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:
(a) False
(b) True
(c) True
(d) True
(e) \(146^{\circ}\)
(f) \(A=53^{\circ}\), \(B=127^{\circ}\) and \(C=127^{\circ}\)
(g) \(37.5^{\circ}\)
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 \(x\)?
(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) \(4\pi\)
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?
(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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