Algebra
Expand:
4(2b + 3)
8b + 12
The price of a shirt including GST is $110. What is the pre-GST price of the shirt?
$100
What is the volume of a rectangular fish tank with dimensions 90 cm, 45 cm and 60 cm?
Give your answer in Litres.
243 L
A 250 mL packet of milk contains 8g of protein and 12.5g of carbohydrate. Give the ratio of protein to carbohydrate in simplest form.
16 : 25
8x - 2 = 30
x = 4
Expand and simplify:
-4(1 + 5x) - 2
-20x - 6
A car salesyard is offering 15% off all new cars. If a car has a sale price of $32500, what is the discount (in $) being offered.
$5735.29
What is the exact (in terms of pi) volume of a cylinder with radius 5 m and height 4 m?
100pi m
Three numbers are in the ratio 2 : 5 : 3. If the largest number is 120, find the other two numbers.
48 and 72
Solve:
x/2 + 3 = -9
x = -24
Factorise:
12ab^2 - 8bc
4b(3ab - 2c)
Fred earns a salary of $450 per week for a 40 hour week. His weekly salary is increased by 10% and his number of hours worked is decreased by 10%.
Calculate his new hourly salary.
$13.75 / hour
A right-angled triangle has hypotenuse of length 41 cm and one of the sides is 9 cm. Find the area of the triangle.
180 cm ^2
It took David an hour to ride 20 km from his house to the nearest town. He then spent 40 minutes on the return journey. What was his average speed?
0.4 km/min
24 km/h
Solve:
-2(3x + 2) + 4 = 5
x = -1/6
Expand and simplify:
5(x + 2) - 3(7 + x)
2x - 11
A dairy farmer found that the milk supplied by his cows was 5% cream and 95% skimmed milk. How much skimmed milk should he add to a litre of milk to reduce the percentage of cream to 4%?
0.25 L or 250 mL
The areas of three faces of a rectangular prism are 10 cm^2, 14 cm^2 and 35 cm^2. Find the volume of the rectangular prism.
70 cm^3
Two equal-sized vats, A and B, each containing 1000 L of oil, are being drained at a constant rate. It takes 4 hours to drain vat A completely and 5 hours to drain vat B completely. Find the time at which the amount of oil in vat B is four times the amount of oil in vat A.
3.75 hours
Solve:
x/3 - (2x)/5 = 1
x = -15
Express as a single fraction:
(2x)/3 + x/2 - (3x)/4
(5x)/12
35% of students in a class have brown hair. Five brown-haired students join the class so that 48% now have brown hair. How many students were previously in the class?
20 students
What is the length of the longest diagonal in a cube with edges of length x m?
sqrt(3) x
Four points A, B, C and D are marked in order on a line such that AB : AC = 3 : 5 and BD : CD = 7 : 2. If CD is 10cm long, find the length of AB.
37.5 cm
Solve:
(x - 4)/5 + (2x - 5)/6 = 3
x = 139/16