Year 10 Yearlyz Flashcards by Adam jesus

How to simplify the surd √108

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How to simplify the surd of 4√45

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How to add the surds 5√11 + 7√11

12√11

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How to add the surds √80 + √20

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Expand and simplify each expression

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Expand and simplify the binomial product

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Expand and simplify the Binomial product using: (a + b)(a - b) = a²- b²

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Expand and simplify the Binomial product using: (a + b)(a - b) = a² - b²

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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

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The total amount of the investment and the compound interest earned using A = P(1 + R)ⁿ

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Calculate the compound Interest monthly when $24500 is invested at 6.3% p.a. for 5 years

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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.

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Using the Depreciation formula of A=P(1 - R)ⁿ

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Simplify The Surd

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What are the symbols of a distance, midpoint and gradient formula question such as P(-5,8) Q(3,6)

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Find the angle of inclination of a line with a gradient of 1/3 using the formula. Answer = -tan (Gradient)

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Find the angle of inclination of a line with a gradient of -4 using the formula. Answer = -tan (Gradient)

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What is the rule with Parallel Lines about how to find their gradient

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What is the rule with Perpendicular Lines about how to find their gradient

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State whether each pair of gradients represent parallel lines or perpendicular lines

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State whether each pair of gradients represent parallel lines or perpendicular lines

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Find the gradient of a line that is perpendicular to a line with gradient: 2

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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

Write the linear equation in general form

using the formula y - y₁= 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 a^mx aⁿ

a^{m + n}

What are the index laws of a^m÷ aⁿ

a^m ---------------------- aⁿ

What are the index laws of: (a^m)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

What does the fractional indice law equal: a^1/2

What does the fractional indice law equal: a^1/3

What does the fractional indice law equal: a^m/n

Evaluate 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

1. 12 ÷ 2 = 6, 6+2 is 8 so not 7, **12 ÷ 3 = 4, _4 + 3 is 7_** 2. (x + 3) (x + 4)

Factorise x² + 9x + 8

1. 8 ÷ 2 = 4, 4 + 2 does not = 9. **_8 ÷ 8 = 1, 8 + 1 = 9_ so 9 is the answer** 2. (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 = ax³ + 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 the hyperbole, find any intercepts and mark the coordinates of one point on the curve.

What is an exponential curve of y = a^x and what are some rules

Abn equation of the form y = a^x, where a is a positive constant and the variable x is a power, is called an exponential equation. \* The y-intercept of y = a^x is 1 since a⁰ = 1

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 T_n = 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

S_n = n/2 (a + L) \<------- Used when we know the last term S_n = 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

T_n = a \* r^{n - 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 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 90^o+ 12^o = 102^o

Write the three-figure bearing of each point from O.

The bearing of T from O is 360^o - 43^o = 317^o

Write the three-figure bearing of each point from O.

The bearing of M from O is 90^o - 38^o = 052^o

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 35^o = cos \_\_\_?

Using the graphical method solve:

Solve using the elimination 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