Maths - Spring Term Assessment - 2018

Inverse operations:
+ > -, - > +, * > /, / > *
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Algebraic Equation: 3x = 18
Get 'x' on its own: 3x / 3 = 18 / 3, x = 6
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4x - 1 = 18
18 + 1 = 19, 4x / 4 = 19 /4, x = 19/4
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Equations with Brackets: 3 (2x - 5) = 2 (x + 4)
Expand brackets: 6x - 15 = 2x + 8, 4x = 23 / 4, x = 23 / 4
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Type 1: Fraction = Fraction: (x + 2) / 3 = (5x - 1) / 4
Solve by cross multiply: 4 (x + 2) = 3 (5x - 1), expand brackets, 11x = 11, x = 1
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Type 2: Fraction + Fraction = Fraction: (x + 1) / 2 + (2x - 3) / 5 = 7
Put bracket around the section which contains x's, cross multiply, expand and simplify, add the top, solve it.
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Straight line graphs:
The horizontal line passes through 2 on y axis: y = 2, the vertical line passes through -1 on the x axis: x = -1
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y = mx + c
m = rise / run, c = y intercept
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To work out the y intercept choose either points A or B and substitute the point into the equation:
B (1 ,2) 1 = x, 2 = y, y = 5 / 4 x + c, 2 = 5 / 4 * 1 + c, 2 = - 5 / 4 + c, 3 / 4 = c. Name of line is y = 5 / 4x + 3 / 4
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Simultaneous equations: 3c + 2b = 660, 2c + 5b = 1320, how much is 1b and 1c
Method: 3c + 2b = 660 > 1, 2c + 5b = 1320 > 2, 1 * 2 = 6c + 4b = 1320 > 3, 2 * 3 = 6c + 15b = 3960 > 4, 4 - 3, 11b = 2640, = 240
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Simultaneous equations using a graphical method: 4x + y = 6 > 1, 5x - 4y = 18 > 2
1 * 5 = 20x + 5y = 30 > 3, 2 * 4 = 20x - 16y = 72 > 4, 4 - 3, -16 - + 5 = 72 - 30, -21 = 42, y = -2. 1 > 4x -2y = 6, 4x = 8 / 4, x = 2. (2, -2)
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What do angles on a line add up to?
180°
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What do angles on a point add up to?
360°
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What do angles in a triangle add up to?
180°
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360°
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What are 'z' angles known as?
Alternate angles.
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What are 'f' angles known as?
Corresponding angles.
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What are 'x' angles known as?
Vertically opposite angles.
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What are polygons?
A shape with any number of straight lines.
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What are regular polygons?
A shape with an equal amount of sides and angles.
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What is the sum of interior angles?
180 * (n - 2)
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What is the sum of all exterior angles?
360° for all polygons, interior and exterior angles make a straight line: interior + exterior = 180°
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What is the equation for the area of a square?
l * l
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What is the equation for the area of a rectangle?
b * h
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What is the equation for the area of a triangle?
1 / 2 * b * h
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What is the equation for the area of a parallelogram?
b * h
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What is the equation for the area of a trapezium?
1 / 2 (a + b) + h
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What is a prism?
A shape that has the same cross section area along its length.
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What is the equation for volume for any prism?
cross section area * length
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Metric conversions:
1 cm = 10mm = 1cm2 = 10mm2, 1m = 100cm, 1m2 = 10000cm2, 1m3 = 1000000cm
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What is the equation for circumference of a circle?
2 * π * r
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What is the equation for area of a circle?
π * r2
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If you are given c then r =
c / 2 * π
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If you are given a then a then r =
√a / π
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How do you work out arc length?
ϴ / 360 * 2 * π * r
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How do you work out the area of a sector?
ϴ / 360 * π * r2
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What is the volume of a cylinder?
π * r2 * h
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What is the surface area of a solid cylinder?
2 * π * r * h + 2 * π * r2
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What is the volume of a pyramid?
1/3 × base area × perpendicular height
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What is the surface area of a pyramid?
area of the base + the area of all the other sides
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What is the volume of a cone?
1/3 * π * r2 * h
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What is the surface area of a cone? (curved)
π * r * l
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What is the surface area of a cone? (l is slant height)
Doesn't include the area of the base, which is a circle, area * π * r * 2
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What is ratio?
Comparing two or more things.
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Type 1:
Add all the values: 5 : 7 : 3 split between 120, 5 + 7 + 3 = 15 parts, A = 5/15 of 120 = 40 etc.
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Type 2:
5 : 7 : 3 (7 and 3 both get 85), 7 + 3 = 10, 1 part = 8.50, 5 x 8.50 = 42.50.
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How to calculate a percentage of a value:
20% of 80: 20/100 x 80 = 16
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How to calculate one value/value as a %:
21/30 = 70%
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How to work out percentage profit/loss:
profit or loss/original value x 100
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How to work out percentage increase/decrease:
Cross multiply:
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How to work out simple interest:
P I T / 100
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How to work out compound interest:
F = P ( 1 + I / 100) T
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Other cards in this set

Card 2

Front

Get 'x' on its own: 3x / 3 = 18 / 3, x = 6

Back

Algebraic Equation: 3x = 18

Card 3

Front

18 + 1 = 19, 4x / 4 = 19 /4, x = 19/4

Card 4

Front

Expand brackets: 6x - 15 = 2x + 8, 4x = 23 / 4, x = 23 / 4

Card 5

Front

Solve by cross multiply: 4 (x + 2) = 3 (5x - 1), expand brackets, 11x = 11, x = 1