S1 Algebra

Question 1

What is the test of divisibility for 6?

Answer 1

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

Question 2

What is the test of divisibility for 11?

Answer 2

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

Question 3

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

Answer 3

a^{b
(a to the power of b)}

Question 4

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

Answer 4

b-a

Question 5

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

Answer 5

-(a/b)

Question 6

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

Answer 6

when b is odd: a^b is negative
when b is even: a^b is positive

Question 7

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

Answer 7

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.

Question 8

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

Answer 8

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

Question 9

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

Answer 9

a_n=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).

Question 10

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

Answer 10

a₈=8²=64
a₇=7²=49
a₈-a₇=15

Question 11

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

Answer 11

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)

Question 12

What is the equation for profit?

Answer 12

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

Question 13

What is the equation for profit percentage?

Answer 13

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

Question 14

What is the equation for loss percentage?

Answer 14

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

Question 15

What is the equation for selling price?

Answer 15

selling price = marked price x discount