10thgradeMathStandardSummerPacket2017 Name:_____________________________________________________________DUEontheFIRSTdayofSCHOOL2017Formulas:DistanceFormula:

MidpointFormula:

Gradient(slope):

m =y2 − y1x2 − x1

PythagoreanTheorem:a2 + b2 = c2 AreaofTriangle:

A = 12bh

A=½absinC

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d = x2 − x1( )2 + y2 − y1( )2

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M =x1 + x22

, y1 + y22

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GeneralFormAx+By=CSlopeInterceptFormy=mx+bPoint–SlopeForm

COSINERULEa2=b2+c2–2bcCOSA°

SINERULE

Circles:

A=𝜋r2

Numbers and Sets Simplify: 1. 2. 15 - 5 x 2 + 3 x 6 = 3. 23 =

4. 32 x 32 = 5. -5 3 = 6. (-5) 3 = 7. -1<X<8X ∈ Z

a. Is X infinite or finite? ________________________________

b. Write all the values of X _________________________________ c. d. Show on a number line the values of X

8.ThesetofREALnumberscontainsthesubsetsof:N=__________________________________________________________________________________________Z=__________________________________________________________________________________________Q=__________________________________________________________________________________________I=__________________________________________________________________________________________

9.A={-9,-7,-5,-3,-1,0,1,2,3}andB={0,2,4,6,8,10}

a. A∩ B = b. n(A∩ B ) = c. A u B = d. (A∩ B)’ =

10. If A is the set of all factors of 28, and B is the set of all factors of 12, list all factors of 28 and 12; then draw and label a Venn Diagram: A= {_____________________________} B= {_____________________________}

34 +

6 5 =

11.{0,1,2,3,4,5,6……}isthesetof__________________________________________12.{….-3,-2,-1,0,1,2,3…….}isthesetof__________________________________13.Thesetofnumbersthatincludefractionsiscalled__________________________________.

Algebraic Thinking 1. Write in words, the meaning of:

a. a+ b2

b. 5+ !

!

c.2N+72. Ifa=-1,b=4,c=-2Evaluate:2(b+c)-b+c23.If 𝑝 = −4, 𝑞 = 2, 𝑟 = −2Evaluate:−3𝑝𝑞 + (𝑝 − 𝑟) Expand and Simplify: 4. (x −4)2 5.(2a+3)2

6. (x−2)−3(x−4) 7. (x - 4) (x +4) 8.(a+2c)(3c–4)9.(x+3)(x–1)10.(8x)(2x)(-1)

11. !! !!!

12. ( 2)2

13. (𝑥 − 2) (𝑥 + 2) 14.(x−4)

15.Expandandsimplify. 2𝑥 − 𝑦 !16.Expandandsimplify.𝑥 𝑥 − 2𝑦 + 2𝑦 𝑦 − 2𝑥 17. Fully Factor:

a) x2+4x+8x+32

b) 3x2+17x–6

c) 16–9c2

d) 25𝑥! − 16

18. Simplify:

2a38a • a

6a2

19. Simplify: !!

!!!"!"!!

20. Solve for x: !!! !

- !!!!

= -3 21. Solve for x: 1 – ( x- 3) = 222.Solve for x:12 – ( x- 1) = 2( 5-x) 23. Write an equation for a line with slope of 5 that goes through point (2, -3)

a. point-slope form:

b. Gradient(slope) intercept form:

c. General (standard) form:

24. Find the distance between points (4, 9) and (-5, 8) 25.Findthedistancebetweenthepoints(5,10)and(13,-1) 25. GivenPandQareendpointsofasegment..Findthecoordinatesofthemidpoint.

P(9,-3)andQ(0,-3)

26.Twolineshaveslopeof3and

!!a10 .

a.) Find“a”ifthelinesareparallel

b.) Find“a”ifthelinesareperpendicular.27.Findthemidpointofthelinethrough(0,-4)and(3,-6)28.Findthedistancebetweenthepoints(5,10)and(13,-1)29.Twolineshaveslopeof3and

!!a10 .

a.) Find“a”ifthelinesareparallel

b.) Find“a”ifthelinesareperpendicular.

30.Findtheequationofalinethroughthepoint(2,0)withaslopeof½inslopeinterceptformandGENERALForm.

Geometry 1. Convert each of the following:

a. 1km = ___________________________ m

b. 1Km = ___________________________ cm

c. 5.67 km = ________________________ cm

d. 700 mm = ________________________ m

e. 1Km2 = ___________________________ m2

f. 18 cm 2 = ________________________ m2

g. 2.3 m3 = ________________________ cm3

e. 0.65 KL = ________________________ L

3. Find the area of a square with sides of 5m 4. Find the area of a rectangle whose base is 10m and height is 4m. 5. Find the perimeter of the 10m by 4m rectangle above. 6. What is the length of the hypotenuse of a right triangle with legs of 3 cm and 4 cm? 7. What is the volume of a rectangular prism with length 5ft, width 6ft and Height 10ft ? 8. Find the:

a) Circumference and area of circle with radius of 6 cm

b) Perimeter of a rhombus with side 10 cm

c) Area of a right angle triangle with one leg 5cm and hypotenuse of 13cm.

9.Usethefigurebelowtofind:

a.)AREAofRectangle=

b)AREAofSemi-Circle= c.)TotalArea=

10.FindthesurfaceareaofthePrismbelow

11. Find the area of the trapezoid below

Statistics / Probability

1. Find the Mean, median, mode, range of the follow data: (9, 7, 8, 3, 5, 5, 5 ,6, 2, 7, 10) a. Mean = b. Median = c. Mode = d. Range=

2. 11 out of 25 measurements are below 12cm and 11 are above 13 cm, Find the

median if the other 3 measurements are 12.1, 12.4 and 12.6.

3. 3. A students has 6 test scores: 78, 98,80, 75, 70 with one test left to take. What is the lowest test score possible on the next test if the student wants at least a B- (80)?

4. Given the data: 27,38,31,30,26,28,24,30, 33, 35, 25, 29,36, 37,25, 29

a. Name the Median, Quartile 1 and Quartile 3 b. What is the Interquartile range?

5. If 52 cards are well shuffled and then one card is drawn from the top what is the probability it will be one of these: a. Jack? b. Black? c. A non Jack? d. A diamond? e. The Ace of Diamonds? f. Either a diamond OR an Ace?

6. A spinner has four equal sectors containing 1,2,3,4. If a dice is tossed each time a

spin is made, what is the probability of each event:

a. P(Head and 4) b. P(Head OR 4)