General Knowledge
What is the difference between an equation and an expression?
An expression is a mathematical phrase without an equals signs.
An equation is a statement that claims two expressions are equal to each other.
Solve x - 8 = 10
x = 18
Solve -13x = -182
x = 14
Solve x2 = 49
x = ± 7
Solve the equation y = 2x + c if
x = 10 and c = -4
y = 16
Write as an equation:
The sum of a number and 12 is equal to 7
x + 12 = 7
Solve x/8 = -48
(/ is the vinculum line of fraction)
x = -6
Solve 13 - 2x = 19
x = -3
Solve x2 + 9 = 109
x = ±10
Solve the equation 4a + 3b = 5c if a = 3 and c = 4
(leave answer as a fraction)
b = 8/3
Write as an equation
The product of a number and 3 is equal to -21
3x = -21
Solve 6 + 3x = 15
x = 3
Solve (x+4)/5 = 12
/ is the vinculum line of the fraction
x = 56
Solve 4x2 = 256
x = ± 8
Justin was in charge of hiring a bus to travel to the football.
He was charged an upfront cost of $40 and charged $4 for each kilometre travelled.
How many kilometres would Justin be able to travel if he was charged $158?
x = 29.5 km.
Write as an equation:
The quotient of x and 4 is equal to 6
x/4 = 6 (/ = the vinculum line of fraction)
Solve -4x + 7 = 21
x = -3.5
Solve (3b-8)/2 = 5
/ is the vinculum line of the fraction
b = 6
Solve 6x - 4 = 3x + 11
x = 5
A civil engineer is surveying a 6-sided (hexagonal) plot of land for a new community park in Western Sydney.
A fundamental rule of geometry states that the sum of the interior angles of any $n$-sided polygon is given by the formula:
(Sum of interior angles) = (n - 2) x 180o
Two of the park's corner angles are dictated by existing structures: one is a right angle (90 degrees), and another is an obtuse corner measured at 150 degrees.
The remaining 4 interior angles of the park are all equal in size, each measuring x.
By first developing an equation for the above scenario, determine the size of the four remaining angles in the park.
x = 120
If a number is multiplied by 6 and added to 8 the result will be 44
6x + 8 = 44
Solve (x/3) + 9 = 21
/ is the vinculum line of the fraction
x = 36
Solve (2x/3) - 1 = 7
/ is the vinculum line of the fraction
x = 12
Solve -3x - 14 = -4x + 14
x = -4
A landscape architect is designing two different garden beds for a new park:
Garden A is in the shape of an equilateral triangle. The length of one side is represented by the expression (2x + 4) metres.
Garden B is in the shape of a square. The length of one side is represented by the expression (x + 6) metres.
The perimeter of Garden A is the same as that of Garden B.
By first developing an equation, determine the perimeter of either Garden A or Garden B.
The perimeter of either Garden A or B will be 48 metres.