Grind #1 - Quadrilaterals

True or false:

**(a)** All quadrilaterals are parallelograms.

**(b)** All rectangles are parallelograms.

**(c)** All squares are parallelograms.

**(d)** All rhombuses are quadrilaterals.

**(e) **Find the angle \(A\) in the following *quadrilateral*:

**(f) **Find the angles \(A\), \(B\) and \(C\) in the following *parallelogram*:

**(g) **Find the value of \(x\) in the following *quadrilateral*:

Answers

**(a) **False

**(b)** True

**(c)** True

**(d)** True

**(e)** \(146^{\circ}\)

**(f)** \(A=53^{\circ}\), \(B=127^{\circ}\) and \(C=127^{\circ}\)

**(g)** \(37.5^{\circ}\)

Grind #2 - Other Shapes

The length of a square’s side is \(x-2\mbox{ cm}\).

**(a)** Write down an expression for the *area* of the square.

**(b)** Write down an expression for the *perimeter* of the square.

**(c)** The perimeter of the square is equal to \(20\mbox{ cm}\). What is the value of \(x\)?

**(d) **Calculate the area of the shape below.

A circle has a *diameter* of \(10\mbox{ cm}\).

Calculate the circle’s:

**(e)** radius

**(f)** circumference

**(g)** area

by using \(3.14\) as an approximation for \(\pi\) where necessary.

The circumference of a particular circle is \(x\mbox{ cm}\) and the area of that same circle is \(x\mbox{ cm}^2\).

**(h)** What is the radius of the circle?

**(i)** What is the value of \(x\)?

Answers

**(a) **\((x-2)^2\mbox{ cm}^2\)

**(b)** \(4x-8\mbox{ cm}\)

**(c)** \(7\mbox{ cm}\)

**(d)** \(400\mbox{ cm}^2\)

**(e)** \(5\mbox{ cm}\)

**(f)** \(31.4\mbox{ cm}\)

**(g)** \(78.5\mbox{ cm}^2\)

**(h)** \(2\mbox{ cm}\)

**(i)** \(4\pi\)

Grind #3 - Quadratic Equations

Solve the following equations:

**(a)** \(x^2+7x+10=0\)

**(b)** \(3x^2-7x+2=0\)

Solve the following equations and write you answers in surd form:

**(c)** \(3x^2+8x+2=0\)

**(d)** \(6x^2-9x-4=0\)

Two numbers have a sum of \(13\).

**(e)** If one of the numbers is \(x\), what is the other number in terms of \(x\)?

**(f)** If the sum of their squares is \(89\), find the numbers.

The length of a rectangle is \(4\mbox{ cm}\) more than its width. The area of that rectangle is \(77\mbox{ cm}^2\).

**(g) **What is the length and the width of the rectangle?

Answers

**(a) **\(x=-2\) and \(x=-5\)

**(b) **\(x=\dfrac{1}{3}\) and \(x=2\)

**(c)** \(x=\dfrac{-4+\sqrt{10}}{3}\) and \(x=\dfrac{-4-\sqrt{10}}{3}\)

**(d)** \(x=\dfrac{9+\sqrt{177}}{12}\) and \(x=\dfrac{9-\sqrt{177}}{12}\)

**(e)** \(13-x\)

**(f)** \(5\) and \(8\)

**(g)** Length is \(11\mbox{ cm}\) and width is \(7\mbox{ cm}\).

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