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Math10FoundationsPre-calculusChapter3UnitTest
MultipleChoice
Identify the choice thatbest completes the statementoranswers thequestion.
1. Write theprime factorization of630.
a.2⋅5⋅7⋅9b.2⋅5⋅63c.2⋅32 ⋅5⋅7d.2⋅3⋅5⋅7
2. Determine thegreatest common factorof84, 210, and 336.
a.14b.1680c.21d.42
3. Determine the least common multipleof48, 72, and 108.
a.432b.216c.31 104d.12
4. Oneneighbour cutshis lawn every8 days. Anotherneighbour cutsher lawn every10 days. Supposeboth neighbours cut their lawns today. How manydayswillpassbeforeboth neighbours cut their lawnson the samedayagain?
a.80 daysb.60 daysc.2daysd.40days
5. There are16 male students and 20 female students in aGrade10 math class. The teacherwants to divide the class into groupswith the samenumberofmales and the samenumberof females in each group. What is the greatestnumberofgroups the teacher can make?
a.12b.4c.8d.16
6. Determine the square rootof250 000.
a.100b.63c.500d.200
7. Determine the cube rootof42 875.
a.1225b.4763.9c.207.1d.35
8. Determine the side length of this square.
a.63 cmb.15.83 cmc.992.25cmd.441cm
9. How manyperfect squarewholenumbers arebetween 5000 and 6000?
a.6b.8c.1d.7
10. How manyperfect cubewholenumbers arebetween 6000 and 8500?
a.3b.2c.1d.15
11. Which of thefollowingnumbers isnotboth aperfect square and aperfect cube?
a.531 441b.12 544c.117 649d.15 625
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12. Factor the trinomial−33b2 +99b +77.
a.−11(3b2 −9b+7)c.−11(3b2 −9b−7)
b.−33(b2 −3b −7)d.33(−b2 +27b+7)
13. Factor the trinomial−42x5y6 −24x4y5 −54x3y7.
a.6x4y5(−7xy−4−9y2)c.−3x3y5(14x2y+8x +18y2)
b.−6x3y5(7x2y+4x+9y2)d.−6x3(7x2y6 +4xy5 +9y7)
14. Simplifythe expressiony2 +8y−6−9y2 −24y−26, then factor.
a.−8(y2 −2y −4)c.−4(2y2 +4y+8)
b.−8(y2 +2y +4)d.−4(2y2 +4y+1)
15. Which of the followingtrinomials can be represented bya rectangle?Use algebra tiles to check.
a. / z2 +33z+9 / c. / z2 +10z+2b. / z2 +12z+63 / d. / z2 +10z+25
16. Which of the followingtrinomials can be represented bya rectangle?Use algebra tiles to check. a.4c2 +33c+8 c. 4c2 +13c+8
b.4c2 +21c+3d.4c2 +4c+15
17. Expand and simplify:(4−r)(7−r)
a.28−11r+r2c.28+3r+r2
b.28−3r+r2d.28+11r+r2
18. Factor:v2 −13v+36
a.(v+3)(v +12)c.(v−4)(v −9)
b.(v−3)(v −12)d.(v+4)(v +9)
19. Factor:−24−2x+x2
a.(6+x)(−4+x)c.(−3+x)(8+x)
b.(3+x)(−8+x)d.(−6+x)(4+x)
20. Complete:(a+6)(a−)=a2 +a−12
a.(a+6)(a−4)=a2 +4a−12c.(a+6)(a−2)=a2 +2a−12
b.(a+6)(a−2)=a2 +4a−12d.(a+6)(a−4)=a2 +2a−12
21. Factor:c2 −4c −117
a.(c−9)(c +13)c.(c+9)(c −13)
b.(c−3)(c +39)d.(c+3)(c −39)
22. Complete. (k−)(k−5)=k2 −k+135
a.(k−27)(k−22)=k2 −5k+135c.(k−27)(k−32)=k2 −5k+135
b.(k−27)(k−5)=k2 −32k+135d.(k−27)(k−5)=k2 −22k+135
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23. Which multiplication sentencedoes this setof algebra tiles represent?
a.(2x−2)(2x+2)b.(2x2 +2)(2x2 +2) / c. d. / (2x2 +2x)(2x2 +2x) (2x+2)(2x+2)
24. / Expand and simplify:(8g −3)(7−3g)
a.−24g2 +65g −21 / c. / −24g2 +47g −21
b.−24g2 −65g −21 / d. / 24g2 +65g−21
25. / Factor:25x2 +58x+16
a.(25x+4)(x+4) / c. / (5x+4)(5x+4)
b.(25x+8)(x+2) / d. / (5x+8)(5x+2)
26. / Expand and simplify:3(1−2t)(9+4t)
a.−24t2 +42t+27 / c. / −72t2 −126t+81
b.−24t2 +66t+27 / d. / −24t2 −42t+27
27. / Expand and simplify:(5m−3n)2
a.25m2 −9n2 / c. / 25m2 −30mn +9n2
b.25m2 −15mn +9n2 / d. / 25m2 +9n2
28. / Expand and simplify:(4d −1)(5d2 +12d −3)
a.20d3 +53d2 +3 / c. / 20d3 +43d2 −24d+3
b.20d3 +48d2 −12d+3 / d. / 20d3 +43d2 +3
29. / Factor:16p2 −81q2
a.(4p−9q)2 / c. / (16p−9q)(p−9q)
b.(4p+9q)2 / d. / (4p +9q)(4p−9q)
30. Find an integer to replace“ so that this trinomial isaperfect square.
64v2 −vw+81w2
a.144c.72
b.648d.18
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31. Factor:49s2 −112st+64t2
a.(7s−8t)2c.(7s−t)(7s−64t)
b.(7s+8t)2d.(7s−8t)(7s+8t)
32. Identifythispolynomial asaperfect square trinomial, adifferenceof squares, orneither.
9a2 +9a+36
a.Differenceof squaresc.Neither
b.Perfect square trinomial
33. Identifythispolynomial asaperfect square trinomial, adifferenceof squares, orneither.
25g2 −9h2
a.Perfect square trinomialc.Neither
b.Differenceof squares
ShortAnswer
34. Find and correct the errors in this factorization.
w2 −2w−80 =(w−8)(w+10)
35. Find and correct the error(s) in this solution of factoringbydecomposition.
90y2 +77y −52 =90y2 +117y −40y−52
=9y(10y+13)+4(10y+13)
=(10y+13)(9y+4)
Problem
36. List all theprimenumbersbetween 120 and 140. How do you know theyareprimenumbers?
37. Germainewants to painta cubewith volume2744 m3.Each tub ofpaint covers79 m2.How manytubsof paintdoesGermaineneed to paint the cube?
38. Factor. Checkbyexpanding.
8z2 −112z+360
39. Factor5x2 +17x+6.Explain your steps.
40. Factor. Explain your steps.
196x2 −16y2
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Math10FoundationsPre-calculusChapter3UnitTest
AnswerSection
MULTIPLE CHOICE
1. ANS: CPTS: 1DIF:Easy
REF: 3.1 Factors and Multiplesof WholeNumbersLOC: 10.AN1
TOP: Algebra and NumberKEY: ProceduralKnowledge
2. ANS: DPTS: 1DIF:Moderate
REF: 3.1 Factors and Multiplesof WholeNumbersLOC: 10.AN1
TOP: Algebra and NumberKEY: ProceduralKnowledge
3. ANS: APTS: 1DIF:Moderate
REF: 3.1 Factors and Multiplesof WholeNumbersLOC: 10.AN1
TOP: Algebra and NumberKEY: ProceduralKnowledge
4. ANS: DPTS: 1DIF:Moderate
REF: 3.1 Factors and Multiplesof WholeNumbersLOC: 10.AN1
TOP: Algebra and NumberKEY: ProceduralKnowledge
5. ANS: BPTS: 1DIF:Moderate
REF: 3.1 Factors and Multiplesof WholeNumbersLOC: 10.AN1
TOP: Algebra and NumberKEY: ProceduralKnowledge
6. ANS: CPTS: 1DIF:Easy
REF: 3.2 PerfectSquares, PerfectCubes, and TheirRootsLOC: 10.AN1
TOP: Algebra and NumberKEY: ProceduralKnowledge
7. ANS: DPTS: 1DIF:Easy
REF: 3.2 PerfectSquares, PerfectCubes, and TheirRootsLOC: 10.AN1
TOP: Algebra and NumberKEY: ProceduralKnowledge
8. ANS: APTS: 1DIF:Easy
REF: 3.2 PerfectSquares, PerfectCubes, and TheirRootsLOC: 10.AN1
TOP: Algebra and NumberKEY: ProceduralKnowledge
9. ANS: DPTS: 1DIF:Moderate
REF: 3.2 PerfectSquares, PerfectCubes, and TheirRootsLOC: 10.AN1
TOP: Algebra and NumberKEY: ProceduralKnowledge
10. ANS: BPTS: 1DIF:Moderate
REF: 3.2 PerfectSquares, PerfectCubes, and TheirRootsLOC: 10.AN1
TOP: Algebra and NumberKEY: ProceduralKnowledge
11. ANS: BPTS: 1DIF:Moderate
REF: 3.2 PerfectSquares, PerfectCubes, and TheirRootsLOC: 10.AN1
TOP: Algebra and NumberKEY: ProceduralKnowledge
12. ANS: CPTS: 1DIF:Easy
REF: 3.3 Common FactorsofaPolynomialLOC: 10.AN5
TOP: Algebra and NumberKEY: ProceduralKnowledge
13. ANS: BPTS: 1DIF:Moderate
REF: 3.3 Common FactorsofaPolynomialLOC: 10.AN5
TOP: Algebra and NumberKEY: ProceduralKnowledge
14. ANS: BPTS: 1DIF:Moderate
REF: 3.3 Common FactorsofaPolynomialLOC: 10.AN5
TOP: Algebra and NumberKEY: ProceduralKnowledge
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15. ANS: DPTS: 1DIF:Easy
REF: 3.4 ModellingTrinomials asBinomialProductsLOC: 10.AN5
TOP: Algebra and NumberKEY: ProceduralKnowledge
16. ANS: APTS: 1DIF:Easy
REF: 3.4 ModellingTrinomials asBinomialProductsLOC: 10.AN5
TOP: Algebra and NumberKEY: ProceduralKnowledge
17. ANS: APTS: 1DIF:Easy
REF: 3.5 Polynomialsof theFormx^2 +bx +cLOC: 10.AN4
TOP: Algebra and NumberKEY: ProceduralKnowledge
18. ANS: CPTS: 1DIF:Easy
REF: 3.5 Polynomialsof theFormx^2 +bx +cLOC: 10.AN5
TOP: Algebra and NumberKEY: ProceduralKnowledge
19. ANS: DPTS: 1DIF:Moderate
REF: 3.5 Polynomialsof theFormx^2 +bx +cLOC: 10.AN5
TOP: Algebra and NumberKEY: ProceduralKnowledge
20. ANS: BPTS: 1DIF:Moderate
REF: 3.5 Polynomialsof theFormx^2 +bx +cLOC: 10.AN4
TOP: Algebra and NumberKEY: ProceduralKnowledge
21. ANS: CPTS: 1DIF:Easy
REF: 3.5 Polynomialsof theFormx^2 +bx +cLOC: 10.AN5
TOP: Algebra and NumberKEY: ProceduralKnowledge
22. ANS: BPTS: 1DIF:Moderate
REF: 3.5 Polynomialsof theFormx^2 +bx +cLOC: 10.AN4
TOP: Algebra and NumberKEY: ProceduralKnowledge
23. ANS: DPTS: 1DIF:Easy
REF: 3.6 Polynomialsof theFormax^2 +bx +cLOC: 10.AN5
TOP: Algebra and NumberKEY: ProceduralKnowledge
24. ANS: APTS: 1DIF:Easy
REF: 3.6 Polynomialsof theFormax^2 +bx +cLOC: 10.AN4
TOP: Algebra and NumberKEY: ProceduralKnowledge
25. ANS: BPTS: 1DIF:Easy
REF: 3.6 Polynomialsof theFormax^2 +bx +cLOC: 10.AN5
TOP: Algebra and NumberKEY: ProceduralKnowledge
26. ANS: DPTS: 1DIF:Moderate
REF: 3.6 Polynomialsof theFormax^2 +bx +cLOC: 10.AN4
TOP: Algebra and NumberKEY: ProceduralKnowledge
27. ANS: CPTS: 1DIF:EasyREF: 3.7 MultiplyingPolynomials
LOC: 10.AN4TOP: Algebra and NumberKEY: ProceduralKnowledge
28. ANS: CPTS: 1DIF:EasyREF: 3.7 MultiplyingPolynomials
LOC: 10.AN4TOP: Algebra and NumberKEY: ProceduralKnowledge
29. ANS: DPTS: 1DIF:EasyREF: 3.8 FactoringSpecialPolynomials
LOC: 10.AN5TOP: Algebra and NumberKEY: ProceduralKnowledge
30. ANS: APTS: 1DIF:EasyREF: 3.8 FactoringSpecialPolynomials
LOC: 10.AN5TOP: Algebra and NumberKEY: ProceduralKnowledge
31. ANS: APTS: 1DIF:EasyREF: 3.8 FactoringSpecialPolynomials
LOC: 10.AN5TOP: Algebra and NumberKEY: ProceduralKnowledge
32. ANS: CPTS: 1DIF:EasyREF: 3.8 FactoringSpecialPolynomials
LOC: 10.AN5TOP: Algebra and NumberKEY: ProceduralKnowledge
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33. ANS: BPTS: 1DIF:EasyREF: 3.8 FactoringSpecialPolynomials
LOC: 10.AN5TOP: Algebra and NumberKEY: ProceduralKnowledge
SHORT ANSWER
34. ANS:
w2 −2w−80 =(w+8)(w−10)
PTS: 1DIF:ModerateREF: 3.5 Polynomialsof theFormx^2 +bx +c
LOC: 10.AN5TOP: Algebra and NumberKEY: ProceduralKnowledge
35. ANS:
90y2 +77y −52 =90y2 +117y −40y−52
=9y(10y+13)−4(10y+13)
=(10y+13)(9y−4)
PTS: 1DIF:ModerateREF: 3.6 Polynomialsof theFormax^2 +bx +c
LOC: 10.AN5TOP: Algebra and NumberKEY: ProceduralKnowledge
PROBLEM
36. ANS:
Theprimenumbersbetween 120 and 140 are127, 131, 137, and 139. These areprimenumbersbecause each numberhas exactly2 divisors, 1 and itself.
PTS: 1DIF:ModerateREF: 3.1 Factors and Multiplesof WholeNumbers
LOC: 10.AN1TOP: Algebra and Number
KEY: Communication |Problem-SolvingSkills
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37. ANS:
To calculatehow manytubsofpaint areneeded, firstdetermine the surface areaof the cube.
The edge length,e, ofa cube is equal to the cube rootof itsvolume.
e=3
e=14
2744
The surface area,SA, ofa cube is the sumof the areasof its6 congruent square faces.
SA=6(14⋅14)
SA=6(196)
SA=1176
Calculatehow manytubsofpaint areneeded:
1176=14.8860...
79
Germaineneeds15 tubsofpaint to paint the cube.
PTS: 1 / DIF:ModerateREF: 3.2 PerfectSquares, PerfectCubes, and TheirRootsLOC: 10.AN1 / TOP: Algebra and NumberKEY: Problem-SolvingSkills
38. / ANS:
8z2 −112z+360
Thegreatest common factor is8.
8z2 −112z+360 =8(z2 −14z+45)
Two numberswith a sumof−14and aproductof45are−5and−9.
So,z2 −14z+45 =(z−5)(z−9)
And,8z2 −112z+360=8(z−5)(z−9)
Checkthat the factors are correct. Multiplythe factors.
8(z−5)(z−9)=8(z2 −14z+45)
=8z2 −112z+360
The trinomial is the same as theoriginal trinomial, so the factors are correct.
PTS: 1DIF:DifficultREF: 3.5 Polynomialsof theFormx^2 +bx +c
LOC: 10.AN5TOP: Algebra and NumberKEY: ProceduralKnowledge
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39. ANS:
Sample answer:
5x2 +17x+6
To factor this trinomial, find factorsof the form(ax+b)(cx+d).
The coefficientofx2 is5, so the coefficientsof the1st terms in thebinomial are factorsof5, which are1 and
5.
So,thebinomialhas the form(x+b)(5x +d).
The constant termin the trinomial is6, so the2nd terms in thebinomial are factorsof6, which are6 and 1, or
2and 3.
So,thebinomials could be:
(x +6)(5x+1)or(x+2)(5x+3)or
(x +1)(5x+6)or(x+3)(5x+2)
Checkwhich of the4 binomialproducts abovehas itsx-termequal to 17x.
(x +6)(5x+1)=5x2 +31x +6(x+2)(5x+3)=5x2 +13x +6(x+1)(5x+6)=5x2 +11x +6(x+3)(5x+2)=5x2 +17x +6
This is the correct trinomial.
So,5x2 +17x+6=(x+3)(5x +2)
PTS: 1DIF:ModerateREF: 3.6 Polynomialsof theFormax^2 +bx +c
LOC: 10.AN5TOP: Algebra and Number
KEY: Communication |Problem-SolvingSkills
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40. ANS:
196x2 −16y2
Aswritten, each termof thebinomial isnotaperfect square. But the termshavea common factor4. Remove this common factor.
196x2 −16y2
=4(49x2 −4y2)
Write each termin thebinomial asaperfect square.
4(49x2 −4y2)=4
ÈÍ
ÎÍÍ
(7x)2 −(2y)2
˘˙
˚˙˙
Write these termsinbinomialfactors.
=4(7x−2y)(7x +2y)
PTS: 1DIF:ModerateREF: 3.8 FactoringSpecialPolynomials
LOC: 10.AN5TOP: Algebra and Number
KEY: Communication |Problem-SolvingSkills
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