Foundations of Math

Question 1

Multiplication Tables up to 15:

3x1=

3x2=

3x3=

3x4=

3x5=

3x6=

3x7=

3x8=

3x9=

3x10=

3x11=

3x12=

3x13=

3x14=

3x15=

Answer 1

3x1=3

3x2=6

3x3=9

3x4=12

3x5=15

3x6=18

3x7=21

3x8=24

3x9=27

3x10=30

3x11=33

3x12=36

3x13=39

3x14=42

3x15=45

Question 2

4x1=

4x2=

4x3=

4x4=

4x5=

4x6=

4x7=

4x8=

4x9=

4x10=

4x11=

4x12=

4x13=

4x14=

4x15=

Answer 2

4x1=4

4x2=8

4x3=12

4x4=16

4x5=20

4x6=24

4x7=28

4x8=32

4x9=36

4x10=40

4x11=44

4x12=48

4x13=52

4x14=56

4x15=60

Question 3

5x1=

5x2=

5x3=

5x4=

5x5=

5x6=

5x7=

5x8=

5x9=

5x10=

5x11=

5x12=

5x13=

5x14=

5x15=

Answer 3

5x1=5

5x2=10

5x3=15

5x4=20

5x5=25

5x6=30

5x7=35

5x8=40

5x9=45

5x10=50

5x11=55

5x12=60

5x13=65

5x14=70

5x15=75

Question 4

6x1=

6x2=

6x3=

6x4=

6x5=

6x6=

6x7=

6x8=

6x9=

6x10=

6x11=

6x12=

6x13=

6x14=

6x15=

Answer 4

6x1=6

6x2=12

6x3=18

6x4=24

6x5=30

6x6=36

6x7=42

6x8=48

6x9=54

6x10=60

6x11=66

6x12=72

6x13=78

6x14=84

6x15=90

Question 5

7x1=

7x2=

7x3=

7x4=

7x5=

7x6=

7x7=

7x8=

7x9=

7x10=

7x11=

7x12=

7x13=

7x14=

7x15=

Answer 5

7x1=7

7x2=14

7x3=21

7x4=28

7x5=35

7x6=42

7x7=49

7x8=56

7x9=63

7x10=70

7x11=77

7x12=84

7x13=91

7x14=98

7x15=105

Question 6

8x1=

8x2=

8x3=

8x4=

8x5=

8x6=

8x7=

8x8=

8x9=

8x10=

8x11=

8x12=

8x13=

8x14=

8x15=

Answer 6

8x1=8

8x2=16

8x3=24

8x4=32

8x5=40

8x6=48

8x7=56

8x8=64

8x9=72

8x10=80

8x11=88

8x12=96

8x13=104

8x14=112

8x15=120

Question 7

9x1=

9x2=

9x3=

9x4=

9x5=

9x6=

9x7=

9x8=

9x9=

9x10=

9x11=

9x12=

9x13=

9x14=

9x15=

Answer 7

9x1=9

9x2=18

9x3=27

9x4=36

9x5=45

9x6=54

9x7=63

9x8=72

9x9=81

9x10=90

9x11=99

9x12=108

9x13=117

9x14=126

9x15=135

Question 8

11x1=

11x2=

11x3=

11x4=

11x5=

11x6=

11x7=

11x8=

11x9=

11x10=

11x11=

11x12=

11x13=

11x14=

11x15=

Answer 8

11x1=11

11x2=22

11x3=33

11x4=44

11x5=55

11x6=66

11x7=77

11x8=88

11x9=99

11x10=110

11x11=121

11x12=132

11x13=143

11x14=154

11x15=165

Question 9

12x1=

12x2=

12x3=

12x4=

12x5=

12x6=

12x7=

12x8=

12x9=

12x10=

12x11=

12x12=

12x13=

12x14=

12x15=

Answer 9

12x1=12

12x2=24

12x3=36

12x4=48

12x5=60

12x6=72

12x7=84

12x8=96

12x9=108

12x10=120

12x11=132

12x12=144

12x13=156

12x14=168

12x15=180

Question 10

13x1=

13x2=

13x3=

13x4=

13x5=

13x6=

13x7=

13x8=

13x9=

13x10=

13x11=

13x12=

13x13=

13x14=

13x15=

Answer 10

13x1=13

13x2=26

13x3=39

13x4=52

13x5=65

13x6=78

13x7=91

13x8=104

13x9=117

13x10=130

13x11=143

13x12=156

13x13=169

13x14=182

13x15=195

Question 11

14x1=

14x2=

14x3=

14x4=

14x5=

14x6=

14x7=

14x8=

14x9=

14x10=

14x11=

14x12=

14x13=

14x14=

14x15=

Answer 11

14x1=14

14x2=28

14x3=42

14x4=56

14x5=70

14x6=84

14x7=98

14x8=112

14x9=126

14x10=140

14x11=154

14x12=168

14x13=182

14x14=196

14x15=210

Question 12

15x1=

15x2=

15x3=

15x4=

15x5=

15x6=

15x7=

15x8=

15x9=

15x10=

15x11=

15x12=

15x13=

15x14=

15x15=

Answer 12

15x1=15

15x2=30

15x3=45

15x4=60

15x5=75

15x6=90

15x7=105

15x8=120

15x9=135

15x10=150

15x11=165

15x12=180

15x13=195

15x14=210

15x15=225

Question 13

1²=

2²=

3²=

4²=

5²=

6²=

7²=

8²=

9²=

10²=

11²=

12²=

13²=

14²=

15²=

16²=

17²=

18²=

19²=

20²=

21²=

22²=

23²=

24²=

25²=

Answer 13

1²=1

2²=4

3²=9

4²=16

5²=25

6²=36

7²=49

8²=64

9²=81

10²=100

11²=121

12²=144

13²=169

14²=196

15²=225

16²=256

17²=289

18²=324

19²=361

20²=400

21²=441

22²=484

23²=529

24²=576

25²=625

Question 14

1³=

2³=

3³=

4³=

5³=

6³=

7³=

8³=

9³=

10³=

11³=

12³=

13³=

14³=

15³=

Answer 14

1³=1

2³=9

3³=27

4³=64

5³=125

6³=216

7³=343

8³=512

9³=729

10³=1000

11³=1331

12³=1728

13³=2197

14³=2744

15³=3375

Question 15

square root of 2 approx =

square root of 3 approx =

square root of 5 approx =

Answer 15

square root of 2 approx = 1.4

square root of 3 approx = 1.7

square root of 5 approx = 2.2

Question 16

List all 25 primes under 100.

Answer 16

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

Question 17

Is 1 a prime number?

Answer 17

No, The definition of a prime number is a positive integer that has exactly two positive divisors. However, 1 only has one positive divisor (1 itself), so it is not prime.

Question 18

2

3

4

5

6

9

10

25

Answer 18

2 - A number is divisible by 2 if it is even

3- A number is divisible by 3 if the sum of the digits is divisible by 3

4- A number is divisible by 4 if the number formed by the last 2 digits is divisble by 4

5-A number is divisible by 5 if it ends in 0 or 5

6-A number is divisible by 6 if the number is even AND divisible by 3

9- A number is divisible by 9 if the sum of its digits are divisible by 9

10- A number is divisible by 10 if it ends in 0

25- A number is divisible by 25 if it ends in 00, 25,50, 75

25

Question 19

(a^x+a^y) =

(a^x)^y=

a^x/a^y=

a^-x=

a⁰=

^yroot|a^x=

10^x =

Answer 19

(a^x+a^y) = a^x+y

(a^x)^y=a^(x)(y)

a^x/a^y= a^(x-y)

a^-x= 1/a^x

a⁰= 1 (the reason that any number to the zero power is one is because any number to the zero power is just the product of no numbers at all , which is the multiplicative identity, 1.)

^yroot|a^x= a^x/y

10^x = 10 followed by the number of 0’s that is the exponent

Question 20

1. The difference of squares: (a-b)(a+b)=
2. The square of a sum: (a+b)²=
3. The square of a difference: (a-b)²=

Answer 20

1. The difference of squares: (a-b)(a+b)= a²-b²
2. The square of a sum: (a+b)²= a²+2ab+b²
3. The square of a difference: (a-b)²= a²-2ab+b²

Question 21

If you multiply or divide by a negative when solving an inequality, what do you do?

Answer 21

Flip the sign

Question 22

6 smallest non-negative even #s:

Answer 22

6 smallest non-negative even #s: 0, 2, 4, 6, 8, 10

Why is 0 an even non-negative?

Question 23

6 smallest non-negative odd numbers:

Answer 23

6 smallest non-negative odd numbers: 1, 3, 5, 7, 9 ,11

Question 24

6 smallest non-negative multiples of 3:

Answer 24

6 smallest non-negative multiples of 3: 0, 3, 6, 9, 12, 15

What is 0 a multiple of 3?

Question 25

The remainder of 5 ÷2 is?

Answer 25

1. If you take an odd number and divide by 2, the remainder is always 1.