Percentages and Ratios
A number is increased by 20% and the result is 72. What was the original number?
60
Find the y-intercept of y=4.5x+1
y=1
Solve
5x-12=3x+8
x=10
A right angled triangle has a hypotenuse of 10cm, and one 6cm side. Find the length of the remaining side.
8cm
A shop advertises 25% off a jacket of $135, then applies a further 10% off the discounted price. What is the final sale price?
$91.13
Find the x-intercept of
y=-3x-5
x=-5/3
Factorise completely:
15x^2-6x
3x(5x-2)
A 20m ladder reaches 16m up a wall. How far is the base of the ladder from the wall?
12m
A quantity is decreased by 15%, then increased by 20%. What is the overall percentage change?
2% increase
What is the gradient of the line passing through (-2,5) and (4,1)?
m=-1
Solve:
6-2(3x-4)=4x+10
x=
A square has a perimeter of 40cm. What is the length of its diagonal (to 2 decimal places).
14.14cm
A drink mixture contains water and cordial in the ratio 4:1. After adding 15mL of cordial, the new ratio becomes 8:3. How much water was originally in the mixture?
40mL
A line passes through (0,-3) and has a gradient of 4. Find the y-value when x=3.
y=9
The product of 5 and a number is the same as the sum of four and twice the original number. What is the number?
4/3
A rectangle has sides 9cm and 40cm. A diagonal is drawn. How much longer is the diagonal than the shorter side?
32cm
Tim and Tom aim to finish their 6km morning run together. Tim runs at an average speed of 10km/h and Tom runs at an average speed of 2m/s. If Tim leaves at 9am, what time should Tom leave if they are to finish their run at the same time?
8:46am
Simplify:
3/x-x/2+7/(6x)
(-3x^2+25)/(6x)