c) -4 < -2
d) -5 ≤ -8
Pre-GCSE Skills List June 2016
N11: Increase & decrease an amount by a given percentage
Key Points:
- To find 50%, divide by 2
50% of 24 = 12
- To find 10%, divide by 10
10% of 70 = 7
- To find 20%, find 10% then multiply by 2
20% of 70 = 14
- To find 30%, find 10% then multiply by 3
30% of 70 = 21
- To find 1%, divide by 100
1% of 300 = 3
To increase by a percentage, add on to the original amount
To decrease by a percentage, take away from the original amount
Find:
50% of 20 =
50% of 18 =
50% of 36 =
50 % of 62 =
10% of 20 =
10% of 70 =
10% of 54 =
10% of 720 =
10% of 351 =
20% of 60 =
20% of 40 =
30% of 80 =
60% of 70 =
80% of 90 =
30% of 54 =
60% of 72 =
5% of 30 =
5% of 66 =
1% of 50 =
1% of 82 =
3% of 80 =
7% of 68 =
54% of 60 =
61% of 32 =
Increase 40 by 20%
Decrease 30 by 5%
Decrease 72 by 15%
Increase 68 by 55%
Increase 28 by 82%
Decrease 300 by 81%
Mathswatch
R9a/b
Pre-GCSE Skills List June 2016
N12: Share in a given ratio and link ratio to fractions
Key Points:
To share in a given ratio:
Example: Dan and Jamie share £24 in the ratio 5:3, how much do each of them have?
- Ratio is 5:3 so 8 parts in total, so 1 part: £24 ÷ 8 = £3
- Dan gets 5 parts: £3 x 5 = £15
- Jamie gets 3 parts: £3 x 3 = £9
Ratio to fraction:
3:7 as a ratio is the same as
3
10
and
Mathswatch
R5a/b
7
.
10
Sharing in a given ratio:
1) Divide £16 in the ratio 1:3
2) Divide £90 in the ratio 5:4
3) Divide 24g in the ratio 5:3
4) Divide 80g in the ratio 3:2
5) Divide £60 in the ratio 3:1
6) Divide £80 in the ratio 5:1:2
7) Divide £36 in the ratio 2:3:4
8) Divide 500g in the ratio 8:5:7
9) In a class the ratio of girls to boys is 4:3. If there are 28 children in the class,
how many girls and how many boys are there?
10) A woman divides £72 between Cath and Ben in the ratio 8:5. How much does
Ben receive?
11) For a school trip there needs to be a ratio of adults to young people of 2:17.
How many adults are needed for a trip with 85 young people?
Ratio to Fraction: Make sure you give your answers in the simplest form
1) The ratio of boys to girls is 4:7, what is the fraction of boys?
2) The ratio of boys to girls is 6:2, what is the fraction of girls?
3) The ratio of x:y is 2:3. Which of the following is correct?
2
x is of y
3
2
y is of x
3
2
x is of y
5
2
y is of x
5
Pre-GCSE Skills List June 2016
A1: Read & plot co-ordinates in 4 quadrants
Key Points:
The position of a point on a grid is given by a coordinate such as (3,5)
The first number is how far horizontally (across).
The second number is how far vertically (up/down).
Give the coordinates for each of the following
Plot a set of axis from x: -10 to 10 and y: -10 to 10.
Plot the following coordinates:
1) (3,5)
2) (-2,5)
3) (4, -2)
4) (-4, -3)
5) (6, 3.5)
6) (2.5, 5.5)
7) (-3.5, 4)
8) (-9, - 8.5)
Mathswatch
A1a/b
Pre-GCSE Skills List June 2016
A2: Simplify algebraic expressions by collecting like terms
Key Points:
a + b cannot be added together because they are different terms
a + 3a = 4a because a and 3a are like terms
Examples:
4x + x = 5x
5c - 8c = -3c
3x + 2y - x - 5y = 2x - 3y
Mathswatch
A6
6x + 2x + 3y - y = 8x + 2y
5x + 6x -2y - 8y = 11x - 8y
Simplify each of the following:
1) 3x + 4x
2) 7x - 3x
3) 5x + 2y - x
4) 6x + 8 + 3x - 5
5) 7x - y - 3x - 4y
6) 5a + 2a - 4c - a + 3c
7) 6p - 3q - 8q + 3p
8) -5r - 2s + 3s - 4r
Circle the statement that is equal to 5x - 3 + 4x
6x
9x - 3
x+3
x-3
Circle the statement that is equal to 5x2 + 3x - x + 2x2
9x
7x2 - 2x
7x2 + 2x
9x2
Find the perimeter of the following shapes. Simplify your answers
Pre-GCSE Skills List June 2016
A3: Expand & factorise expressions with a single bracket
Key Points:
Expanding: Take out of brackets. Whatever is outside the bracket, multiply by what
is inside bracket
3 ( x + 5 ) = 3x + 15
Mathswatch
5 ( 2x - 4) = 10x - 20
Factorising: Put into brackets. Find common factors to take out of both parts. Put
these before the bracket, see what needs to be multiplied for original amount
5x + 15 = 5( x + 3)
6x - 9 = 3( 2x - 3)
Expanding
1) 5(x + 2)
2) 3(x - 6)
3) 6(x - 8)
4) 7(x + 3)
5) 3(4x - 6)
6) 2(8x + 5)
7) 9(3x - 1)
8) 6(4x - 2)
9) 5(2x + 6y)
10) 7(8x - 3y)
Expand and simplify the following
1) 5(x + 3) + 2(3x - 6)
2) 4(2x - 6) + 3(5x + 4)
3) 7(8x + 6) + 4(6x - 3)
Factorising
1) 4x + 6
2) 3x - 9
3) 5x - 20
4) 6x + 18
5) 14x - 21
6) 12x - 24
7) 6x - 9
8) 9x - 15
9) 10x - 20
10) 30x - 18
A8/A9
Pre-GCSE Skills List June 2016
A4: Substitute values into an expression or formula
Key Points:
Replace the letter with the number given
3a means 3 x a
a2 means a x a
𝑎
means a ÷ b
𝑏
3
ab means a x b
7a + 2 means ‘7 x a then add 2’
7(a+2) means ‘a + 2 then multiplied by 7’
3
a means a x a x a
4a means ‘a x a x a then multiplied by 4
(4a)2 means ‘4 times a then square the answer
If a = 3 and b = 5 find the following:
1) 4a
2) 3b
3) a + b
4) a2
5) 3a + 2b
6) b - a
7) 6a - 2b
8) b2 - a
If x = 7 and y = -2 find the following
1) 3x
2) 4y
3) 3x + y
4) 6x - 2y
a = 3b + c , Find the value of a for each given b and c
1) b = 3, c = 2
2) b = 5, c = -2
3) b = -1, c = 7
r = s2 + 4t , Find the value of r for each given s and t
1) s = 3, t = 2
2) s = -1, t = 4
3) s = 6, t = -2
Mathswatch
A10
Pre-GCSE Skills List June 2016
A5: Use & find the nth term of a linear sequence
Key Points:
nth term: ‘What’s the difference, what’s the previous number’
Example: 5, 8, 11, 14, 17, …
nth term is 3n + 2
2, 6, 10, 14 , 18, …
nth term is 4n - 2
10th term: find nth term then substitute 10 instead of ‘n’
Example: nth term is 5n - 3
10th term is 5 x 10 - 3 = 47
20th term is 5 x 20 - 3 = 97
1) Find the nth term for each of the following
a) 4, 7, 10, 13, 16, 19, ….
b) 8, 13, 18, 23, 28, 33, …
c) 2, 8, 14, 20, 26, 32, …
d) -3, -1, 1, 3, 5, 7, 9, …
e) 17, 26, 35, 44, 53, 62, …
f) 38, 32, 26, 20, 14, 8, …
2) Find the 10th term for each of the above sequences
3) Andy makes different huts with matches
Mathswatch
A11a/b/c
Pre-GCSE Skills List June 2016
A6: Plot straight line graphs
Key Points:
Use an x, y table to find points for x and y
y = 3x + 2
x
0
1
y
2
5
2
8
Mathswatch
3
11
A14a/b/c
Draw a set of axes and plot the points onto the graph
Use a straight line to join up points
1) Complete the following table for
y = 2x - 1
x
y
0
1
2
3
Plot these coordinates on the graph and join the coordinates with a straight line
to draw the graph of y = 2x - 1
2) Plot a set of axis from x: -10 to 10 and y: -10 to 10. Draw graphs of the following
a) y = 3x + 2
b) y = x - 4
c) y = 2x - 3
Pre-GCSE Skills List June 2016
A7: Solve 1-, 2- & 3-step linear equations
Key Points: an equation has an ‘=’ sign in it
Solve x + 3 = 7 means ‘find the value of x which fits the equation’ so x = 4
Harder equations:
3x + 2 = 20 (Subtract 2)
3x = 18 (Divide by 3)
x=6
Mathswatch
5x - 4 = 3x + 12
(Subtract 3x)
2x - 4 = 12
(add 4)
2x = 16
(divide by 2)
A12
x=8
Solve the following:
1) x + 3 = 7
2) x - 6 = 2
3) 3x = 18
4) 5x = 25
5) 6x = 36
6) 7x = -21
7) 3x + 1 = 13
8) 5x - 2 = 18
9) 10x + 3 = 63
10) 4x - 6 = 10
Circle the correct solution to:
x=2
𝑥
4
=8
x = 32
x = 12
Solve:
1) 4x + 3 = 3x + 10
2) 5x - 3 = 2x + 18
3) 5x - 6 = 3x + 4
4) 9x + 7 = 2x + 35
5) 4x - 6 = 8x - 10
6) 2x + 10 = 5x - 2
The perimeter of the following triangle is 39cm. Find the value of x
Pre-GCSE Skills List June 2016
G1: Scale axes accurately for co-ordinate & data presentation purposes
Key Points:
-
-
When plotting a set of coordinates using x and y or drawing a
linear/quadratic graph, you will use an x axis (horizontal plane) and y axis
(vertical plane)
For data presentation the axis will be reliant on the variables and the type of
graph used
Ensure all axis are labelled
Mathswatch
A5
Plot a set of axis from x -5 to 5 and y -5 to 5.
Plot a suitable set of axis for the following coordinates
(2,7) (9,4) (-8,5) (-5,-9) (1,10)
Create a bar chart suitable using the table below
Type of indigestion powder
Clear Turns
Indiclear
AcidGone
Fizzacid
pH of hydrochloric acid after 3 minutes
6
6
7
8
For each graph write down as many mistakes as you can and re draw the scales
correctly.
Pre-GCSE Skills List June 2016
G2: Name 2D & 3D shapes
Key Points:
-
The mathematical name for a 2D shape with straight sides is polygon
A regular polygon has equal length sides and equal size angles. Shapes have
different names depending upon how many sides they have
Types of triangles and quadrilaterals have different names depending on
properties other than the number of sides.
You must be able to identify the following 3D shapes:
Sphere, Cube, Cuboid, Cylinder, Cone, Square based pyramid, Triangle based
pyramid, Prisms
MathsWatch
G11, G12
Understand
What is the mathematical name for the following shapes:
a) 6 sides
b) 9 sides
c) 10 sides d) 7 sides
Write 2 facts about the following triangles
a) Equilateral triangle
b) Isosceles triangle
c) Scalene triangle
Write 3 facts about the following quadrilaterals
a) Square
b) Rhombus
c) Parallelogram
Write down the names of the following 3D shapes
d) Trapezium
Pre-GCSE Skills List June 2016
G3: Find the area & perimeter of rectangle, triangle, parallelogram, trapezium &
circle.
Key points:
-
Perimeter represents the length around the outside of the shape
-
The distance around the outside of a circle is known as the circumference.
You must know the formula for this
Area represents how much space there is inside a shape
Different 2d shapes have different formulas to calculate area. You must
know the formula for the following:
Triangle, Square, Rectangle, Parallelogram, Circle
Using a ruler measure the perimeter for the following shapes in cm
Calculate the area of the following shapes
Calculate the circumference and area of the following circles
MathsWatch
G9, G20, G22
Pre-GCSE Skills List June 2016
G4: Know angle rules, including angles in parallel lines.
Key points:
-
Angles on a straight line add up to 180°
Angles around a single point add up to 360°
Vertically Opposite angles are equal
With a set of parallel lines, corresponding angles are equal and alternate
angles are equal
Calculate the missing angles
Using knowledge of parallel lines calculate the missing angles
MathsWatch
G13, G18
Pre-GCSE Skills List June 2016
G5: Find interior & exterior angles of polygons
Key points:
-
3)
The angle inside a polygon is called an interior angle
The total interior angles of an n-sided polygon is (n - 2) X 180°
The angle outside a polygon is called the exterior angle
The exterior angles of a polygon add up to 360°
The interior and exterior angle add up to 180°
Calculate the following total interior angle size for the following:
a) 5 sided shape
b) 7 sided shape c) 12 sided shape
For a regular polygon with 6 sides calculate the size of
a) The total interior angle size
b) The size of an interior angle
c) The size of an exterior angle
Calculate the size of each missing angle
MathsWatch
G19
Pre-GCSE Skills List June 2016
G6: Identify reflection & rotational symmetry in 2D shapes
Key points:
-
Images of a shape which are formed by reflecting a given shape about a line
of reflection (mirror line) are called reflections.
A rotation can be described as a fraction of a turn, or as an angle of turn.
The point about which the shape is turned is called the centre of rotation.
It is useful to use tracing paper to assist in rotating a shape.
Reflection and rotation can sometimes be given on a coordinate grid.
Reflect the shapes using the mirror lines
Rotate the shapes using the centre of rotation
MathsWatch
G3, G4, G6,
G7
Pre-GCSE Skills List June 2016
G7: Calculate volume & surface area of cuboids
Key points:
-
The volume of a 3D shape is the amount of space it takes up
The volume of a prism is the area of the cross-section multiplied by its length
The surface area of a prism is the area of the net that can be used to build
the shape
MathsWatch
Calculate the volume of the following shapes. Use appropriate units
Calculate the surface area of the following shapes. Use appropriate units
G21
Pre-GCSE Skills List June 2016
D1: Draw bar charts, line graphs & pie charts
Key points:
-
MathsWatch
A bar chart can be used to display qualitative or grouped discrete data
Line graph can be used to show a trend over a period of time.
In a pie chart the area of the whole circle represents the total number of
items. The angle of each sector represents the number of items in that
category.
S2, S9
The table below shows the number of houses sold by two agents in four months.
Month
Agent A
Agent B
April
24
32
May
35
48
June
21
10
July
12
5
Draw a comparative bar chart to represent this information
The table below shows the maximum outside air temperature as recorded by a
gardener over a five-day period in January.
Day
Temperature
in °C
Monday Tuesday Wednesday Thursday Friday Saturday Sunday
6
12
8
5
2
1
0
Draw a line graph to represent this information
The table shows the favourite colours of a sample of 30 students.
Colour
Frequency
Blue
10
Red
15
Draw a pie chart to represent this information
Green Black
3
2
Pre-GCSE Skills List June 2016
D2: Calculate mean, median, mode & range for a small data set
Key points:
-
The mean of a set of data is the sum of the values divided by the total
number of observations.
The median is the middle value when the data is ordered from the smallest
to largest.
The mode of a set of data is the value that occurs most frequently
Range is the difference between the highest value and the lowest value.
MathsWatch
S6
Chloe made a list of her homework marks. 4 5 5 5 4 3 2 1 4 5
What are her mode and mean homework marks?
Peter rolled a 6-sided dice ten times. Here are his scores. 3 2 4 6 3 3 4 2 5 4
Work out the median and range of his scores
A rugby team played 7 games. Here is the number of points they scored in each
game. 3 5 8 9 12 12 16
(a) Find the median
The rugby team played another game. They scored 11 points.
(b) Find the median number of points scored in these 8 games
Here are the test marks of 6 girls and 4 boys.
Girls: 5 3 10 2 7 3
Boys: 2 5 9 3
(a) Write down the mode of the 10 marks
(b) Work out the median mark of the boys
(c) Work out the mean mark of all 10 students
The mean of eight numbers is 41. The mean of two of the numbers is 29
What is the mean of the other six numbers?
Pre-GCSE Skills List June 2016
D3: Determine probability for single and multiple events
Key Points:
-
The probability that an event will happen is always between 0 (impossible)
and 1 (certain).
Outcomes are mutally exclusive when they cannot happen at the same time.
For equally likely outcomes the probability that an event will happen is:
MathsWatch
P2, P3
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑢𝑐𝑐𝑒𝑠𝑠𝑓𝑢𝑙 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
Probability = 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
One of these names is to be drawn from a hat. Determine each probability below:
Mary Jenny Bob Marilyn Bill Jack
1. P(3-letter name) =
Jerry Tina
Connie Joe
2
1
or
(Probability of drawing a 3-letter name)
10 5
2. P(4-letter name) = _________
3. P(name starting with B) = ____________
4. P(name starting with T) = _______ 5. P(7-letter name) = ______________
6. P(name starting with S) = ______
7. P(name ending with Y) = _____________
One card is drawn from a well-shuffled deck of 52 cards. What is the probability
of drawing…
a) P(ace) = ________
b) P(picture card; K, Q, J) = _________
c) P(a red 10) = ________
d) P(NOT a diamond) = ________
A coin is tossed and a dice with numbers 1-6 is rolled. What is P(head and 3)?
Two cards are selected from a deck of cards numbered 1 – 10. Once a card is
selected, it is not replaced.
What is P(two even numbers)?