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MPM 1DI Unit 1 Practice TEST β Rational Numbers Name:
Short Answer ~~ 1 mark each 1. Which of the following is NOT a rational number?
A) β99 B) !! C) 2.14156 D) π E) β 49
2. Restate β0.22 as a fraction.
3. Is the sign of the answer to β β !!
! positive or negative?
4. Alexia has 3 !!"
extra large pizzas. She would like to invite friends over and be able to
give them each !! of a pizza. Which calculation should she do to find out how may
friends she can invite?
A) 3 !!"Γ !
! B) 3 !
!"β !
! C) 3 !
!" Γ !
!
!" D) 3 !
!"Γ· !
!
5. In the above question, Alexia had ordered 5 pizzas but her father and brothers had eaten some before she told them it was for a party. How much pizza had they eaten?
6. Evaluate the expression !!
! !
7. Which number is lowest? A) β9.3 B) β9. 3 C) β9 D) β9.039
8. The morning temperature is -5.2 ΒΊC and the afternoon temperature was 15.5 ΒΊC. How much did the temperature increase during the day?
9. If π₯! = 961 then π₯ = ?
10. Evaluate β3! β β1 !
11. The number 12. 451 can be represented as a fraction of one integer divided by another integer. True or False?
12. Evaluate β !!!
!
13. The diagram consists of 2 squares. The outer shaded square has dimensions of 3 !
! inches. The inner white
square dimensions of 1 !! inches. Which formula would
calculate the area of the shaded part of the diagram?
A) 3 !!β 1 !
! B) 3 !
!1 !!
C) 3 !!β 1 !
!
! D) 3 !
!β 1 !
!
! E) 3 !
!
!β 1 !
!
!
Full Solutions Show logical steps to solve the following expressions. Compound Interest Formula:
π΄ = π 1 + π ! Karen received $5,000 from her grandparents to save for her future education. She put the money in a savings bond that pays 6% interest compounded monthly. How much will Karen have if she leaves the money in the investment for 7 years?
You have 105 patio stones that measure 1 !
! ππ‘ by
2 !! ππ‘. You want to make a patio that is 300 ft2. Do
you have enough stones?
β35
!
β β2 !
β127β β1
13
Γ· β17
β47β
3β5
Γ 3 Evaluate π! Γ· !
! if π = β !
! πππ π = !
!
MPM 1DI Unit 1 TEST β Rational Numbers Name:
! calculators allowed " no cell phones ! all answers should be in βlowest termsβ.
Short Answer ~~ 1 mark each
1. Which of the following is NOT a rational number? B) β99 B) !
! C) 2.14156 D) π E) β 49
terminating or repeating decimal -- is rational ! π ππππ πππ‘ ππππππ‘ ππ π‘πππππππ‘π πππ π 2 D
2. Restate β0.22 as a fraction. not in lowest terms β¦ β !!!""
!!!!"
3. Is the sign of the answer to β β !!
! positive or negative? Exponent odd so inside bracket
to 9th is negative THEN apply outside negative ! answer positive = β β !"#!"#$%
= !"#!"#$%
Positive
4. Alexia has 3 !!"
extra large pizzas. She would like to invite friends over and be able to give
them each !! of a pizza. Which calculation should she do to find out how may friends she can
invite? ! Γ·ing by a number tells you how many groups of that size you will have β¦ answer is 9 Β½ β΄ 9 people get 3/8ths of a pizza and 1 could have Β½ of the amount divided by or Β½ of 3/8 of a pizza
B) 3 !!"Γ !
! B) 3 !
!"β !
! C) 3 !
!" Γ !
!
!" D) 3 !
!"Γ· !
!
D
5. In the above question, Alexia had ordered 5 pizzas but her father and brothers had eaten some before she told them it was for a party. How much pizza had they eaten? = 5 β 3 !
!"= 1 !
!" OR adding !
!" would make it 4 full pizzas & 1 more to make it 5
1 !!"
6. Evaluate the expression !!
! ! !
!
!= !!
!!= !"
!"#= 0.08779
!"!"#
7. Which number is lowest? A) β9.3 B) β9. 3 C) β9 D) β9.039 B 8. The morning temperature is -5.2 ΒΊC and the afternoon temperature was 15.5 ΒΊC.
How much did the temperature increase during the day? 20.7 9. If π₯! = 961 then π₯ = ? 961 = 31 31 10. Evaluate β3! β β1 ! = β9 β β1 = β9 + 1 = β8 β8 11. The number 12. 451 can be represented as a fraction of one integer divided by
another integer. True or False? Repeating or Terminating ! Rational True 12. Evaluate β !!
!
! = β !! !
!!= β !
!"= β !
!" β !
!" 13. The diagram consists of 2 squares. The outer shaded
square has dimensions of 3 !! inches. The inner white
square dimensions of 1 !! inches. Which formula would
calculate the area of the shaded part of the diagram?
A) 3 !!β 1 !
! B) 3 !
!1 !!
C) 3 !!β 1 !
!
! D) 3 !
!β 1 !
!
! E) 3 !
!
!β 1 !
!
!
E
Full Solutions
Compound Interest Formula:
π΄ = π 1 + π ! Karen received $5,000 from her grandparents to save for her future education. She put the money in a savings bond that pays 6% interest compounded monthly. How much will Karen have if she leaves the money in the investment for 7 years?
π = 5,000 π = !.!"!" π = 7 Γ12 = 84
π΄ = 5000 1 + !.!"!"
!"
= 7601.848
β΄ Karen will have $7,601.85 after investing for 7 years.
You have 105 patio stones that measure 1 !
! ππ‘ by
2 !! ππ‘. You want to make a patio that is 300 ft2. Do
you have enough stones?
π πΊππππ = πππΓπ
ππ
=ππΓππ=πππ πππ
πΉπππππππ πππ π·ππππ = πππ Γ·πππ
=ππππ Γ
πππ
= ππ ππππππ
Therefore, the 105 stones will be more than enough.
OR β¦ could calculate the area that can be covered by 105 stones and compare that to the 300 ft2 (you would get !"
!Γ105 = 328 !
! ππ‘!
therefore there is more than enough).
πππππ
β35
!
β β2 !
βππ
β127β β1
13
Γ· β17
πππ
β47β
3β5
Γ 3
βππππ
Evaluate π! Γ· !
! if π = β !
! πππ π = !
!
β34
!Γ·
β 34 5 8
= β34
!Γ· β
34Γ·58
NOTEβ¦ you must do the βfractionβ division 1st thatβs why it is in brackets
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