S1 Algebra Flashcards
What is the test of divisibility for 6?
- check if the number ends with an even digit
- check if the sum of digits of the number is a multiple of 3
What is the test of divisibility for 11?
- sum up the digits at odd positions and even positions respectively.
- check if the difference between the two sums is a multiple of 11
For positive a and b, b copies of a multiplied together is equivalent to?
ab
(a to the power of b)
For positive a and b, (-a)-(-b)=?
b-a
For positive a and b, a/(-b)=?
-(a/b)
For negative a and positive integral b, when is ab positive and negative?
when b is odd: ab is negative
when b is even: ab is positive
For positive a and positive integral b, for what b does -ab equal (-a)b?
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.
For positive a and b where a>b, compare the sizes of (-a)/b and (-b)/a
(-b)/a>(-a)/b.
b/a<a/b, so -(b/a)>-(a/b).
Find the general term of the following sequence:
6, 8, 10, 12, 14, …
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).
For a sequence with general term an=n2, a8-a7=?
a8=82=64
a7=72=49
a8-a7=15
For given constants a, b, c, and d, solve for x:
ax+b=cx+d
- subtract terms on both sides to put all terms with x on one side:
ax-cx=d-b - factorise x from the left hand side:
x(a-c)=d-b - divide by a-c on both sides to isolate x:
x=(d-b)/(a-c)
What is the equation for profit?
Profit = selling price - cost
Profit = marked price x discount - cost
What is the equation for profit percentage?
Profit percentage = (profit/cost) x 100%
Profit percentage = (selling price - cost/cost) x 100%
What is the equation for loss percentage?
Loss percentage = (selling price - cost/cost) x 100%
What is the equation for selling price?
selling price = marked price x discount