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Maths > Year 10 Yearlyz > Flashcards

Year 10 Yearlyz Flashcards

1
Q

How to simplify the surd √108

A
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2
Q

How to simplify the surd of 4√45

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3
Q

How to add the surds 5√11 + 7√11

A

12√11

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4
Q

How to add the surds √80 + √20

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5
Q
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6
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7
Q

Expand and simplify each expression

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8
Q

Expand and simplify the binomial product

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9
Q

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

A
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10
Q

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

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11
Q

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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12
Q

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

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13
Q

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

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14
Q

What is Depreciation

A

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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15
Q

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

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16
Q

Simplify The Surd

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17
Q

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

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18
Q

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

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19
Q

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

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20
Q

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

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21
Q

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

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22
Q

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

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23
Q

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

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24
Q

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

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25
Q

Find the gradient of a line that is perpendicular to a line with gradient: -3

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26
Q

Find the gradient of a line that is perpendicular to a line with gradient: 3/4

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27
Q

Find the gradient of a line that is perpendicular to a line with gradient: -0.6

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28
Q

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”

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29
Q

What is the main rule of the equation of horizontal and vertical lines

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30
Q

Find the gradient and y-intercept of the line with the equation y = -4x + 9 using the formula y = mx + b

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31
Q

Find the gradient and y-intercept of the line with the equation y = pic using the formula y = mx + b

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32
Q

Find the gradient and y-intercept of the line with the equation y = pic using the formula y = mx + b

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33
Q

Write the linear equation in general form

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34
Q

Write the linear equation in general form

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35
Q

Write the linear equation in general form

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36
Q
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37
Q

using the formula y - y 1 = m(x - x1)

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38
Q
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39
Q

Find the equation of the line

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40
Q
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41
Q
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42
Q

Find the equation of line k

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43
Q

Find the coordinates of point A

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44
Q

What formula is need to expand a binomial product?

A

(a + b)(a - b) = a2 - b2

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45
Q

What formula is needed to expand a binomial product

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46
Q
A
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47
Q

What are the index laws of am x an

A

am + n

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48
Q

What are the index laws of am ÷ an

A

am

an

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49
Q

What are the index laws of: (am)n

A

a m x n

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50
Q

What are the index laws of (ab)n

A

anbn

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51
Q

What are the index laws of (a/b)n

A

an/bn

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52
Q

What are the index laws of a0

A

whenever something is to the power of 0 it = 1

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53
Q
A
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54
Q

What are the index laws of a -n

A

1/an

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55
Q

What are the index laws of a-1

A

1/a

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56
Q

What are the index laws of (a/b)-1

A

b/a

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57
Q

What are the index laws of (a/b)-n

A

bn/an

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58
Q

Simplify the expression

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59
Q

Simplify the expression

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60
Q

Simplify the expression

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61
Q

What does the fractional indice law equal: a1/2

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62
Q

What does the fractional indice law equal: a1/3

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63
Q

What does the fractional indice law equal: am/n

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64
Q

Evaluate the expression:

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65
Q

Simplify the expression:

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66
Q

Simplify the expression:

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67
Q

Simplify the expression:

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68
Q

Simplify the expression:

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69
Q

Simplify the expression:

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70
Q

Simplify the expression:

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71
Q

Simplify the expression:

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72
Q

Simplify the expression:

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73
Q

Simplify the expression:

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74
Q

Expand and simplify by collecting like terms

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75
Q

How do you factorize an expression

A

Find the HCF by pressing GCD on your calculator and plug the numbers in and then…

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76
Q

Factorise 25b2 - 20ab

A
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77
Q

factorise x(4 + y) + 2(4 + y)

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78
Q

Factorise -b2 + 8b

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79
Q

How to expand a perfect square

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80
Q

expand (n - 5)2

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81
Q

expand (k + 4)2

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82
Q

Expand (3y - 8)2

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83
Q

How to expand the Difference of two squares

A

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.

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84
Q

Expand (d + 3)(d - 3)

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85
Q

Expand (2 + r)(2 - r)

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86
Q

Factorise 3mk + 5pd + 3md + 5pk

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87
Q

Factorise 3dy - 2gy + 9hd - 6gh

A
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88
Q

Factorise 12aw + 20cx - 8cw - 30ax

A
89
Q

How to factorise the difference of two squares

A
90
Q

How to factorize quadratic expressions

A

To find these numbers divide the 2nd number into something that you can plus them together for the first one.

91
Q

Factorise: x2 + 7x + 12

A
  1. 12 ÷ 2 = 6, 6+2 is 8 so not 7, 12 ÷ 3 = 4, 4 + 3 is 7
  2. (x + 3) (x + 4)
92
Q

Factorise x2 + 9x + 8

A
  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)
93
Q

Factorise the expression x2 + x - 6

A
94
Q

Factorise the expression of a2 - 2a - 15

A
95
Q

Factorise the expression: y2 - 6y + 8

A
96
Q

When do you factorise quadratic expressions using x2 +bx + c and when do you factorise quadratic expressions using ax2 + bx + c

A

When the x2 at the start of the expression has a number in front of it

97
Q

factorise 3g2 + 12g - 36

A
98
Q

Factorise 48 - 8p - p2

A
99
Q

Factorise 3x2 + 8x + 4

A
100
Q

Factorise 3x2 - 11x + 10

A
101
Q

Factorise 4x2 - 3x - 7

A
102
Q

Factorise 24k2 - 54k - 15

A
103
Q

Factorise 14 + 29a - 15a2

A
104
Q

When is frequency symmetrical

A

A distribution is symmetrical if the data is evenly spread or balanced about the center

105
Q

When is frequency skewed

A

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’.

106
Q

When is frequency positively skewed

A

When the tail of the line points to the right

107
Q

When is frequency negatively skewed

A

when the tail points to the left

108
Q

When is a distribution bimodal

A

It is bimodal if there are two peaks in the frequency.

109
Q

What is the mode in a bimodal

A

it is the highest peak from the two peaks

110
Q

What is an outlier

A

It is when one of the numbers on the data graph does not have any score on it

111
Q

What is a cluster

A

It is the number that has the most points / score that is large compared to the other numbers.

112
Q

What are quartiles and what order do they go in.

A

LE, Q1 , Q2 , Q3 , UE

113
Q

What is the interquartile range and how does it work

A
114
Q

What is a box plot and how does it work

A
115
Q
A
116
Q
A
117
Q
A
118
Q

What is a parallel boxplot

A

it is literally just 2 box plots but they share the same graph for easy comparison

119
Q
A
120
Q

How to find the mean

A

Sum of Scores

Number Of Scores

121
Q

What is the meidan

A

The middle number

122
Q

How to find the mode

A

it is the number that occurs the most

123
Q
A
124
Q
A
125
Q

Describe the different strengths points can have on a scatter plot

A
126
Q

When are variables directly proportional

A
127
Q
A

∵ 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

128
Q
A
129
Q

What is inverse proportion and what is the formula to do it

A
130
Q

What are the 3 steps to solve inverse proportion problems

A
131
Q
A
132
Q

What is a conversion graph?

A

A conversion graph is used to convert from one unit to another, for example, miles to kilometers or Australian dollars to US dollars.

133
Q

What is a distance-time graph

A

The distance traveled by a moving object can be shown on a distance-time graph, also called a travel graph.

134
Q
A
135
Q
A
136
Q

This graph shows the noise level of a classroom during a lesson. Describe what may have happened in the classroom during the lesson.

A
137
Q
A
138
Q
A
139
Q

What is a parabola

A

The graph of a quadratic equation is a smooth U-shaped curve called a parabola

140
Q

What affects whether the parabola is wide or narrow when the equation is y = ax2

A

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.

141
Q

What does a concave up of a parabola y = ax2 look like

A
142
Q

What does a concave down of a y = ax2 parabola look like

A
143
Q

What is the difference of y = ax2 + c from y = ax2

A

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.

144
Q

Graph each set of Quadratic equations, showing the vertex of each parabola

A
145
Q
A
146
Q

How is The parabola of y= a(x - r)2 different from y = ax2 style parabola

A
147
Q

Graph the parabola clearly showing the vertex and y intercept

A
148
Q

Graph each parabola, clearly showing the vertex and y-intercept

A
149
Q

Graph the parabola, clearly showing the vertex and y-intercept

A
150
Q

What makes a cubic equation for a cubic curve parabola y = ax3 + C

A

An equation in which the highest power of the variable is 3 is called a cubic equation

151
Q

In the cubic parabola what does c do in y = ax 3 + c

A

It does the same thing as before where it determines where the line will be on the y axis

152
Q
A
153
Q

What is the main rule of Power Curves y = axn + C parabolas and what power x is

A

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

154
Q
A
155
Q

What is the hyperbola y = k/x and what does it look like

A
156
Q

What are the rules about hyperbola y = k/x

A

*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

157
Q

Graph each hyperbola and mark the coordinates of one point on the curve.

A
158
Q

Graph each hyperbola and mark the coordinates of one point on the curve.

A
159
Q

Graph the hyperbole, find any intercepts and mark the coordinates of one point on the curve.

A
160
Q
A
161
Q

What is an exponential curve of y = ax and what are some rules

A

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

162
Q

Sketch the exponential equation and mark the y-intercept on each curve

A
163
Q

Sketch the exponential equation and mark the y-intercept on each curve

A
164
Q

What is an arithmetic sequence

A

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

165
Q

How do we calculate arithmetic progression specific terms

A

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

166
Q

calculate the 9th term, for this Arithmetic Sequence:

A

T9 = 3 + (9 - 1) *5

T9 = 3 + 8 * 5

T9 = 3 + 40

T9 = 43

167
Q

What are the 2 formulas for calculating the sum of an Arithmetic progression

A

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

168
Q

What is Geometric Proggresion

A

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

169
Q

How to find the n th term of a Geometric Progression

A

Tn = a * rn - 1

Where n is the number of terms

a is the first term

r is the common ratio

170
Q

How to find the Sum of a GP

A

Sn = a(rn-1)

r - 1

Where n is the number of terms

Where r is the common ratio

a is the first term

171
Q

What information do you need to choose if you should use sin, cos or tan

A

You need a number and you also need that letter. With that choose sin cos or tan.

172
Q

Find the value of the pronumeral, correct to one decimal place using your formula sheet

A
173
Q

Find the value of the pronumeral, correct to one decimal place using your formula sheet

A
174
Q

Find the value of Ø, correct to the nearest minute.

A

Since there is no decimal to plug in you need to press Shift Tan on the calculator

175
Q
A
176
Q
A
177
Q

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

A

The bearing of x from O is 90o + 12o = 102o

178
Q

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

A

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

179
Q

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

A

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

180
Q
A
181
Q

A plane leaves a town and remains on a bearing of 122 for 260 km

A
182
Q

A plane leaves a town and remains on a bearing of 122 for 260 km

A
183
Q

What are the Rules of trigonometric ratios of complementary angles

A
184
Q

If sin 35o = cos ___?

A
185
Q
A
186
Q
A
187
Q
A
188
Q
A
189
Q
A
190
Q
A
191
Q
A
192
Q
A
193
Q
A
194
Q
A
195
Q
A
196
Q

Using the graphical method solve:

A
197
Q

Solve using the elimination method

A
198
Q

Solve using the elimination method

A
199
Q

Solve using the elimination method

A
200
Q

Solve using the substitution method

A
201
Q

Solve using the substitution method

A
202
Q

Find the size of one angle in a regular pentagon.

A
203
Q
A
204
Q

For a regular octagon, find the size of: each (interior) angle

A
205
Q
A
206
Q

Find the number of sides in a regular polygon if: each (interior) angle is 140

A
207
Q

What are the four congruence tests for triangles and what symbol should we use to show that something is congruent to something else

A

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

208
Q
A
209
Q
A
210
Q
A
211
Q
A
212
Q

What is the formula that calculates the scale factor for similar figures

A

Image Length

Original Length

213
Q

Find the scale factor for the figures:

A
214
Q

Find the scale factor for the figures:

A
215
Q
A
216
Q

Test whether each pair of figures are similar

A
217
Q
A
218
Q
A

Maths (9 decks)

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