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- The lengths of two sides of a right triangle are x/2 and x/3. If one of these sides is the hypotenuse, what is the length of the third side of the triangle?

- √7x/12
- √13x/12
- √7x/6
- √5x/6
- √13x/6

Answer: D

The hypotenuse is the longest side so it must be x/2

By Pythagoras’ Theorem, if the third side is s, then (x/2)^{2} = (x/3)^{2} + s^{2}

(x^{2}/4) – (x^{2}/9) = s^{2}

s^{2} = 5x^{2}/36

s= √5x/6

- 9 – x
^{2}= 37 + 11x

x

-x

- Quantity A is greater
- Quantity B is greater
- The two quantities are equal
- The relationship cannot be determined from the information given

Answer: B

Set the quadratic equal to zero: x^{2} + 11x + 28 = 0.

We factorize it: (x + 4)(x + 7) = 0.

There are two solutions:

EITHER (x + 3) = 0 and x = –3

OR (x + 4) = 0 and x = –4

Since both solutions are negative, x < 0 and –x > 0.

- What is the difference between the areas of a square with perimeter P and a square with perimeter 2P?

- P
^{2}/16 - P
^{2}/4 - P
^{2}/8 - 3P
^{2}/16 - 3P
^{2}/4

Answer: D

A square with perimeter P has sides of length P/4 Area = P^{2}/16

A square with perimeter 2P has sides of length P/2 Area = P^{2}/4

Difference: P^{2}/4 – P^{2}/16 = 3P^{2}/16

- Betty is 10 years older than Jenny. In 3 years, Betty will be double Jenny’s age. How old will Betty be in 5 years?

- 12
- 18
- 22
- 23
- 27

Answer: C

Betty is 10 years older than Jenny: b = j + 10

In 3 years, Betty will be double Jenny’s age: b + 3 = 2(j + 3)

But, j = b – 10

So, b + 3 = 2(b – 10 + 3)

b + 3 = 2b – 14

17 = b

In 5 years, Betty will be 22.

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