AUTHOR

EVERYTHING YOU NEED TO KNOW TO GET A GRADE C

ALGEBRA

(FOUNDATION)

www.mistrymaths.co.uk

a + 2 x b + 3 x c

7 + 2 x 3 + 3 x 5

7 + 6 + 15

BODMAS says you multiply before you add

28

a x b x c

Replace the letters with their respective numbers

7 x 3 x 5

105

105 x d = 0 Anything multiplied by zero is zero. So, d must equal zero.

0

C = 16 + 24 x 10 BODMAS says you multiply before you addC = 16 + 240

256

24 months 12 months in a year2

C = d + 24 x m600 = 120 + 24m Solve the equation to work out m

480 = 24m

20 = m20

5 x 420

2 x 4 + 3y = 58 + 3y = 5

3y = -3

-1

3 x 4 - -112 + 1

13

Replace p with 4 and q with -75 x 4 + 2 x -720 - 14

6

Replace u with 5 and v with 3

5 x 5 – 3 x 325 – 9

16

5

£5 + 100 x 5p£5 + 500p£5 + £5

10

£7.50 - £5 = £2.50 Cost for calls after £5 a month charge has been taken offMinutes of calls =

Cost for calls after £5 a month charge has been taken offCost per minute for calls

50

Perimeter is the length around a shape

+ 6y

56 + 6y = 68 Solve the equation to work out the value of y

6y = 12

y = 22

+ 7y

Replace p with 4 and q with -75 x 4 + 2 x -720 - 14

6

Replace u with 5 and v with 3

5 x 5 – 3 x 325 – 9 16

7c

- 3y

12a- 3b

Remember a minus and a minus is only a plus when you multiply, divide or when the signs are together. When you add or subtract you use a number line.

3a

6b + 10

12

- 4 + 18

+ 14

+ 5

a x a x a x a x a x a

When you multiply powers with the same base you can

just add the powers

b x b x b x b x b x b x b x b x bb x b x b

When you divide powers with the same base you can

just subtract the powers

1

When you multiply powers with the same base you can

just add the powers

y x y x y x y x y x y x y x yy x y x y x y x y

When you divide powers with the same base you can

just subtract the powers

y x y x y x y x y x y x y x y x y

When you multiply powers with the same base you can

just add the powers

y x y x y x y x y x y x yy x y

When you divide powers with the same base you can

just subtract the powers

When you have powers and brackets you can just multiply the powers

Part (iii)A negative number to the power of an even number makes a positive

As you multiply a decimal by itself more times the number becomes smallerPart (ii)

4

+ 1 + 1 + 1

+ 2 + 2

7

+ 2

9

+3 +3 +3 +3

16

Add 3 to the previous term

3n+ 4

+ 4

5 x 3 - 1

1414 x 3 - 1

41

1st term

5 x 1

2nd term

5 x 210

3rd term

5 x 315

4th term

5 x 420

+3 +3 +3 +3

16 x 464

Pattern 4

Sequence 1, 4, 7, 10

1 dot 4 dots7 dots

10 dots

Sequence goes up in threes 13

+3 +4 +5 +6 +726

x2 x2

8x2

Multiply the previous term by 2

Add consecutive integers

1 , 2 , 4 , 7

+1 +2 +3

+17 +17

47

47

= 15

+15

32

+15

17 47 15

11 14 17

5, 8, 11, 14, 17

+3 +3 +3 +3 3n + 2

3n + 2Nth term 3 x 99 + 2 297 + 2299

a = 11

11

b = 15

15

2c = 14

c = 7

7

6 + 11 + 4 = 21

10 + 5 + 6= 21

= 217

= 21

3 = 218

3 8 7

15

2y + 3y = 5y5y = 20

y = 4

4

w = 63

63

9

y > 9Any whole number greater than 9

10

3

2y + 10 = 28

2y = 18

y = 99

Always get rid of the smallest valued letter first when you have letters on both sides.10z + 2 = 9

10z = 7

0.7

4

6

8z = 16 z = 2 2

3w - 6 = 9

3w = 15

w = 55

5 x 8

40

8y - 2 = 18

8y = 20

2.5

2.5 33.125 Too big

2.4 30.624 Too big2.3 28.267 Too small

2.35 29.428 Too small

2.4

𝑥 Comment 3 3(3 - 1)(3 + 2) = 30 Too small 4 4(4 - 1)(4 + 2) = 72 Too big

3.5 3.5(3.5 - 1)(3.5 + 2) = 48.125 Too big 3.4 3.4(3.4 - 1)(3.4 + 2) = 44.064 Too big

3.3 3.3(3.3 - 1)(3.3 + 2) = 40.227 Too big 3.2 3.2(3.2 - 1)(3.2 + 2) = 36.608 Too small

3.25 3.25(3.25 - 1)(3.25 + 2) = 38.391 Too small

3.3

𝑥 Comment 2 6 Too small 3 24 Too big

2.5 13.125 Too small 2.7 16.983 Too small

2.8 19.152 Too small 2.9 21.489 Too big

2.85 20.299 Too small

2.9

𝑥 Comment 8 520 Too small 9 738 Too big

8.8 690.272 Too small 8.9 713.869 Too big 8.95 725.87 Too big

8.8

-1, 0, 1

4

S - 40 = 3t

3t < 30

t < 10

y = 2 x 0 - 1-1

y = 2 x 2 - 13

Plot the coordinates from the table above

2

2y = -1 x -1 - 2 y = 1 - 2-1

Plot the coordinates from the table above

Have to make your own table to find the co-ordinates.

-1 4

y = 2 x -1 - 3-5

y = 2 x 4 - 3 5

Plot the coordinates from the table above

y = 4.5

3.7 4.5

Option 1

500 – 300 = 200 minutes to pay for200 x 6p = 1200p = £12250 – 100 = 150 texts to pay for150 x 10p = 1500p = £15Total Cost = £12 + £15 = £27

Option 2

500 – 100 = 400 minutes to pay for400 x 6p = 2400p = £24Texts are free so no texts to pay forTotal Cost = £24

Option 2 ( cheaper)

Where the line crosses the y-axis

25 150

350

17.5

= £0.05

5

14

27

35

35 – 27 = 8 metresYes, he must increase his gap by 8 approximately metres

Stop

10

The steeper the line the faster the speed

8

Stationary ( not moving)

16

8

2pm

Time = 0.6 hoursTime = 0.6 x 60

÷

x= 36 minutes

2pm – 36 minutes

1:24pm