Maths Exam Number Tips
A bus drives 120 miles at a speed of 50mph. How long does it take in hours and minutes?
120 ÷ 50 = 2.4 hours 0.4 x 60 = 24 minutes 2 hours 24 minutes
What is 4.68+9.670?
14.350
What is 3.6 divided by 1.2?
3
How do you work out 3⁴?
3 x 3 x 3 x 3 = 81
What is 4567000 in Standard Form?
4.567x 10^7
If the nth term is 4n + 1, what is the 100th term?
401. 4 x 100 + 1 = 401
A van travels at 60mph for 3 hours 45 minutes. How far does it travel?
60 x 3.75 = 225 miles Tip; 45 minutes is 3/4 hr which is 0.75 hr
A car travels 60 miles in 2 hours 30 minutes. What is it's speed?
60 ÷ 2.5 = 24mph
What is 9/7 divided by 5?
9/35 (TURN then TIMES for fraction division)
How can you tell if a number is divisible by 8
As every multiple of 1000 can be divisible by 8 as 8x125=100 ....you only need to see if the last 3 digits are divisible by 8
What is 10x5-(4+2)²+6÷3?
BIDMAS
What is 0.7 squared?
Do multiplication of whole numbers 7x7=49 Add up total number of decimal places ( 2 places)and then put into the answer Ans=0.49 TIP: Do not need to line them up
What is the Prime factorisation theorem?
Every whole number can be written as a product of its prime factors and this is unique to this number
Find nth term of 1,4,9,16
These are squared numbers nth term =n²
Find the square root of 676 without a calculator.
Use prime factors
What is 2-4?
-2
What is 1/8 in decimals?
0.125
Is 1 a prime number?
No
what is 4 divided by -2
-2 A positive divided by a negative is a negative
what is 4x-5
-20 minus x positive is a negative
What is 1/6 as a decimal?
0.16 ( 6 recurring)
What is 3/8 in decimals?
0.375
What is 5/8 in decimals?
0.625
What is 7/8 in decimals?
0.875
What is the Multiplier to decrease a price by 5%
0.95
What is -2-(-3)?
1
What is a prime number? Is 1 a prime number? What is the only even prime number?
1 is not a prime number as it has only one factor, itself. The only even prime number is 2
How do you share £40 in the ratio 2:3
1) work out the total number of parts 2+ 3 = 5 2) work out the value of 1 part £40 ÷ 5 = £8 in one part 3) work out the value of 2 parts 2 x £8 = £16 4) work out the value of 3 parts 3 x £8 = £24
What are the square numbers to 144?
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 A square number is a number times itself Note; every square number is made up of ADDING together 2 consecutive triangular numbers
What is ...to 2 dec pl? 0.678 0.998
1. 0.68 ( 2 dec pl) 2. 1.00 (2 dec pl) TIP: 5 or MORE.. ADD ONE MORE
What is .....to 2 significant figures? 106,788 0.00567
1. 11,000 (2 sf) 2. 0.0057 ( 2 sf)
Finding the nth term e.g. of 1,4,7,10
1. Find out what the size is increasing/decreasing by. (in this case 3) 2. Write the times tables for that number below the sequence and also 3n 3. See what you would have to do to 3 times tables to get to the sequence... -2 4. Then the nth term is 3n -2
What type of common sequences are there?
1. Multiples with the same +factor each time Even numbers: 2,4,6 (nth term =2n) Odd numbers: 1,3,5 (2n-1) or 3,5,7(2n+1) Multiples of 3; 3,6,9 (3n) 2. a. Square numbers: nth term (nxn) or n squared 1,4,9,16,25, 36, 49, 64, 81, 100, 121.. nth term (nxn) b. Cubed numbers nth term (nxnxn) or n cubed 1,8,27,64,125,216,343,512 3. Triangular numbers nth term = ½ n (n + 1) 1,3,6,10,15 4. Fibonacci (adding 2 proceeding terms) 1,1,2,3,5,8,13,21 5. Prime numbers 1,2,3,5,7,11
How do you find the LCM of two numbers USING THE VENN METHOD? e.g. LCM of 20 and 70
1. Write as a product of primes. 2. Use a venn diagram. 3. Multiply ALL the numbers in the venn diagram.
What is the Multiplier to increase a price by 6%
1.06
What formula can you use for compound interest questions? e.g. 5% interest on 10 pounds over 3 years
10x5³
What is 0.36 recurring as a fraction?
11/30
What is 19.5% in decimals?
19.5/100 = 195/1000 Answer is 0.195
what is -4 divided by -2
2 a negative divided by a negative is a positive
What are the first 10 prime numbers?
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
What is -4x-5?
20 minus x minus is a positive
What is 0.23 as a fraction?
23/100
What is 63x11?
693 Tip: if asked to multiple 3 prime numbers together and find the prime numbers Look to see if the 3 digit number is a multiple of 11 then one of the numbers is 11 and work from there. Recall 2 is the only even prime number.
How can you tell if a number is divisible by 3
Add up the digits of the number and see if that divides by 3
How can you tell if a number is divisible by 9
Add up the digits of the number and see if that divides by 9
How do you estimate a calculation? e.g. 198.7 x 0.203
Always USE 1 sf ROUND ALL NUMBERS TO 1 SIGNIFICANT FIGURE... and then calculate. e.g. 198.7 x 0.203 ≈ 200 x 0.2 = 40
What is √4?
Answer +2 and - 2 as -2x-2 is 4 and 2x2 is 4 The square root is the opposite of finding the square
What is 17½% of 54 pounds?
Convert 17.5% to a decimal ( 17.5 ÷100) which is 0.175 Then 0.175x54=9.45 Non calculator Use equivalent fractions to remove the fraction x2/2 17½/100 = 35/200 then 35/200x54/1=945/100=9.45
What are the factors of 30?
Factors are numbers that divide exactly into a whole number Uses: 1. They can be used to make multiplication easier eg 24x24=2x12x12x2 =144x2x2=288x2= 2. they can be used to help division and algebra
What are prime factors?
Factors of a number that are also prime numbers TIP: Prime factors must always be written in ASCENDING order e.g. little to big
How do you solve reverse percentages questions? The price of a car after a 12% increase was $14000. What was its original value?
Find the multiplier of the increase so 112% of the original value is x1.12 Divide the new value by 1.12 to get the original value
How do you cube root a number? e.g. ³√27
Find what number would be cubed to get the number you are cube rooting. ³√27 = 3
What is the HCF used for?
HCF (Highest or Greatest Common Factor (GCF)) is used for SHARING things out equally: e.g. Different coloured sweets Different flower stems between vases Lengths of ribbon or shelves Used to simplify fractions with larger numbers Used to factorise algebraic equations
How do you find the HCF of two numbers USING THE VENN METHOD ? e.g. HCF of 20 and 70
How do you find the HCF of two numbers? e.g. HCF of 20 and 70 1. Write as a product of primes. 2. Use a venn diagram. 3. Multiply the numbers in the middle as these are the common factors
What is the LCM used for?
LCM (Lowest Common Multiple) is used for working out when things will next occur together eg; 2 bells ringing at different time intervals 2 athletes or cars lapping track 2 lighthouses shining lights together Finding a common denominator to add and subtract fractions
How do you calculate density?
Mass ÷ volume
Example If I score 12 out a possible 15 in a test. What percentage mark do I get?
Method 1. x by 100 e.g. 12/15 OF 100 =12/15x100 (then cross cancel)=80% Method 2 : Fraction to decimal then convert to a % eg 1/8 is 0.125 is 12.5% Method 3; Equivalent fractions / 100 or 1000 eg 3/25 is 12/100 so 12%
What are multiples?
Multiples are numbers that are in the times table of that number eg multiples of 3 3,6,9,12,15
What are cubed numbers?
Multiply the number by itself and by itself again. e.g 5³= 5 x 5 x 5 = 125 1,8,27,64,125,216,343,512
Put these numbers in order 18%, 0.95, 1/4, 22.7%, 6/5 and 0.4 of smallest to largest,
Tips; 1. Convert to decimals then compare
What are triangular numbers
Triangular numbers can be arranged in triangular arrays 1,3,6,10,15 1 1+2=3 1+2+3=6 1+2+3+4=10 1+2+3+4+5=15
Increase 60 pounds by 12%
USE multiplier 12% is 0.12 so new price is 112% or 1.12 so multiply 60 by 1.12 OR non calculator methods: Original price + (12% of original price) =
Convert 2/5 into a percentage and a decimal
a) Find the equivalent fraction overj a hundred 2/5 = 4/10 =40/100 or b) Find 2/5 OF 100 2/5x100 =40 so 40% and 0.4
what is 3/4x1/2?
multiply straight across 3/8
Find the nth term of 2, 5, 10, 17
no easy difference but 1, 4, 9, 16 are square numbers (nxn) then correct by adding 1 so (nxn) +1
What is 1/3+2/5?
when adding and subtracting fractions make the denominator the same first
