Jason Cameron

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9 - MPM1D - General math

Jul 05, 20249 min read

Review

Expand en evaluate

a)

b -333*3 = -81

Write in scientific notation

a) 532000

b) 0.0005679

  • When multiplying powers with the same base you can just add the exponents

  • On powers look for brackets if there isn’t then the exponent just effects the closest num 6x³ ≠ (6x)³

  • On division you can just do for example x⁵/x³ = x²

  • Review of key words

    1: improper fraction: when the numerator (top) is larger then the denominator (bottom)

    2: mixed number - whole number and proper fraction

    3: exponent:

    4: opposite integers - two opposite numbers such as -5 and 5 or -29 and 29

    5: base of a power

    6: denominator

    7: lowest common denominator

    8: power

    9: numerator

    10: Unit fraction: a fraction that has a numerator of 1 examples: 1/5, 1/52 & 1/20

  • What

1/20 1/17 1/14 1/8 1/4 1/2

3/4

HW

02/09/23

### Fractions divide

1) 3/56

2) 2/30 or 1/15

3) 57/108

4) 6/10

5) 77/110

6) 20/7

7) 51/40

8) 117/36

9) 72 / 60

10) 65/48

### Fractions convert

1) $3\frac{1}{3}$

2) $\frac{59}{12}$

3) $\frac{143}{15}$

4) $\frac{74}{9}$

5) $3\frac{5}{8}$

6) $\frac{47}{8}$

7) $\frac{27}{7}$

8) $\frac{46}{15}$

9) $9\frac{3}{8}$

10) $\frac{23}{6}$

### Third page

1) 11/5 + 7/4 = 44/20 + 35/20 = 79/40

2) 7/2 - 8/3 == 21/6 - 16/6 = 5/6

3) 0

4) 1/2

5) 3/2 + 13/5 == 15/10 + 26/10 = 28/20 or **7/5**

6) 7/2 - 23/9 == 63/18 - 161/18 = -98/18 or **-49/9**

7) 11/4 + 6/5 == 55/20 + 24/20 = 79/20

8) 13/4 - 19/8 == 26/8 - 19/8 = 7/8

9) 7/2 - 3/2 = 4/2 or 2/1

10) 11/2 + 21/4 == 22/4 + 21/4 = 43/4

  • 02/10/23

    A = {1,2,3,4,5,6,7,8,9} B = { 2,4,6,8} C = {4,8}

    Subsets:

    A: false, 1 isn’t in b

    B: true all numbs are contained

    C: true all contained

    D: true all contained

    E) b is larger then C

  • 02/14/23

    1. Imani’s resting heart rate is 76 beats per minute (bpm). At this rate,

    a) how many times will her heartbeat be in 3 minutes: 228

    b) how many times will her heartbeat be in 1 hour: 4560

    c) how many times will her heartbeat be in 30 seconds: 38

    1. Yanush can type 110 words in 2.5 minutes. Approximately how many words can he type per minute: 44

    2. At a constant rate, a car travels 216 kilometres in 2 hours.

    a) How far will the car travel in 3 hours: 324

    b) How long does it take to travel 54 km: 30m

    1. By definition, one inch is equivalent to 2.54 cm. Calculate the following conversions.

    a) 5 inches to centimetres: 12.7cm

    b) 16.5 inches to millimetres: 419.1mm

    c) 30 cm to inches 11.8”

    d) 1 metre to inches: 39.3

    1. Solve each proportion (find the value of x).

    a) ¾ = x/8 x = 6

    b) 5/3 = x/18: x = 30

    c) 40/50 x/10: x = 8

    d) 1 12 4 x = 3

    e) 28 4 21 x = 3

    f) 36 4 x 11: x = 99

    1. The ratio of violinists to cellists in an orchestra is 8 : 3. If the orchestra has 12 cellists, how
      many violinists does it have:
      36

    2. Proportional relationships are relationships between two variables where their ratios are equivalent

    3. a) 1/5 = x/12 = x = 2.4

      b) 15/8 = n/6 = 3.2

      c) 6/11 = y/50 27.2

      d) 14/x = 3/5 23.3 repeating

      e) 9/5 - 4/p 2.2 repeating

      f) t/7 = 11/6 = 3.8

    4. a) How many centimetres is a distance that equals 17 boot lengths?

    • The answer is 476 cm.

      b) How many metres is a distance that measures 32 boot lengths?

    • The answer is 8.96 m.

      c) How many boot lengths are needed to measure a distance of 350 cm?

    • The answer is 12.5 boot lengths.

      d) How many boot lengths are needed to measure a distance of 7 m?

    • The answer is 250 boot lengths.

    1. a) A jerk chicken recipe calls for ½ cup of lime juice. Express this volume in milliliters.

    • The answer is 125 mL.

      b) A cake recipe requires 320 mL of sugar. Express this measurement in tablespoons.

    • The answer is 20 tablespoons.

    /tog

  • 02/15/23

    1. a) 0.45/can c) 0.009/mL

    2. Snuggies, by approximately $0.04/diaper.

    3. Percent means per 100, or in other words, out of 100.

    4. a) 73% b) 84% c) 70% d) 78.3% e) 45% f) 63.3% g) 134% h) 120%

    5. a) 20 b) 10 c) 14 d) 152.22 e) 5.2

    6. 60%

    7. 192 minutes

    8. $1.25

    9. Ayobami, by 2 words/minute.

    10. $180.79

    11. a) 809.97

  • 02/22/23

    a) {5.9, 5.99, 5.999…}

    b) no, as whole numbers contain 0 while natural starts at 1

    c) yes, integers are a subset of rational numbers as they are larger on the venn diagram and they contain all integers in them.

  • 02/23/23

    1. 7 to the power of 4

    2. 3 to the power of 4 is. bc 3x3x3x3 (81) > 4x4x4 (64)

    3. depending on how you word it either 1 times or 8 times.

    4. a) 41 c) 85 e) -4

    5. a) 10, 1, 1/10 1/100 1/100 c) 3, 1, 1/3, 1/9

    6. 7, 1, -16, 1, 0, 0

    7. 129, 3298. 1/204

    8. it is 6 times larger.

    9. 12 / 3(3) = 12

    10. a) 5¹ c) 3⁵ d) 5-¹

    11. a) 16 c) 16 e) -1 g) -1

    12. a) 1 c) -1 e) 1/9 g) -1

    13. a) 1 / a² b) 1 / b¹ d) 1 / d⁷

    14. Yes. There is 9 zeros following the 16.

  • 02/27/23

    1. Show why 2⁴2³=2⁷. - 2222222 =2⁷

    2. 2³2⁵ or 222 + 22222 = 2222222 or 2⁷

    3. a) 7 b) 7 c) 12 d) 9 e) 6 f) 12

    4. a) 9-4 c) 8-1 e)

  • 03/02/23

    1. x⁵
    2. x²
    3. x⁶
    4. x³+x²
    5. (4x)⁵

    Homework

    1. 1 -9 parts acegik

    a)

    j) 4⁶ a⁹ b¹⁸

  • 03/03/23

    1. -8+20k,k=4. 80-8 = 72
    2. 3/5x17, x=13
    3. -3(0)²+4(0)(-1)-2(-1)² = -2

    Homework

    1. a)3 b)4 c)3 d)5
    2. a)2,3 b)4,3 c) 4,9
    3. a) like b) unlike c) like d) unlike
    4. a) 8 b) 15 c) -4 d) 1 e) -1
    5. a) 4x b) 7y c) 8x d) 9a e) 0 (0x) f) -4k g) -3w h) -1z
    6. a)2x 3y b) 7a 16b c) 13h 7g d) 6c 5d e) -3x 1y
    7. No, 5x+2 is not 7x that would be 5x+2x as what Shaun thought is really (5x)+ 2
    8. Marc was correct. It’s not that deep bro.
    9. a) 7x +14 c) -2p + 16
    10. a) 7x+14 c) -2p -q6 e)5t -4
    11. a) -2x c)17x+8y e)-5x + 3
    12. a) -36 c) 18
    13. a) unlike c) like
    14. A) 6x²+18x b) 17x+3x c) -3y²+5y
    15. a) 4x-3x: 22 c) x²+6y²:58 e)-10y+y+20;-67

  • 03/08/23

    a) 2(x + 3)

    b) -12x-8 / x +1 = 11x-7

    C) 3(x² + 2x+3) - (3x+1)(2x) = (3x² + 1x+8)

    D) a) by multiplying the length times width b) 3x¹ * x+5¹ = 3x²+5

    C) X * x+1 = x² + 1

    D) = (3x² + 5) - (x² + 1)

  • 03/10/23

    1. a) Subtraction c) subtraction e) addition

    2. a) division c) division e) division

    3. a) subtraction c) addition e) subtraction

    4. a) x = 7 c) n = -4 e) x=8

    5. a) 2x=18 c) 5x = 20

    6. a) x = 6 c) x= 3 e) x = -16

    7. a) iv c) I e) v

    8. a) x=11 c) y = -2 e) y = -3

    9. a) C = 12.35 / 0.95 b) 13

    10. a) x = 180/5 b) x = 36

    11. a) x = 168cm / 16 b) x = 10.5 c) L= 21, W = L * 3 ( 63)

  • 03/20/23

    1. a) subtraction→ division c) subtraction→ division e) subtraction→ division
    2. a) x = 3 c) x = -10 e) x = 3
    3. a) 2x+7 = 15 c) 6x-10x-3 = 51 e) -10y-9+4y+3 =-48
    4. a) x = 3 c) y = 7 e) m=16
    5. a) N = (126- 10)/2 b) 58
    6. a) N = (146 + 40 ) / 3 b) 62
    7. (a=3, b=-12) 39
    8. a) x = 11 3(11)+5+8 = 46 c) 4x+7x-4+12=-40 = (⁴⁸/¹¹) e) x= 3 -11= -3-8
    9. a) Y = (201 - 25)/ 16) b) 11

  • 03/21/23

    1. a) x = 5 c)
      1. T = (21-12) / 1.5 2. (6)
    3. M = 5500 / 600 (9)

  • 03/22/23

    1. b) (10h+3) = 18 -3(5+2h) | (10h -3) = 18- -15 -6h H = 0
    2. a) x+2 = 24 x=11 b) x-4/3 = -5 e)

    One var:

    1. 4/9a = 21 | a = 189/4

    2. 3b=3 | b=

    3. 3-(2)x=30

  • 03/23/23

    1. a) x + 4 = 12 | x = 8 b) x = 26 c) y = 6 d)

    D) 10+b/5 = -1 = b = -55

    1. c) w + 3 = 8 | w = 8 -3 | x = 5

    d) y -5 = 30 | y = 30-5 (25)

    e) 2a +3 = 15 | 12 / 2 = y (y=6)

    HOMEWORK:

    1. a) 2) x = 8 | x = 4 c) 4y =-22 | -22/4 = y = 5.5

    2. e) -2.3x = 39.1 = x = -17

    3. G) -2x = -25 + 18 (-7) -7/-2 = y = 3.5 I) 31 = 4t | 31/4 = t | t = 7.75

    4. A) 3x + 10 = 2x + 15 b) x = 5

    5. a) 2y - 22 = 4y + 15 b) y= 9

  • 03/24/23

    1. 4x+8 = 3x+15, 4x-3x = -8+15, x = 7
    2. 6n+9 = 10n-2, 6n-10n = -2-9, n = 11/4
    3. 8x+5/2 + 6/1 = 7/3, 3(8x+5) + 6*6/1 = 14, 24x+15 + 36 = 14, 24x= 14-51 (-37) = -1.5

  • 03/29/23

    1. Let D be Derek’s age and L be Luke, so L + D = 52 and D = L+10 So if we do 52-10 (42) then 42/2 (21) we get Luke’s age (21 and Derek’s age (31)
    2. Let n be the unknown numbers, so n + n + 1 = 47 so we can remove the 1 to get , 46 then isolate x by dividing 46 by two to get 23 (aka x) so we know the numbers are 23 and 24

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