Arizona College Algebraic Expression Math Review Exercises

Mercy High School – Summer Math ReviewName___________________________________
Students Entering Algebra 2
Write each as an algebraic expression.
1) 7 more than w is 37
2) the quotient of a and 8 is greater than or equal to 50
3) u decreased by 4 is equal to 8
4) n increased by 5 is greater than 45
5) w increased by 9 is equal to 13
6) the difference of n and 7 is less than 50
Evaluate each using the values given.
7) x − (4 − y) − 1; use x = 3, and y = 4
8) z(3 ÷ 3 + x); use x = 2, and z = 6
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Worksheet by Kuta Software LLC
9) k ÷ 5 − (h − h); use h = 3, and k = 5
10) 3 − (c + b); use b = 6, and c = 4
11) ( y(z + x)) ÷ 6; use x = 6, y = 3, and z = 2
12) y + 3 − z ÷ 4; use y = 1, and z = 4
13) (m + p 2 ) ÷ 2; use m = 6, and p = 2
14) 3m − n ÷ 4; use m = 6, and n = 4
3
15) p ÷ 5 + mp; use m = 5, and p = 5
Solve each equation.
16) 5(1 + 8n) = 125
17) 8(3 + 5x) = 264
18) 3(1 − 4x) − 8 = 91
19) 2(−3 + 8n) − 2n = −6(1 + 8n)
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Worksheet by Kuta Software LLC
20) 8( x + 6) − 2 = −5 − 5(6x + 5)
21) 4(k + 7) = 7(k − 2)
Write the slope-intercept form of the equation of the line described.
22) through: (−1, −5), parallel to y = 8x + 2
1
23) through: (5, 5), perp. to y = − x + 4
2
Write the slope-intercept form of the equation of each line.
24)
y
4
2
−5 −4 −3 −2 −1
1
2
3
4
5 x
−2
−4
Write the slope-intercept form of the equation of each line given the slope and y-intercept.
4
25) Slope = , y-intercept = −1
5
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Worksheet by Kuta Software LLC
Write the slope-intercept form of the equation of the line through the given points.
26) through: (0, −5) and (5, −1)
Solve each compound inequality and graph its solution.
27) 8x > 24 or x + 4 < 2 28) −9 ≤ −8 + v < −6 Solve each inequality and graph its solution. 29) 9 + 8v ≥2 4 Solve each system by elimination. 30) 5x − 2 y = 2 −8x − 5 y = 5 31) 0 = 5y − 2x + 19 −9x + 27 = −3y Solve each system by substitution. 32) −7x − 6 y = 15 y = −5x + 9 -4©\ e2Q0p2H1j _KSuHtJai fSBoofBtBw_aLrseo JLHLZCw.] p ZAplelB frWiOgAh]tesl Srkexspe^r_v[eWdM.y M SMtaAdBeS \wCittRhE XIinbfxidnfiHtPeZ IAdlCgOeSb[rwaZ B1O. Worksheet by Kuta Software LLC Simplify. Your answer should contain only positive exponents. 33) 35) (−2a 4b −1) 0 −2 0 0 −3 2 2 34) (2u) 3 −2a b ⋅ −a b (−a −4b 4) 2 ⋅ 2a 3b 3 37) − b −3 2nm 36) 4 (2m −1) 4 ⋅ 2n −1 (−2a 3b 0) 2 4 2 2a b ⋅ −a 3 38) −2 4 2u v ⋅ −u v −2 0 3 x ⋅ −x y ( x −4 y 4) 3 Factor each completely. 39) n 2 − 2n − 48 40) v 2 − 15v + 56 41) x 2 − x 42) 3n 2 + 10n -5©l \2Y0L2H1V KKPuAtkae TSDoWfZtRwfaKrHei fLWLnCr.] u [APljlT QrSingHhitBs^ \rKezsbe\rVvJeGdY.K a uMZaEdbes awDiStpht eI`n_fZiDnPietheH jARlrgTe^bJrgac \1U. Worksheet by Kuta Software LLC 43) 5n 2 − 19n − 30 44) 9n 2 + 71n − 90 45) 21r 3 − 24r 2 + 56r − 64 46) 5n 3 − 7n 2 + 40n − 56 Simplify each expression. 47) 4p + 4 3p + 10 p − 10 3 48) 3p 5p − 3 p + 18 p 2 49) 8(2k + 9) 3(2k + 9) ÷ 8k 3 50) n + 3 8n(n + 3) ÷ 7 7(n − 3) 51) 2 (n − 2)(n + 7) (n − 2)(n + 7) 8n 2 ÷ n + 10 -6©s i2b0z2q1I wKTuKt[a_ jSDoyfbt_wbajrweD aLqLlCh.v s GA\lxly hrqiJgGhrtQsH crMeSs`elrLvXeUdz.Z b [MRacdqew pwqistchO wIpnDfJiHnAiBtgeI EAllzgAeNbTrRat A1H. Worksheet by Kuta Software LLC Simplify. 52) 2 24 − 24 54) − 6 (3 − 2 6 ) 53) 2 45 − 3 45 4 55) 2+ 3 Find the value of each trigonometric ratio to the nearest ten-thousandth. 56) cos A 57) sin A C C 25 A 25 A 24 7 B 24 B 7 58) tan Z X 35 Z 21 28 Y -7©V _2d0M2o1q JKVuOtEaB PSqoUfZtxwGa_reeV KLPLSCb.F x tAvl_lg vrwibgZhttfsk prnemsLezruvPeqdC.N D IMpaBdleE wwkiPtuhk fIznWf_i`ntiftZe^ kAolvgEerbTrtaI P1X. Worksheet by Kuta Software LLC Find the missing side. Round to the nearest tenth. 59) 60) 17 x 27° x 11 74° 61) 18 35° x 62) Brenda's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 5 senior citizen tickets and 8 child tickets for a total of $44. The school took in $39 on the second day by selling 6 senior citizen tickets and 5 child tickets. Find the price of a senior citizen ticket and the price of a child ticket. Simplify each expression. 63) (5x 4 + 4x 3 − 8) + (1 + 3x 3 − 2x 4 ) 64) (4n 2 + 3 + 2n 4 ) + (3 − 7n 2 − 2n 3 ) -8©B A2L0o2v1w VKHuftCa[ lSvodf]tyw`atrren `LRLVCk.O z PAul^li NrziTg_hOtQsn trqess^ezrovoeRda.f b eMFa]dDeR IwYiotOho LI^nsfSiMnCi\tve^ `ARlrgbeMbYrbaY y1k. Worksheet by Kuta Software LLC Answers to Students Entering Algebra 2 1) w + 7 = 37 a ≥ 50 8 6) n − 7 < 50 10) 17 14) 17 18) {−8} 22) y = 8x + 3 2) 5) w + 9 = 13 9) 1 13) 5 17) {6} 21) {14} 4 25) y = x − 1 5 27) x > 3 or x < −2 : 3) u − 4 = 8 4) n + 5 > 45
7) 2
11) 4
15) 26
19) {0}
23) y = 2x − 5
8) 18
12) 3
16) {3}
20) {−2}
1
24) y = x − 3
4
4
26) y = x − 5
5
−6 −5 −4 −3 −2 −1 0
1
2
3
4
4
5
6
7
5
6
28) −1 ≤ v < 2 : −5 −4 −3 −2 −1 0 1 2 3 1 17 29) v ≥ − or v ≤ − : 8 8 −7 −6 −5 −4 −3 30) (0, −1) 31) (2, −3) v6 4u 3 x 15 38) − 9 y 42) n(3n + 10) 46) (n 2 + 8)(5n − 7) 34) − 50) 54) 58) 62) 64) −2 −1 0 2b 14 a5 39) (n + 6)(n − 8) 35) 43) (5n + 6)(n − 5) 5 p2 − 3 p + 2 47) 5( p − 1) n−3 n + 10 51) 8n 8n 2 −3 6 + 12 55) 8 − 4 3 1.3333 59) 11.4 senior citizen ticket: $4, child ticket: $3 2n 4 − 2n 3 − 3n 2 + 6 1 2 3 4 5 32) (3, −6) 2a 4 b2 40) (v − 8)(v − 7) a2b3 2 m8n2 37) − 16 41) x( x − 1) 44) (n + 9)(9n − 10) 2 − 5 p 2 − 30 p 48) 2( p + 6) 52) 2 6 45) (3r 2 + 8)(7r − 8) 1 49) k 53) −3 5 56) 0.2800 60) 7.7 63) 3x 4 + 7x 3 − 7 57) 0.2800 61) 14.7 36) − 33) -9©M ]2D0I2]1z [KXuetiaq JSWokfEtyw^aernet `LjLQCY.A [ DAUlSlD xrjiNgwhWtpsJ _rUezsceercv_ezdp.z p YMXazdte_ EwqiitQhm FINnNfQilnjiytQex ^AwlogIeIbqrgaZ Y1C. Worksheet by Kuta Software LLC