Lady Cadet Course Academic Test - Mathematics Syllabus

How do you convert a fraction to a percentage?

Multiply the fraction by 100 and add the percent sign. For example, 3/5 = (3/5) x 100 = 60 percent.

How do you find x percent of a number N?

Compute (x/100) x N. For example, 20 percent of 50 = (20/100) x 50 = 10.

How do you calculate percentage increase?

Percentage increase = (Increase / Original value) x 100.

If a value increases by x percent and then decreases by x percent, what is the net change?

There is a net decrease of (x squared / 100) percent. For example, +10 percent then -10 percent gives a net 1 percent decrease.

Define Cost Price (CP) and Selling Price (SP).

CP is the price at which an article is bought. SP is the price at which it is sold.

What is the formula for profit and profit percent?

Profit = SP - CP (when SP > CP). Profit percent = (Profit / CP) x 100.

What is the formula for loss and loss percent?

Loss = CP - SP (when CP > SP). Loss percent = (Loss / CP) x 100.

How do you find SP given CP and profit percent?

SP = CP x (100 + profit percent) / 100.

How do you find CP given SP and profit percent?

CP = SP x 100 / (100 + profit percent).

What is the difference between marked price, discount, and selling price?

Marked Price (MP) is the listed price. Discount is a reduction on MP. SP = MP - Discount, where Discount = (discount percent/100) x MP.

State the formula for Simple Interest.

SI = (P x R x T) / 100, where P is principal, R is rate percent per annum, and T is time in years.

State the formula for the Amount in Simple Interest.

Amount = Principal + Simple Interest = P + (P x R x T)/100 = P(1 + RT/100).

State the formula for Compound Interest amount (compounded annually).

Amount A = P(1 + R/100) to the power n, where n is the number of years. CI = A - P.

How is compound interest amount adjusted when compounded half-yearly?

Use rate R/2 and time 2n: A = P(1 + (R/2)/100) to the power 2n.

Why is compound interest greater than simple interest for the same P, R, and T (T > 1)?

Because in CI interest is calculated on the accumulated amount (interest on interest), whereas SI is only on the original principal.

State the basic formula relating speed, distance, and time.

Speed = Distance / Time. Therefore Distance = Speed x Time and Time = Distance / Speed.

How do you convert km/hr to m/s?

Multiply by 5/18. For example, 36 km/hr = 36 x 5/18 = 10 m/s.

What is relative speed for two objects moving in opposite directions and in the same direction?

Opposite directions: add the speeds (s1 + s2). Same direction: subtract the speeds (s1 - s2).

What is the average speed for equal distances at speeds a and b?

Average speed = 2ab / (a + b), the harmonic mean of the two speeds.

If A can do a work in n days, what is A's one-day work?

A's one-day work is 1/n of the total work.

If A does a work in x days and B in y days, how long do they take together?

Together they take xy / (x + y) days, since combined one-day work = 1/x + 1/y.

State the formula relating men, days, and work (work equivalence).

M1 x D1 / W1 = M2 x D2 / W2. With equal work: M1 x D1 = M2 x D2.

What is a term in an algebraic expression, and what are like terms?

A term is a part separated by + or - signs. Like terms have the same variables raised to the same powers, e.g. 3xy and 5xy.

What is the degree of a polynomial?

The highest power of the variable in the polynomial. For example, 4x cubed + 2x has degree 3.

Expand (a + b) squared and (a - b) squared.

(a + b) squared = a squared + 2ab + b squared. (a - b) squared = a squared - 2ab + b squared.

State the identity for (a + b)(a - b).

(a + b)(a - b) = a squared - b squared (difference of two squares).

What is a linear equation in one variable and how many solutions does it have?

An equation of the form ax + b = 0 (a not 0), with the variable to the first power. It has exactly one solution.

What is the standard form of a quadratic equation?

ax squared + bx + c = 0, where a, b, c are constants and a is not 0.

State the quadratic formula.

x = [-b plus or minus sqrt(b squared - 4ac)] / (2a) for ax squared + bx + c = 0.

What does the discriminant tell you, and what is its formula?

Discriminant D = b squared - 4ac. If D > 0 roots are real and distinct; if D = 0 roots are real and equal; if D < 0 roots are imaginary (no real roots).

How do you factorize a quadratic of the form x squared + bx + c?

Find two numbers whose product is c and whose sum is b, then write x squared + bx + c = (x + p)(x + q). For example, x squared + 5x + 6 = (x + 2)(x + 3).