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mathematics UK Year 9 Mathematics (KS3)

Solved problems for the chapter:

Positive and negative integers

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Multiples and expressions for KS4

1. Monomials, binomials and multinomials

2. Breaking down numbers

2.1. Breaking down numbers into prime factors

3. Calculating expressions

3.1. The square of the sum of two terms

3.2. The square of the difference of two terms

3.3. The cube of a binomial

3.4. The difference of squares

3.5. The difference of cubes

3.6. The sum of cubes

3.7. Difference of n-th power

3.8. Vieta's formula

4. Exposing common factors

5. Forum

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Indices with rational exponents

1. Rules for calculating powers with rational exponent

1.1. Multiplication and division of Indices with the same bases

1.2. Multiplication and division of indices with equal exponents

1.3. Exponents

2. Forum

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Natural numbers for KS4

1. Representation of natural numbers on a number line

1.1. Calculation operations of natural numbers

1.1.1. Addition of natural numbers

1.1.2. Multiplication of natural numbers

1.2. Properties of arithmetic operations

1.2.1. Commutative property

1.2.2. Associative law or factor aggregation law

1.2.3. Distribution law

1.2.4. Existence of a neutral multiplier element

2. Prime numbers and compound numbers

2.1. Product of prime factors

2.2. Factorizing the common factor

3. Forum

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Integers for KS3

1. Presenting integers on a number line

2. Arithmetic operations of integers

2.1. Subtraction of Integers

2.2. Properties of arithmetic operations

2.2.1. Existence of an identity element

2.2.2. The sum of any integer and its additive inverse

2.2.3. The negation of an additive inverse is its positive value

2.2.4. The additive inverse of a sum

2.2.5. Identity element for multiplication

2.2.6. Multiplication by (-1)

2.2.7. Multiplication by 0

2.2.8. The product of positive and negative integers

2.2.9. The product of a negative and a positive integer

3. Removing brackets

4. Order of integers

4.1. Greater than " > "

4.2. Less than " < "

4.3. Equals to " = "

4.4. Less than or equal to "

4.5. Greater than or equal to " >= "

4.5.1. Properties of "Less than"

4.5.2. Properties of "less than or equal to"

4.5.3. Properties of "greater than or equal to"

5. Forum

↓ Show theory [4] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:positive_and_negative_integers/4145/

Example 1.

Write the set of odd integers using set builder notations.

Example 2.

Write the set of the multiples of 14 less than 78 in two different ways.

Obtain the set of the multiples of 9 less than 66 in two different ways.

Evaluate:

Calculate:

and

Calculate the following ( Add or subtract numbers in order, from left-hand side to right-hand side):

Calculate:

We calculate:

Calculate:

Calculate:

Calculate:

We add six times the sum of the numbers and to four times the number . What number do we get?

14.

Subtract from seven times the sum of and three times . What is your result?

15.

A student learns speed reading. Each day, he manages to read more pages of the book than he read in the previous day. The first day he reads pages of the book, the second day he reads twice as many as the first day, and the third day reads pages more than the second day. How many pages does he read in these three days?

16.

Calculate the following expressions:

17.

Calculate the following expressions:

18.

Calculate the following:

19.

Calculate:

20.

Calculate:

21.

Calculate:

Which law is shown in the above task?

22.

What is the quotient if the dividend is and the divisor is ?

23.

Find how best you can calculate the following using the splitting strategy:

24.

Calculate the difference between the largest and smallest five-digit number.

25.

In the evening the thermometer shows 1 degrees Celsius. Overnight the air temperature drops by 8 degrees Celsius. How many degrees does the thermometer show the next morning?

26.

What is obtained by subtracting 200 from four times the difference between 99 and twice 59?

27.

There are 1676 visitors at an event, of which 578 are women. Calculate the number of men at the event.

28.

Three friends, Martin, Bojan and Jure agreed to save for the purchase of a weekend joint. Martin will contribute 92 euros per month, Jure will contribute 15 euros more than Bojan, who will contribute 10 euros less than Martin. How much money do the friends save per month and how much money will they have saved in a year?

29.

An event organizer prepared 129 cups and 87 plates. Visitors used 82 cups and 63 plates. How many cups and plates were left clean at the end of the event?

30.

The largest Slovenian cities in terms of population are Ljubljana, Maribor, Celje and Kranj. Ljubljana has a population of 272,000, Maribor 95,000, Celje 38,000 and Kranj 37,000. Answer these questions:

By how much is the population of Ljubljana higher than Kranj?
By how much is the population of Maribor higher than Celje?
By how much is the population of Celje smaller than Ljubljana?
By how much is the population of Kranj lower than Maribor?

31.

Before his father bought a new computer, he had in his bank account. After the purchase, however, the father was in the red. How much did he deduct for the computer?

32.

If five times 74 is added to three times the difference between 909 and 789. What do we get?

33.

Subtract twice the difference between 186 and 353 from eight times -44. What do we get?

34.

From which number do we subtract ten times 1719 and add seven times 4293 to get 20119?

35.

At the end of the year, a bank paid 9270 euros as performance bonuses to four employees. The first received 2366 euros, the second received 1047 less than the first, the third received 250 less than the first and second combined, and the fourth received the rest. How much did each of the successful employees receive?

36.

Calculate: