Money Matters
A shirt costs $80 and is reduced by 25%.
What is the sale price?
Answer: $60
A rectangle is 8 m long and 5 m wide.
Find its area.
Answer: 40m2
A taxi fare is given by Fare = 5.50 + 3.20d, where d is distance in km. Find the cost of a 18 km trip.
Answer: $63.10
What is the gradient of:
y=3x+5
Answer: 3
A ladder leans against a wall, making an angle of 65° with the ground. If the ladder is 4.7 m long, how high up the wall does it reach?
Answer: 4.26m
A grocery bill totals $86.20. If GST is 10%, how much GST is included in the total price?
Answer: $7.84
note:
Add GST: × 1.10
Remove GST: ÷ 1.10
A right-angled triangle has legs of 6 cm and 8 cm.
Find the hypotenuse.
Answer: 10cm
The cost of hiring a hall is $150 plus $8 per guest. Write a linear equation to represent the total cost C for g guests.
Answer: C=8g + 150
What type of matrix has the same number of rows and columns?
Answer: Square matrix
A triangle has sides 8 cm and 11 cm with an included angle of 40o. Which rule should you use to find the third side?
Answer: Cosine Rule
An investment of $5000 earns 4.5% p.a. simple interest for 3 years.
How much interest is earned?
Answer: $675
A map has a scale of 1:50 000.
Two towns are 6 cm apart on the map.
What is the actual distance?
Answer: 3km
A mobile plan has a base fee of $25 and charges $0.25 per minute for calls. If the total bill was $45, how many call minutes were made?
Answer: 80 minutes
A 2×3 matrix is multiplied by a 3×1 matrix. What is the order of the resulting matrix?
Answer: 2 x 1 matrix
A triangle has sides 7 cm, 8 cm and 10 cm. Which method could you use to find its area?
Answer: Heron's Rule
Which of the following laptop brands offers the best value for money based on cost per GB of storage
Brand A: $1,050 for 512 GB storage
Brand B: $1,200 for 1 TB storage
Brand C: $950 for 256 GB storage
Brand D: $1,400 for 1.5 TB storage
Ans: Brand D (93c per GB)
A cylinder has radius 4 cm and height 10 cm. Determine its volume.
Answer: 502.7cm3
y=x+3
6x+y=17
Answers: x=2 and y=5
A matrix contains the number of adult, student and child tickets sold on two different days. A second matrix contains the ticket prices. What operation would you use to calculate the revenue for each day?
Answer: Matrix multiplication
A dataset has:
3, 5, 7, 8, 10, 12, 15
Find:
a) the median
b) the IQR
Answer:
Median = 8
Q1=5, Q3 = 12
IQR = 7
A loan of $20 000 is charged at 6% p.a. simple interest for 4 years.
Determine the total amount that must be repaid.
Answer: $24800
A triangular prism has a triangular cross-section with base 8 cm and perpendicular height 5 cm. The prism is 12 cm long. Determine its volume.
Answer: 240cm3
The weight of a box of nails and a box of screws is 7kg. Four boxes of nails and box of screws weight 19kg. Determine the weight of each box.
Answers:
Box of nails = 4kg
Box of screws = 3kg
A square matrix A is multiplied by itself. What is this written as?
Answer: A2
A triangle has two sides of 9 cm and 12 cm with an included angle of 50∘.
a) Determine the third side.
b) Determine the area of the triangle.
Using Cosine rule:
a) c = 9.33cm
b) A = 41.36cm2