Year 10 Yearlyz Flashcards
How to simplify the surd √108
How to simplify the surd of 4√45
How to add the surds 5√11 + 7√11
12√11
How to add the surds √80 + √20
Expand and simplify each expression
Expand and simplify the binomial product
Expand and simplify the Binomial product using: (a + b)(a - b) = a2 - b2
Expand and simplify the Binomial product using: (a + b)(a - b) = a2 - b2
The total amount and the total amount of compound interest of $26,750 is invested at 4% p.a. for 3 years with interest compounded annually using P(1 + R)n
The total amount of the investment and the compound interest earned using A = P(1 + R)n
Calculate the compound Interest monthly when $24500 is invested at 6.3% p.a. for 5 years
What is Depreciation
Depreciation is the decrease in value of an item over time. When items we buy lose value because of age or frequency of use, they are said to depreciate.
Using the Depreciation formula of A=P(1 - R)n
Simplify The Surd
What are the symbols of a distance, midpoint and gradient formula question such as P(-5,8) Q(3,6)
Find the angle of inclination of a line with a gradient of 1/3 using the formula. Answer = -tan (Gradient)
Find the angle of inclination of a line with a gradient of -4 using the formula. Answer = -tan (Gradient)
What is the rule with Parallel Lines about how to find their gradient
What is the rule with Perpendicular Lines about how to find their gradient
State whether each pair of gradients represent parallel lines or perpendicular lines
State whether each pair of gradients represent parallel lines or perpendicular lines
Find the gradient of a line that is perpendicular to a line with gradient: 2
Find the gradient of a line that is perpendicular to a line with gradient: -3
Find the gradient of a line that is perpendicular to a line with gradient: 3/4
Find the gradient of a line that is perpendicular to a line with gradient: -0.6
How to find the x and y intercepts by using the method of “For the x intercept y = 0 and For the y intercept x = 0”
What is the main rule of the equation of horizontal and vertical lines
Find the gradient and y-intercept of the line with the equation y = -4x + 9 using the formula y = mx + b
Find the gradient and y-intercept of the line with the equation y = pic using the formula y = mx + b
Find the gradient and y-intercept of the line with the equation y = pic using the formula y = mx + b
Write the linear equation in general form
Write the linear equation in general form
Write the linear equation in general form
using the formula y - y 1 = m(x - x1)
Find the equation of the line
Find the equation of line k
Find the coordinates of point A
What formula is need to expand a binomial product?
(a + b)(a - b) = a2 - b2
What formula is needed to expand a binomial product
What are the index laws of am x an
am + n
What are the index laws of am ÷ an
am
an
What are the index laws of: (am)n
a m x n
What are the index laws of (ab)n
anbn
What are the index laws of (a/b)n
an/bn
What are the index laws of a0
whenever something is to the power of 0 it = 1
What are the index laws of a -n
1/an
What are the index laws of a-1
1/a
What are the index laws of (a/b)-1
b/a
What are the index laws of (a/b)-n
bn/an
Simplify the expression
Simplify the expression
Simplify the expression
What does the fractional indice law equal: a1/2
What does the fractional indice law equal: a1/3
What does the fractional indice law equal: am/n
Evaluate the expression:
Simplify the expression:
Simplify the expression:
Simplify the expression:
Simplify the expression:
Simplify the expression:
Simplify the expression:
Simplify the expression:
Simplify the expression:
Simplify the expression:
Expand and simplify by collecting like terms
How do you factorize an expression
Find the HCF by pressing GCD on your calculator and plug the numbers in and then…
Factorise 25b2 - 20ab
factorise x(4 + y) + 2(4 + y)
Factorise -b2 + 8b
How to expand a perfect square
expand (n - 5)2
expand (k + 4)2
Expand (3y - 8)2
How to expand the Difference of two squares
A difference of two squares is different from a normal binomial product due to it is the same equation in the both brackets but there is just a change in the plus and minus.
Expand (d + 3)(d - 3)
Expand (2 + r)(2 - r)
Factorise 3mk + 5pd + 3md + 5pk
Factorise 3dy - 2gy + 9hd - 6gh
Factorise 12aw + 20cx - 8cw - 30ax
How to factorise the difference of two squares
How to factorize quadratic expressions
To find these numbers divide the 2nd number into something that you can plus them together for the first one.
Factorise: x2 + 7x + 12
- 12 ÷ 2 = 6, 6+2 is 8 so not 7, 12 ÷ 3 = 4, 4 + 3 is 7
- (x + 3) (x + 4)
Factorise x2 + 9x + 8
- 8 ÷ 2 = 4, 4 + 2 does not = 9. 8 ÷ 8 = 1, 8 + 1 = 9 so 9 is the answer
- (x + 1)(x + 8)
Factorise the expression x2 + x - 6
Factorise the expression of a2 - 2a - 15
Factorise the expression: y2 - 6y + 8
When do you factorise quadratic expressions using x2 +bx + c and when do you factorise quadratic expressions using ax2 + bx + c
When the x2 at the start of the expression has a number in front of it
factorise 3g2 + 12g - 36
Factorise 48 - 8p - p2
Factorise 3x2 + 8x + 4
Factorise 3x2 - 11x + 10
Factorise 4x2 - 3x - 7
Factorise 24k2 - 54k - 15
Factorise 14 + 29a - 15a2
When is frequency symmetrical
A distribution is symmetrical if the data is evenly spread or balanced about the center
When is frequency skewed
A distribution is skewed if most of the data is bunched or clustered at one ‘end’ of the distribution and the other ‘end’ has a ‘tail’.
When is frequency positively skewed
When the tail of the line points to the right
When is frequency negatively skewed
when the tail points to the left
When is a distribution bimodal
It is bimodal if there are two peaks in the frequency.
What is the mode in a bimodal
it is the highest peak from the two peaks
What is an outlier
It is when one of the numbers on the data graph does not have any score on it
What is a cluster
It is the number that has the most points / score that is large compared to the other numbers.
What are quartiles and what order do they go in.
LE, Q1 , Q2 , Q3 , UE
What is the interquartile range and how does it work
What is a box plot and how does it work
What is a parallel boxplot
it is literally just 2 box plots but they share the same graph for easy comparison
How to find the mean
Sum of Scores
Number Of Scores
What is the meidan
The middle number
How to find the mode
it is the number that occurs the most
Describe the different strengths points can have on a scatter plot
When are variables directly proportional
∵ d = k*r
so k = 950 ÷ 540 = 1.759
so 950 = 1.759 x 540
when r = 800
d = 1.759 * 800
d = 1407 m
After 800 rotations, the distance travelled will be 1407 m
What is inverse proportion and what is the formula to do it
What are the 3 steps to solve inverse proportion problems
What is a conversion graph?
A conversion graph is used to convert from one unit to another, for example, miles to kilometers or Australian dollars to US dollars.
What is a distance-time graph
The distance traveled by a moving object can be shown on a distance-time graph, also called a travel graph.
This graph shows the noise level of a classroom during a lesson. Describe what may have happened in the classroom during the lesson.
What is a parabola
The graph of a quadratic equation is a smooth U-shaped curve called a parabola
What affects whether the parabola is wide or narrow when the equation is y = ax2
It is the coefficent of x2 As the size of a increases the parabola becomes narrow. If a is negative then the parabola is concave down.
What does a concave up of a parabola y = ax2 look like
What does a concave down of a y = ax2 parabola look like
What is the difference of y = ax2 + c from y = ax2
it is the exact same where a and c are the constants. The + C determines the place where the parabola will sit on the y-axis. If the C is -C then the bottom of the parabola is somewhere on the -y side of the graph depending on what the -C is.
Graph each set of Quadratic equations, showing the vertex of each parabola
How is The parabola of y= a(x - r)2 different from y = ax2 style parabola
Graph the parabola clearly showing the vertex and y intercept
Graph each parabola, clearly showing the vertex and y-intercept
Graph the parabola, clearly showing the vertex and y-intercept
What makes a cubic equation for a cubic curve parabola y = ax3 + C
An equation in which the highest power of the variable is 3 is called a cubic equation
In the cubic parabola what does c do in y = ax 3 + c
It does the same thing as before where it determines where the line will be on the y axis
What is the main rule of Power Curves y = axn + C parabolas and what power x is
if the power of y = axn is even then the parabola is a usual parabola with the (: shape.
If the power of y= axn is odd then the parabola will be a cubic curve parabola.
The higher the power, the narrower the graph
What is the hyperbola y = k/x and what does it look like
What are the rules about hyperbola y = k/x
*If k is positive, the graph is in the 1st and 3rd quadrants.
*If k is negative, the graph is in the 2nd and 4th quadrants.
*The higher value of k, the further the hyperbola is from the x and y axis
*As x becomes larger y gets closer to 0
* As y becomes larger x gets closer to 0
*The graph should never touch the axis
Graph each hyperbola and mark the coordinates of one point on the curve.
Graph each hyperbola and mark the coordinates of one point on the curve.
Graph the hyperbole, find any intercepts and mark the coordinates of one point on the curve.
What is an exponential curve of y = ax and what are some rules
Abn equation of the form y = ax , where a is a positive constant and the variable x is a power, is called an exponential equation.
* The y-intercept of y = ax is 1 since a0 = 1
Sketch the exponential equation and mark the y-intercept on each curve
Sketch the exponential equation and mark the y-intercept on each curve
What is an arithmetic sequence
It is a sequence of numbers such that the difference between the consecutive terms is constant. For example 7,9,11,13,15 all have the difference of 2
How do we calculate arithmetic progression specific terms
Use the formula Tn = a + (n-1)d
where n is number of terms you want to get to
where a is the 1st term
where d is the common difference
calculate the 9th term, for this Arithmetic Sequence:
T9 = 3 + (9 - 1) *5
T9 = 3 + 8 * 5
T9 = 3 + 40
T9 = 43
What are the 2 formulas for calculating the sum of an Arithmetic progression
Sn = n/2 (a + L) <——- Used when we know the last term
Sn = n/2 {2a + (n-1)d} <——- Used when we don’t know the value of the last term
n is the number of terms
a is the first term
l is the last term
d is the common difference
What is Geometric Proggresion
Geometric progression is a sequence of numbers where each new term after the first is formed by multiplying the previous term by a fixed amount
How to find the n th term of a Geometric Progression
Tn = a * rn - 1
Where n is the number of terms
a is the first term
r is the common ratio
How to find the Sum of a GP
Sn = a(rn-1)
r - 1
Where n is the number of terms
Where r is the common ratio
a is the first term
What information do you need to choose if you should use sin, cos or tan
You need a number and you also need that letter. With that choose sin cos or tan.
Find the value of the pronumeral, correct to one decimal place using your formula sheet
Find the value of the pronumeral, correct to one decimal place using your formula sheet
Find the value of Ø, correct to the nearest minute.
Since there is no decimal to plug in you need to press Shift Tan on the calculator
Write the three-figure bearing of each point from O.
The bearing of x from O is 90o + 12o = 102o
Write the three-figure bearing of each point from O.
The bearing of T from O is 360o - 43o = 317o
Write the three-figure bearing of each point from O.
The bearing of M from O is 90o - 38o = 052o
A plane leaves a town and remains on a bearing of 122 for 260 km
A plane leaves a town and remains on a bearing of 122 for 260 km
What are the Rules of trigonometric ratios of complementary angles
If sin 35o = cos ___?
Using the graphical method solve:
Solve using the elimination method
Solve using the elimination method
Solve using the elimination method
Solve using the substitution method
Solve using the substitution method
Find the size of one angle in a regular pentagon.
For a regular octagon, find the size of: each (interior) angle
Find the number of sides in a regular polygon if: each (interior) angle is 140
What are the four congruence tests for triangles and what symbol should we use to show that something is congruent to something else
SSS: If there are three sides
SAS: If there are two sides and an angle
AAS: There are two angles and one side
RHS: There is a right angle and another side
The symbol is
What is the formula that calculates the scale factor for similar figures
Image Length
Original Length
Find the scale factor for the figures:
Find the scale factor for the figures:
Test whether each pair of figures are similar
