8 Maths Enrichment Sem 2 Revision Challenge!

Statistics

100

For the Box-Plot shown, state the range and IQR

Range = 60 - 10 = 50

IQR = Q₃ - Q₁ = 50 - 25 = 25

200

The data below represents the number of days students in class were absent from school this year. Represent it as a stem-and-leaf plot.

4    12    5    9    0    21    10    48    12

300

Consider the following values:

3, 33, 15, 8, 33, 47, 22

State the mean, median and mode

Mean = 23

Median = 22

Mode = 33

400

Write down a set of 6 integers with the mean < median < mode, and range = 10

Many solutions exist. One example:

1, 6, 8, 10, 11, 11. 

(Mean = 7.8, Median = 9, Mode = 11, Range = 10)

500

The following data represents the sale price of 10 houses in a Melbourne street. Calculate the upper and lower fences to determine if there are any outliers.

$510,000   $546,000   $560,000   $578,000   $595,000

$637,000   $693,000   $840,000   $952,000   $1,295,000

Min = 510,000, Q₁ = 560,000, Med = 616,000 Q₃ = 840,000, Max = 1,295,000, therefore IQR = Q₃ - Q₁ = 840,000 - 560,000 = $280,000

Lower Fence = Q₁ - 1.5 x IQR = 560,000 - 1.5 x 280,000 = $140,000

Upper Fence = Q₃ + 1.5 x IQR = 840,000 + 1.5 x 280,000 = $1,260,000

So $1,295,000 is an outlier because it is above the upper fence.

Linear Relationships

100

Calculate the gradient of the line that connects (1, 8) and (3, 12)

m = (12-8)/(3-1) = 4/2 = 2

200

Find the equation of the line that is parallel to y = 2x +1 and passes through the point (1, 7).

Parallel means same gradient, so y = 2x + c.

Let x = 1, y = 7: 7 = 2x1 + c, so c = 5

So equation is y = 2x + 5

300

Find the coordinates of the x and y intercepts for the line with the rule 3x + 2y = 12

For x-int, let y = 0

3x + 0 = 12

x = 4

x-int is (4,0)

For y-int, let x = 0

0 + 2y = 12

y = 6

y-int is (0,6)

400

Find the equation of the following line:

y = (-2)/3 x+3

500

Sketch a graph of the following two lines on the same set of axes and find the coordinates of their intersection:

y = x - 1

y = -x + 5

Geometry

100

The triangle A(1,2), B(3,4), C(0,2) is reflected in the x-axis. State the coordinates of the image points A', B' and C'.

A' = (1,-2)

B' = (3,-4)

C' = (0,-2)

200

Given that the following triangles are similar, find the values of the pronumeral to 2 decimal places

Scale Factor = Image / Original = 2/11

therefore x = 12 xx 2/11 = 24/11 = 2.18cm

300

Heron's formula for the area, A, of a triangle with side lengths a, b and c is given by:

A=sqrt(s(s-a)(s-b)(s-c)) and s=(a+b+c)/2

Find A when a=3cm, b=4cm and c=5cm

s=(a+b+c)/2 = (3 + 4 + 5)/2 = 6

A=sqrt(s(s-a)(s-b)(s-c))

A = sqrt(6(6-3)(6-4)(6-5))

A = sqrt(6xx3xx2xx1) = sqrt(36) = 6cm^2

400

Define the following triangles:

Equilateral, Isosceles, Scalene

BONUS: Which triangles can be right-angled?

Equilateral = All sides and angles are equal. 

Isosceles = 2 sides are equal. 2 angles are equal.

Scalene = All sides and angles are different.

Right-Angled = A triangle where one of the internal angles is 90^O. Therefore equilateral cannot be R-A (all angles 90^O), isosceles can if the other two angles are 45^O and scalene can if the other two angles are not 45^O

500

A square starts with coordinates (-3, 1) , (2, 1) , (2, 6), (-3, 6). It then undergoes the following translations and transformations:

Translated 3 units up, reflected in the y-axis, translated 4 units left then rotated 180^o clockwise about the origin. What are the new coordinates of the corners of the square?

(-3, 1) -> (-3, 4) -> (3, 4) -> (-1, 4) -> (1, -4)

(2, 1) -> (2, 4) -> (-2, 4) -> (-6, 4) -> (6, -4)

(2, 6) -> (2, 9) -> (-2, 9) -> (-6, 9) -> (6, -9)

(-3, 6) -> (-3, 9) -> (3, 9) -> (-1, 9) -> (1, -9)

Pythagoras Theorem

100

Determine if the following is a right-angled triangle:

If right angled, then: c² = a² + b²

21^2 = 12^2 + 15^2

441 = 144 + 225

441 != 369

LHS != RHS

NOT a right-angled triangle

200

The following word related to Pythagoras' Theorem is misspelled. State the correct spelling:

High-pott-and-yous

Hypotenuse

300

The following represent the 3 side lengths of 3 triangles. For each triangle, determine whether it is a right-angle triangle or not.

A: 8cm, 15cm, 17cm

B: 9m, 16m, 25m

C: 12cm, 13cm, 50mm

A: YES - Satisfies Pythagoras Theorem

B: NO - Does not satisfy Pythagoras Theorem

C: YES - Satisfies Pythagoras Theorem (after making units the same)

400

Find the value of x, correct to 2 decimal places (if required):

c^2 = a^2 + b^2

therefore x^2 = 14^2 + 3^2

therefore x^2 = 205

therefore x = sqrt(205)

x ~ 14.32cm

500

Find the value of the pronumeral in the following composite shape, correct to 2 decimal places. Then, find its area (also correct to 2dp).

Area = A_rectangle + A_triangle     OR use Trapezium rule (A = (a+b)/2 x h)

A = (26+39)/2 xx sqrt(272) = 32.5 xx sqrt(272) = 536.00m^2 (allow 535.93m^2)

Lucky Dip

100

What date is your Semester test for Maths?

Thursday 24th November 2022

200

Name this song & artist:

Never Gonna Give You Up - Rick Astley

300

Combine the following numbers together using addition, subtraction, multiplication and division to reach the target number. Each number can be used only once. You do not need to use all numbers.

100, 9, 6, 2, 8, 5     TARGET: 538

Many solutions exist. Some possible combinations:

5x100 + 2x(9+6) + 8 = 500 + 30 + 8 = 538

5x(100+6) + 8 = 530 + 8 = 538

5x(100+8) - 2 = 540 - 2 = 538

etc.

400

Recite pi to as many digits as you can. Most digits accurately remembered = 400 points, 2nd = 300 points, 3rd = 200 points, 4th = 100 points

pi =

3.1415 92653 58979 32384 62643 38327 95028 84197 16939 93751 05820 97494 45923 07816 40628 62089 98628 03482 53421 17067 9...

500

Name five year 8 maths teachers (100 points for each).

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