Maths and Logic Fundamentals

Exam Topics:

● Number Systems, Families of numbers, Natural, Integer, Rational, Irrational, Squares, Primes, Divisors, Remainders, Pi, e and Perfect numbers

● Algebra - Basics

● Arithmetic - Binary, Decimal and Hexidecimal

● Number system Conversion

● Vectors (2D/3D)

● Trigonometry ratios and Wave function - Triangles, Circles, Angles and Distance

● Matrices - Positive/Negative, Adding/Subtracting, Multiplication (Constant/Matrix), Division, Transpose

● Scalar Product - Angles between directions

● Vector Product - Determining Up, Right and Forward

● Probability - Throwing dice, Coin tossing and probability line

● Averages - Mean, Median, Mode and Range

● Standard Deviation - Comparing Datasets

● Random Numbers - Perception, Pseudorandom, Noise and Perlin

Number Sets:

Algebra - Expressions from Logic Worksheet

1. There are x grains of sand in a desert . If I take 10 grains of sand away there will now be x-10 grains of sand.

2. There are x people in a race. If 7 more people join the race there will x+7 people in the race.

3. There are x fish in the Atlantic Ocean. If another 200 fish arrive. There will be x+200 fish.

4. I have £w and lose £10. I now have £w-10

5. Summer is k years old. In 5 years from now she will be k+5 Years old.

6. Archie cycles 6km to school. He then cycles j km to meet Jess. Altogether he cycles j+6 km.

7. Izzy scores 20 in a test. She has z marks taken away for copying. Izzy now scores 20-z marks.

8. I have some money in my wallet (x). I spend £8. I now have £x-8.

9. Ronan is 45kg. He loses some weight (x). He now weighs 45-x kg

10. Jake is 193.5cm tall. He grows a few more centimetres (x). Jack is now 193.5+x cm tall.

11. Eduard has a piece of wood (x). He cuts 50 cm off the wood. The new length of the wood is x-50 cm.

Simplifying Algebraic Expressions Worksheet

1. -3p +6p = 3p

2. b - 3 + 6 - 2b = -b + 3

3. 7x - x = 6x

4. 7p - 10p = -3p

5. -10v + 6v = -4v

6. -9r + 10r = r

7. 9 + 5r - 9r = -4r + 9

8. 1 - 3v + 10 = -3v + 11

9. 5n + 9n = 14n

10. 4b + 6 - 4 = 4b + 2

11. 1 + 7(1 - 3b) = 8(1 - 3b) = 8 - 24b

12. 35n - 1 + 46 = 35n + 45

13. -33v - 49v = -82v

14. 30n + 8n =

Averages

Mean - Add up all numbers and divide them by the number of numbers.

Median - The middle number.

Mode - The most frequent number.

Range - The largest value divided by the smallest.

Mean Worksheets

Worksheet 1:

1. 1, 3, 4, 5, 7 mean = (1+3+4+5+7)/5 = 4

2. 1, 3, 3, 4, 4 mean = (1+3+3+4+4)/5 = 3

3. 3, 4, 4, 5, 6, 6, 7 mean = (3+4+4+5+6+6+7)/7 = 5

Worksheet 2:

1. 3, 5, 6, 10 mean = (3+5+6+10)/4 = 7

2. 1, 7, 10, 12, 15 mean = (1+7+10+12+15)/5 = 9

3. 6, 8, 10, 12, 14 mean = (6+8+10+12+14)/5 = 10

Median Worksheets

1a. 4,6,3,4,5,1,6,6 median = (4+5)/2 = 4.5

b. 22,24,27,21,23,26,25,25,24 median = 23

c. 7,11,6,15,12,11,10 median = 15

d. 102,108,106,110,98,94,109,111,105 median = 98

2a. 14,17,15,16,18,12 median = (15+16)/2 = 10.5

b. 3,6,4,6,3,7,0,2,6,8 median = (3+7)/2 = 5

c. 84,62,73,77 median = (62+73)/2 = 67.5

d. 103,109,107,111,99,95,110,112 = (111+99)/2 = 105

3a. 18,20,23,18,24 median = 23

b. 1.5, 2.2, 1.78, 2.36, 1.47 median = 1.78

c. 104,105,103,102,108,100 median = (103+102)/2 = 102.5

d. 35,14,20,24 median = (14+20)/2 = 17

4a. 1,1,10,1,1

b.1,1,8,1,1

c. 1,1,14,1,1

d. 1,1,12,1,1

5. 17,12,23,8,7,17,18,22,30 median = 17

Mode and Range Worksheet

1. 11,15,20,11,16,12,11,15,9,5,8,7,11,12,13,11,5,8,4

mode = 11

range = 20 - 4 = 16

2. 15,30,10,15,22,28,9,15,11,15,12,26,14,15,13,17

mode = 15

range = 30-9 = 21

Averages Worksheets

Dog IIII/

Cat IIII

Fish II

Horse IIII

Rabbit II

Turtle I

2. 3, 3, 4, 5, 20

mode = 3

range = 18

median = 4

3. 3, 5, 7, 8, 8, 8, 8, 9, 10, 10, 11, 14, 16, 16, 17, 18, 18, 20, 22

mode = 8

range = 19

median = 10

mean = (3+5+7+8+8+8+8+9+10+10+11+14+16+16+17+18+18+20+22)/19

Class Height Average(cm)

182,152,187,185,180,170,165,165,198,167,190,182,177,177,175,172,182,177,180,180,175

mean = (182+152+187+185+180+170+165+165+198+167+190+182+177+177+175+172+182+177+180+180+175)/21=177.04

median = 190

mode = 177

range = 190-152 = 38

Pythagoras

a^2+b^2=c^2

1. a=4 b=3 4*4=16 3*3=9 sqr(9+16) = 5

2. a=8 b=6 8*8=64 6*6=36 sqr(64+36) = 10

3. a=5 b=12 5*5=25 12*12=144 sqr(25+144) = 13

4. a=2.5 b=6 2.5*2.5 = 6.25 6*6=36 sqr(6.25+36)=6.5

5. a=12 b=9 12*12=144 9*9=81 sqr(144+81) = 15

6. a=24*24=576 b=7*7=49 sqr(576+49)=25

7. a=8 b=15 8*8=64 15*15=225 sqr(64+225)=17

8. a=9 b=40 9*9=81 40*40=1600 sqr(1600+81)=41

1. 10^2 - 6^2 = 100-36=64 sqr64 = 8

2. 17^2 - 8^2 = 289 - 64 = sqr225 = 15