JHS General 3rd Year Book 3.2 Part 1

Solve 5x - 1 = 3x + 13

5x - 3x = 13 + 1 2x = 14 x = 14 ÷ 2 x = 7

Write 64500000 in scientific notation?

6.45 x 10⁷

Write 6.73 x 10⁵ out in full

673000

What is 7+(-5)?

7 - 5 = 2

Solve 7x - 5 = 23

7x = 23 + 5 7x = 28 x = 28 ÷ 7 x = 4

Solve 9(x + 4) = 45

9x + 36 = 45 9x = 45 - 36 9x = 9 x = 1

Multiply out and simplify 6 + 3(2c + 3)?

=6+6c+9 =6c+15

Multiply out and simplify 3(2a +5) - 4?

=6a + 15 - 4 =6a+11

What is a prime number?

A number which can only be divide by 1 and itself and has exactly 2 factors.

What is a factor of a number?

A number which divides in without a remainder.

What is VAT?

A tax on some goods bought currently 20%

How do you simplify terms like x + 5y - 6x - 2y?

Add like terms -5x + 3y

Solve x + 4 = 9.

x = 9 - 4 x=5

Factorise y² + 3y

y ( y + 3 )

What are the rules for multiplying two positive and negative numbers?

+ x + = + + x - = - - x + = - - x - = +

How do you find 65% of £200 using a calculator?

0.65 x 200 = £130

How do you work out 1% of a quantity without a calculator?

1) 1% is 1/100 2) Divide by 100

How do you work out 10% of a quantity without a calculator?

1) 10% is 1/10 2) Divide by 10

How do you work out 20% of a quantity without a calculator?

1) 20% is 1/5 2) Divide by 5

How do you work out 25% of a quantity without a calculator?

1) 25% is 1/4 2) Divide by 4

How do you work out 30% of a quantity without a calculator?

1) 30% is 3/10 2) Divide by 10 and multiply by 3

How do you work out 33 1/3 % of a quantity without a calculator?

1) 33 1/3% is 1/3 2) Divide by 3

How do you work out 40% of a quantity without a calculator?

1) 40% is 2/5 2) Divide by 5 and multiply by 2

How do you work out 50% of a quantity without a calculator?

1) 50% is 1/2 2) Divide by 2

How do you work out 60% of a quantity without a calculator?

1) 60% is 3/5 2) Divide by 5 and multiply by 3

How do you work out 66 2/3% of a quantity without a calculator?

1) 66 2/3% is 2/3 2) Divide by 3 and multiply by 2

How do you work out 70% of a quantity without a calculator?

1) 70% is 7/10 2) Divide by 10 and multiply by 7

How do you work out 75% of a quantity without a calculator?

1) 75% is 3/4 2) Divide by 4 and multiply by 3

How do you work out 80% of a quantity without a calculator?

1) 80% is 4/5 2) Divide by 5 and multiply by 4

How do you work out 90% of a quantity without a calculator?

1) 90% is 9/10 2) Divide by 10 and multiply by 9

How do split £60 in the ratio 2:3 ?

1) Add 2 and 3 to get 5 2) Divide 60 by 5 to get 12 3) Multiply 12 by 2 and 3 to get £24:£36

How do you add or subtract fractions ?

1) Change into top heavy fractions if necessary. 2) Find a common denominator. 3) Add or subtract the numerators.

How do you multiply fractions ?

1) Change into top heavy fractions if necessary. 2) Simplify by dividing numbers on the top and bottom by the same number if possible. 3) Multiply numerators and denominators.

To make orange paint the ratio of red:yellow paint needs to be 3:4. If I have 33 litres of red how much yellow do I need?

1) Divide 33 by 3 to get 11 2) Multiply 11 by 4 to get 44 litres

How do you work out ¾ of a number?

1) Divide by 4 2) Multiply by 3

How do you find a fraction of a quantity?

1) Divide by the number on the bottom 2) Multiply by the number on the top

Factorise 4a² + 6a

2a(2a + 3)

Round 5.55 to 1 decimal place

2nd number after decimal 5 so round up to 5.6

Round 7.24 to 1 decimal place

2nd number after decimal point is less than 5 so round down to 7.2

Write 0.0000000017 in scientific notation?

1.7 x 10⁻⁹

Round 9.76 to decimal place

2nd number after decimal point is more than 5 so round up to 9.8

What is the general trend of a graph?

Whether the graph is going up or down?

How do you add a negative number ?

You change the +(-) into a - and subtract e.g. 7 + (-3) = 7 - 3 = 4

Solve 5x = 35

x = 35 ÷ 5 x = 7

How do you change from a top heavy fraction into a mixed number?

1) Divide number on top by number on bottom to get an answer and a remainder 2) The answer is the whole number and the remainder goes on the top of the fraction with the bottom number staying the same

How do you change a number into scientific notation ?

1) Move the decimal point forwards (+) or backwards (-) to make a number between 1 and 10. 2) Multiply this by 10 to the power of the number of places the point has moved.

How do you change a mixed number into a top heavy fraction?

1) Multiply the whole number by the number on the bottom of the fraction and add on the number on top of the fraction 2) Write the answer to (1) on the top and the number on the bottom stays the same

How do you multiply a mixed number by a whole number ?

1) Multiply the whole number in the mixed number by the whole number 2) Multiply the top of the fraction by the whole number 3) If number on top is top heavy change it to mixed number and add to the whole number

How do you simplify terms like 3(b + 2a) - 2(3b-a)?

1) Remove brackets 3b + 6a - 6b +2a 2) Add like terms -3b + 8a

How do you work out 15% without a calculator?

1) Work out 10% 2) Half this to find 5% 3) Add the two together

How do you work out 5% of a quantity without a calculator?

1) Work out 10% by dividing by 10 2) Half the answer

How do you work out a hire purchase price ?

1) Work out the deposit if it is a percentage of the cash price. 2) Multiply the cost of each instalment by the number of instalments.

Write 2.4 x 10⁻⁶ out in full

1) Write 6 zeros(the same as the power) 2) Write 24 after the zeros. 3) Put a decimal point between the first two zeros. 0.0000024

What are the squares of the first ten numbers?

1, 4, 9, 16, 25, 36, 49, 64, 81, 100

What numbers from 1-100 can we find the square root of without a calculator ?

1, 4, 9, 16, 25, 36, 49, 64, 81, 100

Multiply out 5(2x +4y)

10x +20y

Factorise 4x + 6

2(2x+3)

What is the order in which you do calculations ?

BOMDAS Brackets Of / Ordinals Multiply & Divide Add & Subtract

How do you work out a hire purchase price?

Deposit + (installment x number of weeks/months)

What 3 things should you always add to a stem and leaf diagram?

Heading, number of numbers, key

What is the line of best fit on a scatter diagram?

It is a straight line passing through the diagram as close to as many points as possible.

What is a standing charge?

It is an amount you pay in the bill for rental of equipment or for the service which does not depend on you using it?

What is the formula for calculating loss?

Loss = Cost(Buying) Price - Selling Price

How do you remove a single bracket ?

Multiply everything inside the bracket by the term outside the bracket.

How do you add V.A.T. to the cost of an item ?

Multiply the original price by 1.2

What sign can replace the word "of" in a calculation?

Multiply x

What is the formula for calculating percentage profit/loss ?

Percentage Profit/Loss = Profit/Loss ÷ Cost Price x 100

What is the formula for calculating profit?

Profit = Selling Price - Cost (Buying) Price

What is a multiple of a number?

The answers to the numbers multiplication table starting at number x 1