everything you need to know to get a grade c algebra (foundation)
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EVERYTHING YOU NEED TO KNOW TO GET A GRADE C
ALGEBRA
(FOUNDATION)
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