Quadratic Expressions
What is the equation x² = 25?
x= -5,5
You invest $600 at 4% simple interest for 3 years. How much interest do you earn?
=$72
What is the gradient and y intercept of y= 2x +7
Gradient = 2
Y intercept = 7
Solve the following equations for x .
5x + 6 = 51
X = 9
2^4 X 2^3
2^7 = 128
Null factor law x (x − 7) = 0
x=0,7
You deposit $2,000 at 5% p.a., compounded annually, for 3 years. What is the future value?
=$2,315.25
The temperature increases by 2°C every hour after sunrise. At sunrise, it is 8°C.
Write a linear equation that gives the temperature T after h hours.
T=2h + 8
Solve the following linear equations.
2(x + 4) = 18
X = 5
9^9 Divided by 9^6
9^3=729
quadratic equations in standard form,
3 ( x²− 2) = 4x
= 3x²−4x−6=0
You want $10,000 in 5 years. The interest rate is 6% compounded annually. How much must you deposit now?
=$7,472.58
A taxi charges a $4 starting fee plus $2 for every kilometre travelled.
Write a linear equation that shows the total cost C for travelling k kilometres.
C=2k+4
Solve the following inequalities. − 4x + 2 ⩽ 5x − 16
X ≥ 2
12d^10 over 36d^5
d^5 over 3
What is the equation (x – 6)² = 0
x = 6
You deposit $500 at the end of each year for 6 years, earning 8% p.a.. What is the future value?
=$3,667.95
A taxi company charges according to the rule:
C=1.8d+12
where C is the cost and d is the distance travelled.
How far can you travel with $48?
20km
The solution to the simultaneous equations.
x + 2y = 16 and y = x − 4
(X = 8) (X = 4)
9b^4 over 2g^3 X 4g^4 over 3b^2
6b^2g
The equation for the area of this rectangle is x 2 + 2x − 48 = 0 , which has
solutions x = − 8 and x = 6 . Which solution do you ignore and why?
You ignore x = –8 because a rectangle’s side length cannot be negative.
Only x = 6 makes sense as a real, positive measurement for a length.
An investment grows at 4% p.a. for the first 3 years, then 9% p.a. for the next 2 years.
If the final value after 5 years is $12,000, what was the initial amount invested?
= $8,990
The cost of hiring a boat is linearly related to the number of hours used.
When used for 3 hours, it costs $42.
When used for 7 hours, it costs $90.
Use this equation to find the cost for 12 hours.
C=12h + 6 and C(12) = 150
Solve the following quadratic equations. 6 x 2 + 2 = 8, x < 0
X = -1
9m^5 n^2 X 4mn^3 over 12mn X m^4 n^2 X m^3 n^2 over 2m^3n
3m^2 n^3 over 2