Financial maths
Emma earns $18 per hour.
She works 6 hours on Saturday.
How much does she earn?
18×6 = $108
Simplify:
3x+7x−2x
8x
What is the Y-value for x-intercepts for any graphs?
Y=0
A right-angled triangle has two right angle side lengths:
Find the value of the hypotenuse.
c2=62 + 82
c=10 cm (reject negative solution)
Expand and simplify:
(x+4)(x+3)
x2+3x+4x+12
A student deposits $2000 into a bank account earning 4% simple interest per year.
How much interest is earned after 3 years?
I=Prt
I=2000×0.04×3
I=$240
Simplify:
8ab2−9ab−ab2+3ba
7ab2 - 6ab
A line has gradient 4 and passes through the point (0,−3).
Find its equation.
y=mx+c
m=4
c=-3
y=4x-3
A right-angled triangle has:
Find the other shorter side.
x2+52=132
we can solve and get x=12
Fully Factorise: x2+11x+24
(x+3)(x+8)
A student invests $1000 at 5% compound interest per year.
What is the value of the investment after 2 years?
Compound interest formula:
A=P(1+r)n
A=1000(1.05)2
A= 1102.50
Solve:
2(x+3)−4x=8
2x+6−4x=8
−2x+6=8
−2x=2
x=−1
Rearrange 4x + 2y = 20 into the form y=mx + c
y=-2x+10
A right-angled triangle has:
Find sinθ
sinθ = 12/13
Expand: (x+4)(x−4) into x2 - a2 where a is a natural number.
x2-16
Two banks offer the following savings accounts:
Bank A offer 6% simple interest.
Bank B offer 5% compound interest.
A student invests $5000 for 4 years.
Which bank gives the higher final balance?
Bank A:
I=5000(0.06)(4)
I=1200
Final balance:$6200
Bank B:
A=5000(1.05)4
A≈6077.53
Bank A have higher balance after 4 years.
A number is multiplied by 7 and then divided by 3.
The final result is 8.
What is the number?
Let the number be x.
7x/3=8
7x=24
x=24/7
Find the coordinates for the y-intercept of 6x + 3y = 30
Let x=0
3y=30
y=10
Therefore, the coordinates for y-intercepts is (0,10)
A ladder 10 m long leans against a wall.
The base of the ladder is 6 m from the wall.
How high up the wall does the ladder reach?
h2+62=102
h=8 m
A quadratic expression can be factorised as
(x+a)(x+b)
where a and b are positive integers. The expanded form is x2+15x+56
Determine the values of a and b.
a+b=15
a*b=56
Therefore a=7 and b=8.
A mobile phone plan costs:
A student's bill for one month is $47.
How many text messages were sent?
20+0.10x=47
0.10x=27
x=270
The perimeter of a rectangle is 30 cm.
Its length is x+2 and its width is x−1.
Find the value of x.
Perimeter formula: 2L+2W=30
Substitute: 2(x+2)+2(x−1)=30
Expand: 2x+4+2x−2=30
Solve: x=7
Find the equation of a line that passes through (0, 8) and (2, 10)
Gradient intercepts form: y=mx+c
c=8 since the y intercepts is (0,8)
m=rise/run=(10−8)/(2-0)=2/2=1
y=x+8
A right-angled isosceles triangle has a hypotenuse of length 10 cm.
Find the exact length of each shorter side.
Let each shorter side be x.
x2+x2=102
x=5*sqrt(2)
The expression (x+3)(x+k) expands to x2+10x+21.
Find the value of k.
Expand:
(x+3)(x+k)=x2+(k+3)x+3k
Compare coefficients:
k+3=10 which gives us k=7
3k=21 which gives us k=7 as well.
Therefore k=7.