Int 2 Checklist (Unit 1) Int 2 Checklist (Unit 1) Percentages

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1 Percentages Know that appreciation means an increase in value and depreciation means a decrease in value Calculate simple interest over 1 year Calculate simple interest over a certain number of months (less than 12) Compare different loans using simple interest, for example borrowing for 3 months using (i) 1 5% per month or (ii) 18 5% per annum Calculate the appreciation or depreciation value when told the starting value (s ), the fixed rate of appreciation or depreciation (r %) and the number of time units, normally (but not always) in years (n) over which the value increases or decreases using the formulae: Appreciation = s 1 + n r 100 Depreciation = s 1 n r 100 Know that compound interest is an example of appreciation and differs from simple interest in that interest is added to interest Calculate compound interest M Patel (August 2011) 1 St. Machar Academy

2 Volumes Know that the volume of a sphere of radius r is given by: 4 V = 3 πr 3 Calculate the volume of a sphere given the radius or diameter Calculate the radius or diameter of a sphere given the volume Know that the volume of a cylinder of radius r and height h is: V = πr 2 h Calculate the volume of a cylinder given the height and the radius Calculate the volume of a cylinder given the height and the diameter Calculate the height of a cylinder given the volume and radius Calculate the height of a cylinder given the volume and diameter Calculate the radius of a cylinder given the volume and height Calculate the diameter of a cylinder given the volume and height Calculate the difference in volume between 2 cylinders of the same height but of differing radii Know that the volume of a cone of base radius r and height h is: V = 1 3 πr 2 h Calculate the volume of a cone given the height and the radius Calculate the volume of a cone given the height and the diameter Calculate the height of a cone given the volume and radius Calculate the height of a cone given the volume and diameter Calculate the base radius of a cone given the volume and height Calculate the volume of the solid formed by subtracting the volumes of 2 cones with the same vertex, but different heights Calculate the volume of a prism of cross-sectional area A and length l using: V = A l Given the volume and cross-sectional area of a prism, calculate l Given the volume and length of a prism, calculate A Calculate the volume of a prism consisting of a cuboid and a quarter cylinder Calculate the volume of a prism consisting of a cuboid and a M Patel (August 2011) 2 St. Machar Academy

3 triangular prism Find the volume of a prism consisting of a cuboid with 2 congruent half cylinders attached to each end of the cuboid Calculate the volume of a cone attached (at the common circle) to a hemisphere Given the volume and height of a prism consisting of a quarter of a cuboid, calculate the radius of the cuboid Given 2 solids with the same volume, find an unknown length in one of the solids Linear Relationships Interpret gradient as rate of change Calculate the gradient of a straight line given two points (, 1 1 ) ( x, y 2 2 ) on the line using the gradient formula : m = y x Know that the equation of a straight line with gradient m and y - intercept c is: y x x y and y = mx + c Given a straight line equation in the form P x + Q y = R, rearrange it into the form y = mx + c Find the equation of a straight line given 2 points on it Given the graph of a straight line, find its equation Given the graph of a straight line with the gradient and y - intercept stated, find its equation Given the equation of a straight line, find where it crosses the x - axis Given the equation of a straight line, find where it crosses the y - axis Given the equation of a straight line, make or complete a table of values and draw the graph of the line Sketch a straight line given its equation Sketch the graph of a straight line when told its equation with no actual values for m and c, but generic information about m and c (for example, m > 0 and c < 0 ) M Patel (August 2011) 3 St. Machar Academy

4 Algebraic Operations Multiply algebraic expressions and collect like terms, for example: (3x + 2) (x 1) (2a b) (3a + 2b) 5x + (x 4) (3x + 1) (4x + 2) (x 5) + 3x (3x + 2) (x 5) + 8x 5x + (3x + 2) (2x 7) Multiply expressions and collect like terms, for example: (x + 4) (2x 2 + 3x 1) (x 3) (x 2 + 4x 1) (2y 3) (y 2 + 4y 1) (x + 3) (x 2 + 4x 12) (x + 5) (2x 2 3x 1) (3x + 2) (x 2 + 5x 1) Factorise expressions such as: 9a 2 25b 3y 2 6y Factorise fully expressions such as: 2x 2 18 Know the meaning of difference of 2 squares when factorising Factorise a difference of 2 squares, for example: M Patel (August 2011) 4 St. Machar Academy

5 4p 2 49 x 2 y 2 Make simple algebraic equations in practical contexts and solve them, for example: 4 (2x + 2) = 2y + 2 (x + 3) (solve for y) 4x + 4 = 18 Know the meaning of (quadratic) trinomial Factorise quadratic trinomials such as: x 2 + 2x 15 y 2 + y x x 2 3x 2 7x + 2 2p 2 5p 12 x 2 5x 24 x 2 + x 6 x 2 4x 21 M Patel (August 2011) 5 St. Machar Academy

6 Circles Know that the angle fraction of a circle s sector is the angle at the centre (aka sector angle) θ divided by 360 Calculate the arc length L of a sector given its radius r and sector angle θ using the Arc Length Formula : L = Angle Fraction 2πr Calculate a circle s sector angle given its radius and arc length Calculate a circle s radius given its sector angle and arc length Calculate the sector area A of a circle given its radius r and sector angle θ using the Sector Area Formula : A = Angle Fraction πr 2 Calculate a circle s sector angle given its radius and sector area Calculate a circle s radius given its sector angle and sector area Find perimeters of shapes consisting of arcs of circles joined together Find the perimeter of a shape consisting of an arc of a circle with the two longer sides of a kite Given a triangle in a circle with one side the diameter, find a missing angle Know that a tangent to a circle is a straight line that touches the circle exactly once Know that a tangent to a circle is at 90 to a radius which meets the tangent at a common point Know that a line drawn at 90 to the radius endpoint P is tangent to the circle at P Know that a line drawn at 90 to a circle s tangent (at the point of contact) passes through the centre of the circle Know that any triangle inside a semi-circle, with one side the same as the surrounding circle s diameter (and opposite vertex on the circle), has a right angle opposite that side Know that a triangle in a circle, with one vertex coinciding with the circle s centre and the other 2 vertices on the edge of the circle, is isosceles Use the properties of a circle, its chord and perpendicularity to calculate unknown lengths Use the properties of a circle, triangles inside semi-circle s and perpendicularity to calculate unknown angles M Patel (August 2011) 6 St. Machar Academy