S2 (2.4) Algebra.notebook - Weebly€¦ · S2 (2.4) Algebra.notebook November 06, 2017 Daily Practice 19.4.2017 Q1. Round 17.85 to the nearest unit Q2. 20 - 2 x 3 Q3. Find 50% of

S2 (2.4) Algebra.notebook November 06, 2017

Daily Practice 18.4.2017

Q1. Find 50% of 780

Q2. 34 (5 x 6)

Q3. Find the median and range of 9, 1, 2, 3, 6, 5

Q4. Round 87.55 to 1 decimal place

Q5. 17.26 x 700

Today we will be learning how to simplify algebraic expressions.

Algebra

The word algebra originates from an Arabic word Al-jabr which means the reunion of broken parts which comes from a method of solving equations.

Algebra is from roughly 850AD which is 1165 years ago and originated in the middle east

Simplifying Algebraic Expressions

• Algebra is used to work out difficult mathematical problems by replacing numbers with letters.

• We let the letters be the unknowns in our problems and then we can use the rules of arithmetic to solve the problems.

• Working with only letters helps us simplify problems and work with them without having the need for numbers to be involved.

Collecting Like Terms Collecting Like Terms



Q1. Round 17.85 to the nearest unit

Q2. 20 - 2 x 3

Q3. Find 50% of 700

Q4. Write as a decimql

Q5. What type of angle is 3200?

Today we will be continuing to learn how to simplify algebraic expressions.

Collecting like terms

g

g y

y

ggg

g y y

y

y

Collecting Like Terms

ggg


Q1. Find 25% of 72

Q2. (-2) x 3 x 5

Q3. 56 ÷ 2000

Q4. 0.5 x 600

Q5. Find the mean, median, mode and range of 2, 1, -3, 4, 7, 1

Collecting like terms

Examples: Simplify the following

1) 3a + 2b + 4c + a 3) 2w + 3 - 8w + 7

2) 5y - 3y + 2k + 4k 4) 3h - 4f + 2h - f



Q1. Round 817.225 to 2 decimal places

Q2. (1 - 5) + (3 x 8)

Q3. Write 104 056 in words

Q4. Simplify 6c + 2c - c + 3c

Q5. 7.88 x 200

Today we will be continuing to learn how to simplify expressions.

Collecting like termsQuestions: Simplify the following


Q1. Round 18.159 to 1 decimal place

Q2. ‐14 + 18 ‐ 3

Q3. 5.46 x 300

Q4. Write as a decimal


Today we will be learning about substitution.

Substitution

Note:

• 5 x a is written as 5a

• a x a is written as a2

• a x b is written as ab

• 3 x a x b is written as 3ab

Substitution means replacing letters with numbers.

We then usually work through to find the answer.


Substitution

Examples: Given a = 3 and b = 4

Find the value of the following

(i) 3a (ii) 2a + b (iii) a - b (iv) b2

(v) a (vi) 5ab b


Q1. Simplify 8g + 3h ‐ 2g + 5h

Q2. State the lowest common multiple of 7 and 4

Q3. Use a factor tree to find all the prime factors of 64

Q4. 6.25 + 1.018 ‐ 4.9 (Do a chimney sum for this one, ensure point is in line)

Q5. 29.3 x 50


20 Questions Mental Maths


Today you will be completing a calculated colouring on substitution.

Colours required are:

Red, Yellow, Orange, Grey, Blue, Pink, Black


Q1. Round 187.345 to the nearest whole number

Q2. Simplify 6y + 3h - 2y + h

Q3. Find the LCM of 15 and 20

Q4. If h = 2 and g= 4, what is the value of 3g + 5h?

Q5. -3 x 2 + 4

Today we will be learning to multiply out brackets.

Homework Online due Monday 8.5.2017

Multiplying out brackets

Sometimes algebraic expressions are written with brackets and we need to multiply them out and simplify the expression.

E.g. 2(3x + 5)

This means multiply everything in the bracket by 2

Examples: Multiply out

(i) 5(x - 1) (ii) 7(3 - h) (iii) 4(2h + 5)


Q1. (3 x 4) ‐ 2 + 7 Q5. ‐30 ÷ ‐6

Q2. Find 75% of 800

Q3. ‐4 ‐ (‐6)

Q4. Find the HCF of 24 and 16

Today we will be continuing to multiply out brackets and simplify.

Homework due Monday!





Q1. Multiply out 6(2x - 1)

Q2. 5 - 6 x 4

Q3. 15 - (-18)

Q4. Find the HCF of 24 and 30 Q5. Find p510

p0

Today we will be continuing to multiply out brackets and

also to simplify afterwards.

Homework due today!


Multiplying out and simplifying

Examples:

(i) 2(w + 2) + 3 (ii) 3(m - 5) + 2m (iii) 5k + 4(k + 1)


Q1. Round 71.2285 to 2 decimal places

Q2. Multiply out and simplify 7(2g + 4) 3g

Q3. 2.348 x 70

Q4. 14 + (3)

Q5. What is the LCM of 3 and 6?

Today we will be continuing to learn how to multiply out brackets and simplify.


Examples:

(i) 2(3x + 4) + 5(x - 1) (ii) 8(2h + 3) - 4(h + 7)



Questions:Daily Practice 11.5.2017

Q1. -3 + 15 Q5. 6.7 x 800

Q2. Multiply out 2(x + 8)

Q3. 15 x 3 - 2

Q4. How many lines of symmetry does an equilateral triangle have?

Today we will be learning to factorise.

Factorising

Factorising is the opposite of multiplying out brackets.

5(x + 2) 5x + 10

5(x + 2) 5x + 10

Multiplying Out

Factorising

Factorising

Fill in the blanks! (What are you multiplying by to get the answer?)

(a) _(x + 3) = 4x + 12 (e) _(2m - 3) = 18m - 27

(b) _(d + 5) = 3d + 15 (f) _(2v + 7) = 14v + 19

(c) _(2c + 1) = 10c + 5 (g) _(8p - q) = 40p - 5q

(d) _(8k - 4) = 32k - 16 (h) _(a + b) = ca + cb

We factorise by finding the highest common factor of an expression.

E.g. 5 is the HCF of 15a + 20b

Factorising


Factorising

Write down the highest common factor of the expressions below:

(i) 14a + 21 (iv) 10t + 15p

(ii) 15h + 20b (v) 5a + 5b

(iii) 12a + 36b (vi) 24c + 36b + 48


Q1. 17 - 19 + 3 Q2. 4 - 2 x 5

Q3. 73 x 2000

Q4. Multiply out 3(4x - 8)

Q5. If a = 2 and b = 3 what is that value of ab?

Today we will be continuing to learn how to factorise.

Factorising

Take out the HCF

Examples: Factorise fully the following

(i) 7a + 7c (ii) 3a + 9p (iii) 16g + 24h

(iv) 24a - 32g

Factorising


Daily Practice - Number work

Complete Sheet!


Q1. 4 + 2 x 7

Q2. 3 - 16

Q3. Multiply out 2(3c + 5)


Q5. Factorise 16h + 24b

Today we will be continuing to learn how to factorise.

Check up on algebra - Thursday

E.g. 5a is the HCF of 15a + 20ab

Look for HCF and common letter.

Examples: Factorise the following

(i) a + ab (ii) 5p + 15pq (iii) 9ac + 6a2


Complete the factorising worksheet



Q1. -15 + 5

Q2. 40 - 2 x 7

Q3. 56 x 3000

Q4. Multiply out 2(3p + 4)

Q5. Factorise 6p - p2

Today we will be learning how to write algebraic expressions.

Writing expressions algebraicallyAlgebra can be used to model real life problems and help with their solutions.

Examples: (i) Jackie is x years old, Dave is 3 years older than Jackie. Write an expression for Dave's age

(ii) The cost of tiling a floor is £120 plus £4 multiplied by the number of tiles. Write an expression for this

Write each phrase as an algebraic expression

1. A number add 72. 3 less than a number3. 5 times a number4. 6 times a number, then add 7 to it5. 10 times a number, subtract 4 from it. 6. A number multiplied by itself.7. A number multiplied by itself and then 5 is added onto the result. 8. The sum of 2 times a number and then 5 times another number.9. The product of 2 numbers10. 4 times a number and the result if squared. 11. John is m years old and Sadie is 3 years older than him. Martha is twice John’s age. Write an expression for (i) Sadie’s age and (ii) Martha’s age12. Kevin is a decorator. He charges a flat rate of £100 to paint a room and then an additional £3 per litre of paint. Write an algebraic expression for how much he charges.

Today we will be completing a check‐up on algebra.


Documents

S2 (2.4) Algebra.notebook - Weebly€¦ · S2 (2.4) Algebra.notebook November 06, 2017 Daily Practice 19.4.2017 Q1. Round 17.85 to the nearest unit Q2. 20 - 2 x 3 Q3. Find 50% of