Show:
Data Collection & Analysis
Right-Angled Triangles
Trigonometry
Exponents/Scientific Notation
Mixed
100

Find the mean and median, then state which better represents the data: 4, 6, 7, 8, 15, 32

Mean: 12

Median: 7.5

100

A right‑angled triangle has hypotenuse 13cm and one shorter side 5cm. Find the length of the other side.

12cm

100

In a right‑angled triangle, the adjacent side is 8cm and the hypotenuse is 13cm. Find the angle (nearest degree).

52 degrees

100

Write 0.0000478 in correct scientific notation.

4.78×10^−5

100

A Year 8 maths class has 10 boys and 20 girls. To decide which students are chosen to participate in a survey, the teacher assigns each student a number from 1-30. She ignores the number allocation and instead ensures there is a fair number of boys and girls in the sample based on their distribution in the class. What type of sampling is this? 

stratified 

200

A data set is right‑skewed.

  1. Would the mean be greater or less than the median?
  2. Explain briefly why.


If a data set is right‑skewed, the mean is greater than the median.

In a right‑skewed data set, the mean is greater than the median because high outliers pull the mean to the right, while the median remains relatively unaffected.



200

Find the distance between the points (−3,4) and (5,−2). Leave answer in simplest surd form.

10

200

From the top of a cliff, the angle of depression to a point on the ground is 18∘. The horizontal distance is 45m. Find the height of the cliff to the nearest metre.

15cm

200

Calculate and give your answer in scientific notation:

(4.8×10^6)÷(1.6×10^2)

3 x 10^4

200

A triangle is enlarged by a scale factor of 1.5

  1. By what factor does the perimeter change?
  2. By what factor does the area change?
  • Perimeter: multiplied by 1.5
  • Area: multiplied by 2.25
  • Lengths & perimeter → multiply by the scale factor
  • Areas → multiply by the square of the scale factor
300

The mean score of 9 tests is 68. A tenth test score is added, increasing the mean to 70. Find the score of the tenth test.

88

300

A rectangle has area 96 m2 and diagonal length 20m.
Find the length of each side.

16m x 12m

300

A ladder of length 7.5m makes an angle 63∘ with the ground.

  1. Find how high up the wall the ladder reaches
  2. State which trig ratio you used and why
  • The ladder reaches approximately 6.7 m up the wall.
  • Trigonometric ratio used: sine
  • Reason: sine relates the opposite side to the hypotenuse, which are the two sides involved.
300

Simplify fully:

(2a^3b^−1)2÷(4ab^2)

a^5 / b^4

300

(x^4y)^2 x (x^3y)^4

x^21 y^6

400

A data set has:

  • mean = 14
  • median = 11

Describe the shape of the distribution and justify using both statistics.

  • The mean is 14, which is greater than the median of 11.
  • In a right‑skewed distribution, larger values (high outliers) stretch the data to the right.
  • These higher values pull the mean upward, while the median remains closer to the centre of the data.
400

Two similar right‑angled triangles have corresponding hypotenuse lengths of 10cm and 16cm.

  1. Find the scale factor
  2. Find the area of the larger triangle if the smaller area is 25 cm2

1. 1.6

2. 64cm^2

400

A surveyor stands 12m from a building.
The angle of elevation to the top of the building is 35∘. After walking 4 m closer, the new angle is measured.

  1. Will the new angle be greater or smaller?
  2. Find the new angle, nearest degree.
  • The new angle will be greater.
  • The new angle is approximately 46∘
400

7.45 x 10^3 + 8.2 x 10^5

8.2745×10^5

400

Example 4. A person on top of a building sees a dog on the ground across the street at an angle of depression of 72°. The building is 45m tall. Calculate the direct distance between the dog and the person.

sin72∘≈0.9511


500

PART A: A data set has a mean of 12. One value of 30 is added to the data set. Will the mean increase, decrease, or stay the same? Explain briefly.

PART B: A data set is right‑skewed. Is the mean greater than or less than the median?


PART A: 

  • The mean will increase.
  • Because the added value (30) is greater than the original mean (12), it pulls the mean up.

PART B:

  • The mean is greater than the median. Because the long tail on the right includes larger values, which pull the mean to the right.
500

A triangle has side lengths 9, 12 and 15cm.

  1. Determine whether the triangle is right‑angled
  2. Justify your answer mathematically

225=225

500

A piece of origami paper must be a square. Calculate its dimensions if the length of the diagonal is 21cm.

14.85cm

500

(2x^−3y^2)^2 x (4x^5y^−1) divided by 8x^−2y^3

2x

500

A phone tower stands on flat ground. From point A, the angle of elevation to the top of the tower is 28°.
From point B, which is 15 m closer to the tower than point A, the angle of elevation is 43°.

Question

  1. Determine the height of the tower to the nearest metre.
  2. Explain why trigonometry is more appropriate than Pythagoras’ theorem for this problem.

19m