Arithmetic and Algebra Study Notes

Module 1: Mathematics - Arithmetic and Algebra Study Notes

• A car travels 24 miles in 45 minutes, its average speed is 32 mph
• The result of 15.4/2 - 2*(6.2 - 15.6) is 26.5
• The volume of a cuboid with dimensions 4 cm, 6 cm, and 12 cm is 0.000288 m^3
• A scalene triangle has all 3 sides unequal
• 4 {2 (5-1) -3} + 8 equals 28
• A rectangle with dimensions 11cm x 120cm has an area of 0.132 m^2
• A cone with height 10 cm and diameter 8 cm has a surface area of 40π cm^2
• 4 3/8 – 2 1/4 + 1/8 = 2 1/4
• 11/16 + 5/8 = 21/16
• 3/4 multiplied by 0.82 equals 0.615
• 7/6 expressed as a decimal is 1.166
• The ratio 6:5 can be expressed as 24:20
• 14^3 can be expressed as 14 * 14 * 14
• 0.0000413 can be written as 413 x 10^7
• 5/8 + 3/4 = 11/8
• The Lowest Common Denominator for 1/6 + 1/5 + 1/17 + 1/2 is 510
• The area of a right-angled triangle is ½ (base * height)
• A circle with a circumference of 12cm has an area of approximately 11.3 sq.cm
• A right circular cone with base radius r, and height l, has an area of π * r * l
• (+ 3)-(-4) equals +7
• To convert imperial gallons to litres, multiply by 3.78
• 9/20 expressed as a percentage is 45%
• To find the area of a circle, multiply the square of the radius by π
• A specific torque loading for a bolt is 50 lbs.ins, needing a 2-inch extension to an 8-inch torque wrench, results in an actual reading of 40 lb.ins
• The fraction 7/8 expressed as a decimal is 0.875
• 0.75 x 0.003 equals 0.00225
• 162 knots is equivalent to 186 mph
• Four percent of 0.01 is 0.0004
• (6 + 2)^2 * 2 - (2 * 45) equals 38
• 17 degrees 49 minutes and 10 seconds added to 22 degrees 22 minutes and 59 seconds equals 40 degrees 12 minutes and 9 seconds
• A cylinder with a diameter of 200 cm and a height of 20 cm has a volume of 628000 cm^3
• The comparison of the power input to the power output of an inverter is a ratio
• The ratio 6:4 can be expressed as 150%
• 200 kilovolts can be expressed as 2 * 10^5 volts
• A cone with an 8cm base diameter and 10cm height has a surface area of 40π
• A rectangle with a height of 11cm and a width of 120cm has an area of 0.132 m^2
• 4 3/8 – 2 ¼ + 1/5 = 2 13/40
• 4*(4 *(4 – 1) –1) –1 = 43
• The lowest common factor of 36, 66 and 126 is 6
• 3% of 0.001 is 0.00003
• 11/16 divided by 5/8 is 11/10
• An aircraft uses 1680 gallons of fuel, with 45% used by the left tank and 32.5% by the right tank, leaves 378 gallons used by the center tank
• The fraction 1/7 in decimal form is 0.14286
• The supplement of 13 degrees is 167
• A ring with an outer diameter of 90 inches and an inner diameter of 80 inches has an area of 425π
• A rectangle with a base of 160cm and a height of 12cm has an area of 0.192 m^2
• An aircraft flying 1350nm in 2 hrs 15 minutes has an average speed of 600kts
• 0.000006 volts can be written as 6 microvolts
• The median of the values 20, 28, 17, 34, 40, 11, 34, 26 is 27.0
• The mode of the following 28, 17, 34, 28, 34, 35, 28, 40 is 28.0
• 0.004 amperes can be written as 4mA
• A sphere with a radius of 2 cm has a surface area of 16π cm^2
• The sum of an odd and an even number is always odd
• A copper pipe with a radius of 7/32 inch has a decimal equivalent of 0.21875
• Millibar is the unit of pressure
• A ball rolls down a hill initially at 60 ft/s, slowing down at a rate of 5 ft/s^2 for 7 seconds, resulting in a final speed of 25 ft/s
• A dial gauge is calibrated to an accuracy of 0.001 inch, the answer should be rounded off to the calibrated value
• In a flight control system, a control cable with a manufacturer's length of 78cm and an allowed elongation of 3% due to wear has a maximum used length of 80.34 cm
• Making 20% profit, with current balance is £900, the pre-profit balance was £750
• One of the square roots of a positive number is positive; the other is negative
• A cylinder with a radius of 20cm and a length of 40cm, using π as 3.1, has a volume of 49600cm^3
• The cube root of a negative number can be found
• Removing roots from the denominator of fractions is rationalizing the denominator
• A cylinder with a diameter of 20cm and length 10cm has a curved surface area of 1256 cm^2
• The conversion factor of litres to pints is 1.76
• The volume of a pyramid is 1/3 times b times h
• The square root of 1600 is 40
• The ratio of 5 feet to 30 inches is 2:1
• Evaluate 5[ 3 + 6(7-4)-2] equals 95
• Evaluate 3[ 5-2( 4-7)] equals 33
• The cube root of -64 is -4
• The cube root of 8^2 is 4
• An engine of 96 horsepower running at 75% power develops 72 horsepower
• A blueprint showing a hole of 0.3751 to be drilled requires a 3/8 fraction size drill bit
• If 120 out of 125 bolts are of acceptable tolerance, 4% are not acceptable
• Evaluate 1/4 + 3/8-1/2, the result is 1/8
• 3 3/4 + 4 2/3 = 8 5/12
• An aircraft travels 1400 nautical miles in 1 hour 45 minutes, its average speed is 800 knots
• The square root of 4 raised to the fifth power is 32
• -3[8-3(5+√9)-( 7-9)] equals -42
• 3/40 is equivalent to 0.075
• The fraction 3/8 expressed as a percentage is 37.5%
• If an aeroplane flies 1000 miles with 80 gallons of fuel, it will need 200 gallons for a 2500-mile flight
• A pinion gear with 16 teeth driving a spur gear with 48 teeth at 120 RPM, finds the pinion gear speed is 360 RPM
• The piston displacement of a master cylinder with a 4cm diameter bore and a piston stroke of 10 cm is 40π cu.cm
• The curved surface area of a right cone is πRL
• There are 25.4 millimetres in an inch
• The area of a circular ring with an outer diameter of 10 cm and inner diameter of 6 cm is 16π sq. cm
• The area of the sector shown is 52 ⅓ cm, taking π=3.14
• 24/0 (twenty four divided by nothing) is infinity
• If 20% of 120 is 24, then 24% of 20 is 4.8
• A shop keeper sold his car for £120, 80% of the buying price, resulting in a £30 loss
• 3 + 4-5(4-2) = -3
• Solving the equation 5x = 3x + 2, x is 1
• Simplify (w + z)(x - y)(y - w) / (y - x)(w - y)(w + z), the answer is +1
• Given 43-x = 21, the value of x is 43-21
• Make L the subject of the formula 2pfL = x results in L = x / 2pf
• Given A = X+BY, setting Y as the subject is (A-X) divided by B
• If y/x = 4 and y = 5 then x = 1 ¼
• (x - 3)(x + 5) = x^2 +2x-15
• 21=43- , is equal to. 43-21
• Evaluate. 2X^2 Z^2 (3X-Z^2 ) = 6x^3 z^2 -2x^2 z^4
• (a * b)(a * b) = a^2 + 2ab + b^2
• If y/x = 4 and x = 5 then y = 20
• Factorise the following : x^2 -x-6=0 is (x+2)(x-3)
• Factorise the following : 4x^2 -6x-28 = 0 results to (2x+7) (x-2)
• Solving for x in the equation: 3(x + 2) = 30 + 2(x-4), x is 16
• Solving 2x = 4(x-3), Evaluate x equals 6
• Solving with 12x/2y + 14 = 50, When y = 2, solving for x equals 12
• 27y = 3 so y is equal to: 1/9
• Values of x that Determine 111. (2x-1)(3x+2) = 0 is x = -0.67, 0.5
• (x + y + z)(x + y + z) = (x + y + z)^2
• If x in an equation equals Ly + 7cb, define the formula for finding the subject y . x-7cb/L
• 64y = 64, then y = 1
• Simplify 3a-2b +6a-3b-2a to 7a-5b
• Simplify 3x-2xy-3y +5xy-2x +2y to x + 3xy-y
• Simplify 5(x-2y) + 3(2y-x) to 2x-4y
• The simplified form of (a+b)(a-c)(b-c) divided by (b+a)(c-a)(c-b) is 1
• Setting P as the subject with this formula I =PRT/100 result in P = 100I/RT
• Making u the subject of the formula v^2 = u^2 + 2as: u = √(v^2 -2as)
• Removing the brackets and simplifying: (x-y)(x-y) equals x^2 -2xy+y^2
• Evaluate (3X^2 -6xy) / (x-2y). Cannot be simplified further
• Evaluate (3a + 2b)(2a-3b) equals 6a^2 -5ab-6b^2
• Solving 4x+8y=64 and 2x-8y=86 for x equals 25
• 11001+11001 = 5010
• 100000 in binary is 32 in decimal
• D in hexadecimal is 13 in decimal
• 128.10101^2 +11001^2 = 4610
• 738 in binary coded decimal is 11100111000
• (A+B)4 is (A+B)^2
• log 9-log 3= log 3
• To isolate y in a=(X+B)/y one would use the forumla y = (X +B)/ a
• 67 divided by 127 is equal to 1/128
• If, 2x-8y=14 and 4x+8y=16; then x= 5
• If 2x-3 = 4; then x = 3.50
• Isolating a from V = (a+b) r^2 results to V / r^2 – b
• Make m the subject of the formula in y=mx+c is y-c/x
• Making x the subject with y = mx+c results in x = (y-c)/m
• Setting c as subject in y = mx+c results in c = y-mx
• Octal has a base of 8
• 101110 in binary is 46 base 10
• Octal 13 in base 10 is 11
• The equation ax^2 +bx+c = 0 is a Quadratic equation
• (X^2 * X^3 )^3 is X ^15
• Hexadecimal has a base of 16
• y=mx+c can also be written x=y-c/m
• The log of 20000.2 is 4.7892
• A quadratic equation has the real roots x=6 and x=9. This correlates to x^2 -15x+54=0
• 10111^2 -1001^2 = 1100 ^2
• The characteristic of 5.74 is 0
• Log63 is 3log6
• In the problem Solve for x: 5x-7=3, the answer is x=2
• Octal is the word given to base 8
• The quadratic equation being 3x^2 +2x+1=0 is a quadratic equation
• Log 1000 is 3.0787
• Log AB is log A+log B
• LogA/B is log A-Log B
• log 100+2 = 1
• If there are two similar angles in a right triangle, these angles are complementary
• The three angles of a triangle summed together equal 180o
• The circumference of a circle is found by multiplying the diameter by 3.142
• Calculating the height of an obtuse triangle whose base is X cm and the area is Y square cm is Y x 2/Χ
• A right-angled triangle has sides of 3 inches and 4 inches, the third side will be 5 inches
• To work out the circumference of a circle use D * 3.142
• An equilateral triangle has three equal sides
• A quadrilateral with only two parallel sides is a Trapezium
• A triangle with equal angles is called equilateral
• If two gears are in mesh, one is larger than the other, the smaller gear rotates at a faster speed
• An acute angle is less than 90 degrees
• A straight line which goes from one point on the circumference to another is called a chord
• A quadrilateral with two pairs of adjacent sides equal and the diagonals intersect at right angles is a kite
• The size of the other two angles of an isosceles triangle with one angle of 100° is 40°, 40°
• A triangle always has at least two acute angles
• The locus of a point which stays the same distance from a given point is a circle
• In the equation 4y = 2x + 8, the y-intercept is 2
• In the equation y = x^2 -3 the x-axis crosses one time
• On a graph with the equation 4y = x + 8, the intercept of y is 2
• With graph points(9, 3) and (3, 1) the slope is 1/3
• With stright line equation 3y = 12x−3 thegradient is 4/1