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Flashcards in Year 10 Deck (17)
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1
Q

ab x ac

ab ÷ ac

(ab)c

a0

a x ab

A

ab+c

ab-c

abxc

1

ab+1

2
Q

a-b

xa/b

(a/b)c

a1/b

√X x √X

A

1/ab RECIPROCAL

(x1/b)a OR (b√X)a REMEMBER: ath power of the bth root

ac/bc

b√a

X

3
Q

(a+b)2

(a+b)3

(a+b)4

A

a2+2ab+b2

a3+3a2b+3ab2+b3

a4+4a3b+4ab3+b4

4
Q

(X+a)(X-a)

A

X2-a2

5
Q

ax2+bx+c / [2x2+11x+12]

A

Times a by c / 2 X 12

Find two factors of this number (ac / 24) that add to make b / 11

Replace bx / 11x with those two numbers (+3 and +8)

ax2+nx+nx+c / 2x2+3x+8x+12

Factorise both sides / x(2x+3) +4 (2x+3)

Factorise the brackets / (2x+3) (x+4)

6
Q

ax2+bx+c=0 / 2x2+11x+12=0

A

ac method to give factors / (2x+3) (x+4)

If pq=0 EITHER p=0 OR q=0

So EITHER 2x+3=0 OR x+4=0

Either x= -1.5 OR x= -4

7
Q

When you multiply or divide an inequality by a negative number, you must…

< becomes

> becomes

≤ becomes

≥ becomes

A

Reverse the inequality symbol i.e. “FLIP THE SIGNS!!!!”

>

<

8
Q

Define independent event

How do you work out the probability that A and B will both happen independently?

How do you work out the probability that either A or B will happen independently?

When the order doesn’t matter?

Define conditional probability

A

The outcome of one does not affect the other

P(A) x P(B)

P(A) + P(B)

P(A x B) +P(A x B)

When conditions change later events or are dependent upon earlier events

9
Q

What type of data are frequency diagrams used to display?

Bar charts?

Histograms?

A

Grouped discrete data

Ungrouped discrete data

Grouped continuous data with unequal class widths

10
Q

Volume of a prism

Volume of a pyramid

Volume of a sphere

Volume of a cone

1 litre in cm3

1 m3 in cm3 then in mm3

1 m3 in litres

A

Area of cross section x length

1/3 A h (1/3 x base area x height)

4/3 π r3

1/3 π r2 h

1,000cm3

1,000,000cm3 or 1,000,000,000mm3

1,000L

11
Q

Surface area of a sphere

Surface area of a hemisphere

Surface area of a cone. What is L?

1 m2 in cm2 and then mm2

A

4πr2

3πr2 [2πr2 + πr2]

πr2 [bottom surface]+ πr L [curved area] . L is slant height [√(h2+r2)]

10,000cm2 . 1,000,000mm2

12
Q

When plotting a cumulative frequency diagram from GROUPED data, which points do you plot (along the x axis)? Is it: a) the mid-point b) the upper bound c) the lower bound

A

b) The UPPER bound

13
Q

What is the cosine rule? (cosA and a2 as subjects)

A

a2 = b2 + c2 - 2bc cosA

cosA = (b2 + c2 - a2) ÷ 2bc

14
Q

√a x √b = ?

√a ÷ √b = ?

C√a x D√b = ?

C√a ÷ D√b = ?

Rationalising means ?

A

√(ab)

√(a/b)

CD√(ab)

C/D√(a/b)

Writing a fraction in the form SURD / INTEGER

15
Q

What is a random sample (proper definition)?

A

Each member of the population has an equal chance of selection

16
Q

To convert a recurring decimal into a fraction…

A
  1. Make x = the recurring decimal
  2. Multiply both sides by 10n, where n is the number of recurring digits
  3. Subtract the two equations
  4. Simplify the resultant equation
17
Q

Vectors: what do the following mean?

—> —>

AB = 5CD

—> —>

AB = 2AX

A

The lines AB and CD are parallel

AB and AX are parallel; A, B and X are part of the same straight line (A is common); X is the midpoint of AB