MPM 1DI Unit 1 Practice TEST – Rational Numbers Name:

Short Answer ~~ 1 mark each 1. Which of the following is NOT a rational number?

A) −99 B) !! C) 2.14156 D) 𝜋 E) − 49

2. Restate −0.22 as a fraction.

3. Is the sign of the answer to − − !!

! 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 !!"×  !

! B) 3 !

!"−  !

! C) 3 !

!"  ×   !

!

!" D) 3 !

!"÷  !

!

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) −9.3 B) −9. 3 C) −9 D) −9.039

8. The morning temperature is -5.2 ºC and the afternoon temperature was 15.5 ºC. How much did the temperature increase during the day?

9. If 𝑥! =  961 then 𝑥 =  ?

10. Evaluate −3! − −1 !

11. The number 12. 451 can be represented as a fraction of one integer divided by another integer. True or False?

12. Evaluate − !!!

!

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 !!− 1 !

! B) 3 !

!1 !!

C) 3 !!− 1 !

!

! D) 3 !

!− 1 !

!

! E) 3 !

!

!− 1 !

!

!

Full Solutions Show logical steps to solve the following expressions. Compound Interest Formula:

𝐴 = 𝑃 1 + 𝑖 ! 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 !

!  𝑓𝑡 by

2 !!  𝑓𝑡. You want to make a patio that is 300 ft2. Do

you have enough stones?

−35

!

− −2 !

−127− −1

13

÷ −17

−47−

3−5

× 3 Evaluate 𝑎! ÷ !

! if 𝑎 = − !

!  𝑎𝑛𝑑  𝑏 = !

!

MPM 1DI Unit 1 TEST – Rational Numbers Name:

! calculators allowed " no cell phones ! all answers should be in “lowest terms”.

Short Answer ~~ 1 mark each

1. Which of the following is NOT a rational number? B) −99 B) !

! C) 2.14156 D) 𝜋 E) − 49

terminating or repeating decimal -- is rational ! 𝜋  𝑑𝑜𝑒𝑠  𝑛𝑜𝑡  𝑟𝑒𝑝𝑒𝑎𝑡  𝑜𝑟  𝑡𝑒𝑟𝑚𝑖𝑛𝑎𝑡𝑒   𝑎𝑙𝑠𝑜   2 D

2. Restate −0.22 as a fraction. not in lowest terms … − !!!""

!!!!"

3. Is the sign of the answer to − − !!

! positive or negative? Exponent odd so inside bracket

to 9th is negative THEN apply outside negative ! answer positive = − − !"#!"#$%

= !"#!"#$%

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? ! ÷ing by a number tells you how many groups of that size you will have … answer is 9 ½ ∴ 9 people get 3/8ths of a pizza and 1 could have ½ of the amount divided by or ½ of 3/8 of a pizza

B) 3 !!"×  !

! B) 3 !

!"−  !

! C) 3 !

!"  ×   !

!

!" D) 3 !

!"÷  !

!

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 − 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) −9.3 B) −9. 3 C) −9 D) −9.039 B 8. The morning temperature is -5.2 ºC and the afternoon temperature was 15.5 ºC.

How much did the temperature increase during the day? 20.7 9. If 𝑥! =  961 then 𝑥 =  ? 961 = 31 31 10. Evaluate −3! − −1 !  =  −9 − −1 =  −9 + 1 =  −8 −8 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 − !!

!

!    =  − !! !

!!=  − !

!"=  − !

!" − !

!" 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 !!− 1 !

! B) 3 !

!1 !!

C) 3 !!− 1 !

!

! D) 3 !

!− 1 !

!

! E) 3 !

!

!− 1 !

!

!

E

Full Solutions

Compound Interest Formula:

𝐴 = 𝑃 1 + 𝑖 ! 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?

𝑃 = 5,000              𝑖 = !.!"!"              𝑛 = 7  ×12 = 84

𝐴 = 5000 1 + !.!"!"

!"

= 7601.848

∴ Karen will have $7,601.85 after investing for 7 years.

You have 105 patio stones that measure 1 !

!  𝑓𝑡 by

2 !!  𝑓𝑡. You want to make a patio that is 300 ft2. Do

you have enough stones?

𝟏  𝑺𝒕𝒐𝒏𝒆 = 𝟏𝟏𝟒×𝟐

𝟏𝟐

=𝟓𝟒×𝟓𝟐=𝟐𝟓𝟖  𝒇𝒕𝟐

𝑹𝒆𝒒𝒖𝒊𝒓𝒆𝒅  𝑭𝒐𝒓  𝑷𝒂𝒕𝒊𝒐 = 𝟑𝟎𝟎   ÷𝟐𝟓𝟖

=𝟑𝟎𝟎𝟏  ×

𝟖𝟐𝟓

=  𝟗𝟔  𝒔𝒕𝒐𝒏𝒆𝒔

Therefore, the 105 stones will be more than enough.

OR … could calculate the area that can be covered by 105 stones and compare that to the 300 ft2 (you would get !"

!×105 = 328 !

!  𝑓𝑡!

therefore there is more than enough).

𝟏𝟗𝟏𝟐𝟓

−35

!

− −2 !

−𝟏𝟑

−127− −1

13

÷ −17

𝟑𝟑𝟓

−47−

3−5

× 3

−𝟏𝟓𝟑𝟐

Evaluate 𝑎! ÷ !

! if 𝑎 = − !

!  𝑎𝑛𝑑  𝑏 = !

!

−34

!÷

− 34      5      8

 = −34

!÷ −

34÷58

NOTE… you must do the ‘fraction’ division 1st that’s why it is in brackets