Year 8 Maths Sem 1 Review

Rational Numbers

1

Complete the following:

Positive x Positive = ???

Positive x Negative = ???

Negative x Positive = ???

Negative x Negative = ???

Positive x Positive = Positive

Positive x Negative = Negative

Negative x Positive = Negative

Negative x Negative = Positive

2

Find the value of the following using order of operations:

18 -2 xx (4+6) divide 5

18 -2 xx (4+6) divide 5 

= 18 - 2 xx 10 divide 5

= 18 - 20 divide 5

= 18 - 4

= 14

3

Calculate:  9.856 divide 0.05 

= 985.6 divide 5

= 197.12

4

One night Ricky and her brother Micky decide to have some fun at their father's lolly shop. In the shop, they find 7 tins each containing 135 jellybeans, 9 packets of 121 choc buds, 12 jars of 70 smarties and 32 packets of 5 liquorice sticks.

Find the total number of lollies that Ricky and Micky find that night.

Total = Jellybeans + Choc Buds + Smarties + Liquorice

= (7 x 135) + (9 x 121) + (12 x 70) + (32 x 5)

= 945 + 1089 + 840 + 160 = 3034

Ricky and Micky find 3034 lollies that night.

5

The side lengths of a cube are all increased by 20%. As a percentage, by how much does the volume change?

Let x = length of cube

V = x^3

New: V = (1.2x)^3

= 1.2 xx 1.2 xx 1.2 xx x^2

=1.728x^3, so 72.8% increase

Proportional Reasoning

1

Solve the following:

2/3 xx 1/10

=2/30

=1/15

2

Solve the following:

3 1/4 - 2 2/5

3 1/4 - 2 2/5 = 13/4 - 12/5

= 65/20 - 48/20

= 17/20

3

Simplify the ratio:

1 1/4 :2

 5/4 : 2     x 4

5:8

4

Gabe has 1-quarter of a cake. Regina has 1-fifth of a cake. Amber has 1-sixth of a cake. Evan has half of what Amber has. How much cake is leftover for everyone else?

Gabe + Regina + Amber + Evan = 

1/4 + 1/5 + 1/6 + (1/2 xx 1/5)

15/60 + 12/60 + 10/60 + 6/60

=42/60

So 18/60 = 3/10 = 30% of the cake remains for everyone else.

5

Max travels at 50km/h for 10km. For the next 10km, Max wants to drive fast enough to make his average speed 100km/h over the 20km trip. Advise Max about how to reach this average speed.

A 20km trip at 100km/h takes 1/5 hour (12 mins), which Max has used to drive the first 10km (t = d/s = 10/50 = 1/5 hour).

The second 10km cannot be travelled in zero time, hence it is impossible for Max to achieve a 100km/h average speed.

Statistics

1

Find the mode of the data set below:

56, 52, 61, 63, 43, 44, 44, 72, 70, 38, 55

44

2

Using the information in the column graph below, how many students don't walk to school?

50 + 100 + 150 = 300 students don't walk to school.

3

What is the median age for the group shown below?

12 years old

4

Find the 5 figure summary and IQR of: 1, 5, 10, 12, 14, 20

Min = 1, Q1 = 5, Med = 11, Q3 = 14, Max = 20

IQR = Q3 - Q1 = 14 - 5 = 9

5

Find a set of three numbers that have a range of 9, a mean of 10 and a median of 11.

One number (2nd) must be 11.

Range combinations that = 9: 2 & 11, 3 & 12, 4 & 13, 5 & 14, 6 & 15, 7 & 16, 8 & 17, 9 & 18, 10 & 19 or 11 & 20

For mean = 10, sum must be 30. Only true for 5, 11 and 14

Algebra

1

Describe the difference between an expression and an equation

An expression does not include an = sign (e.g. 2x + 1). An equation does include an = sign (e.g. y = 2x +1).

2

Expand and simplify 4(x - 5)

4x - 20

3

Factorise 12pm + 8p

4p(3m + 2)

4

Expand and simplify 3(y - 4j) - 2(2j - 7y)

3y - 12j - 4j + 14y

= 17y - 16j

5

Simplify the following expression:

(3x)/4 - (x+2)/3 + (x+2)/12

(3xx3x)/12 - (4(x+2))/12 + (x+2)/12

(9x)/12 - (4x+8))/12 + (x+2)/12

(9x - 4x - 8 + x + 2)/12

(6x-6)/12 = (6(x-1))/12 = (x-1)/2

Equations

1

D

2

Solve for x,

x = 4

3

Solve for x

2x - 2 = 24

2x = 26

x = 13

4

If t = 5 and u = 9, evaluate

u(t + 6) + t(12 + 2)

9(5+6) + 5(12+2)

=9x11 + 5x14

=99 + 70

=169

5

Solve:

5x^2+5=50

 5x^2 = 45

therefore x^2 = 9

therefore x = +- 3

Lucky Dip

1

The following maths words are misspelled. Give the correct spelling.

Noomyourateher & Deenormeenateher

Numerator & Denominator

2

How many Houses are at Carey (MS/SS)? NAME THEM ALL

10: Cartwright, Dunshea, Fullard, Gadsden, Hickman, Moore, Newnham Steele, Sutton, Tranter

3

What is the answer to the following problem?

10xx9xx8xx7xx6xx5xx4xx3xx2xx1xx0 = ?

0

(anything multiplied by 0 is 0!)

4

Find the value of a cone, a scoop of vanilla ice cream and a scoop of strawberry ice cream:

3x3x3=27, so Cone = 3.

2 cones + 2 vanilla = 10. Since cones = 3, 2x3 + 2 vanilla = 10, so Vanilla = 2

2 cones + 2 vanilla + strawberry = 11. Since 2 cones + 2 vanilla = 10, Strawberry = 1.

OR

3 cones + 2 vanilla + 2 strawberry = 15. Since cones = 3 and vanilla =2, 3x3 + 2x2 + 2 strawberry = 15, so Strawberry = 1.

5

How many minutes are there in a year?

60 mins x 24 hours x 365 days

= 525,600 minutes