S1 Algebra Flashcards

1
Q

What is the test of divisibility for 6?

A
  1. check if the number ends with an even digit
  2. check if the sum of digits of the number is a multiple of 3
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2
Q

What is the test of divisibility for 11?

A
  1. sum up the digits at odd positions and even positions respectively.
  2. check if the difference between the two sums is a multiple of 11
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3
Q

For positive a and b, b copies of a multiplied together is equivalent to?

A

ab
(a to the power of b)

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4
Q

For positive a and b, (-a)-(-b)=?

A

b-a

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5
Q

For positive a and b, a/(-b)=?

A

-(a/b)

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6
Q

For negative a and positive integral b, when is ab positive and negative?

A

when b is odd: ab is negative
when b is even: ab is positive

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7
Q

For positive a and positive integral b, for what b does -ab equal (-a)b?

A

When b is an odd number.
The first expression is always negative since exponents are operated before negation sign. The second expression is only negative when b is odd.

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8
Q

For positive a and b where a>b, compare the sizes of (-a)/b and (-b)/a

A

(-b)/a>(-a)/b.
b/a<a/b, so -(b/a)>-(a/b).

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9
Q

Find the general term of the following sequence:
6, 8, 10, 12, 14, …

A

an=2n+4
The difference between adjacent terms is 2, suggesting that the coefficient of n in the general term is 2. (so when n increases by 1, the term in the sequence increases by 2.)
Then, we solve the equation 2(1)+a=6 to find the constant term in the expression (4).

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10
Q

For a sequence with general term an=n2, a8-a7=?

A

a8=82=64
a7=72=49
a8-a7=15

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11
Q

For given constants a, b, c, and d, solve for x:
ax+b=cx+d

A
  1. subtract terms on both sides to put all terms with x on one side:
    ax-cx=d-b
  2. factorise x from the left hand side:
    x(a-c)=d-b
  3. divide by a-c on both sides to isolate x:
    x=(d-b)/(a-c)
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12
Q

What is the equation for profit?

A

Profit = selling price - cost
Profit = marked price x discount - cost

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13
Q

What is the equation for profit percentage?

A

Profit percentage = (profit/cost) x 100%
Profit percentage = (selling price - cost/cost) x 100%

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14
Q

What is the equation for loss percentage?

A

Loss percentage = (selling price - cost/cost) x 100%

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15
Q

What is the equation for selling price?

A

selling price = marked price x discount

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