BODMAS
5.25 / 0.015
350
Thomas invested $1498 at 6% simple interest per annum. How much interest has he earned after 6 months?
$44.94
SI = P x R x T / 100
SI = 1498 * 0.06 * 0.5 = 44.94
Simplify (x-2)/3 + (x+1)/4
(7x - 5)/12
Put it over the same denominator: 12
What is the formula for the inverse of a square matrix?
A-1 = 1/|A| * (Adj A) or
= 1/(ad-bc) * [d -b]
[-c a]
F shape = corresponding angles = are equal
Z shape = alternate angles = are equal
C shape = co-interior angles = add up to 180 degreees
Square root of 6.5025 to 2 s.f.
2.6
The calculator will give you 2.55 BUT with significant figures, it'd be 2.6
4 mangoes and 2 pears cost $24, but 2 mangoes and 3 pears cost $16.
Write an expression to represent these!
let mangoes be m and pear be p
4m + 2p = 24
2m + 3p = 16
If q = 8, what is p?
1
3p + 5 = 8
3p = 8 - 5
3p = 3
p = 3/3 = 1
If we have 2 matrixes A and B, is AB = BA?
FALSE!
1. To be able to multiply matrices depends on whether the number of columns in the first matrix matches the number of rows in the second matrix.
2. The order matters in matrix multiplication!
B = {multiples of 3}
What is n(AnB)?
3
A = {12,14,16,18,20,22,24,26}
B = {12,15,18,21,24}
AnB = {12,18,24}, so the cardinality of AnB = 3
3.142 x (2.236)2 to 3 s.f.
15.7
The cash price of a laptop is $1299. But you can buy it on hire purchase with a deposit of $350 and 10 monthly payments of $120 each. How much would you save with the better deal?
$251
Hire purchase = $350 + ($120x10) = $1550
Cash Price = $1299
Savings = $251
If f(2) = 4
What is f-1(4)?
2!
The function f-1(a) tells us what the value of x is when we put it in f(x) to get a!
A = [ 1 2]
B = [5 -1 ]
2A + B =
[7 3]
2A + B = 2[1 2] + [5 -1]
= [2 4] + [5 -1]
= [7 3]
When we have an algebraic function (e.g. 2x/(x+1)) what would the condition be for the function to be undefined?
When the denominator is 0, the function is undefined
Because anything divided by 0 is undefined
If a = -1, b = 3, c = -3,
Find b2 - c2
5
b2 - c2 = 32 - 22 = 9 - 4 = 5
Jack bought 150 shirts for $1920 from a factory, and sold them at $20 each. What was his profit percentage, to the nearest whole number?
56%
CP = $1920
SP = 150*$20 = $3000
Profit = $1080
Profit % = Profit/CP * 100
= 1080/1920 * 100 = 56.25% = 56% to the nearest percent
Solve the simultaneous equations
2x + 3y = 9
3x - y = 8
x = 3, y = 1
You can use the substitution or elimination method!
I would use the substitution and make y of eq'n 2 the subject of the formula!
The coordinates of P and Q are (2,4) and (8,2) respectively.
What is the vector for PQ?
6i -2j
OP = 2i + 4j
OQ = 8i + 2j
PQ = PO + OQ = -(OP) + OQ
= -2i -4j + 8i + 2j
What is the formula for an arithmetic progression/sequence?
(For Math students: when we have a pattern question!)
a + d(n-1)
a = first term
d = how much we increase each number by as we go on
n = the number in the progression we've reached
Solve for 8 - x <= 5x + 2
8 - x <= 5x + 2
8 - 2 <= 5x + x
6 <= 6x
1 <= x
x >= 1
Josh is paid $3,140 per month in fixed salary and an annual commission of 2% on the number of computers he sells. If he sold $72,000 of computers this year, what is his total income for the year?
$39,120
Fixed salary = $3,140*12 = $37,680
Commission = 2%($72,000) = $1,440
Total salary = $37,680 + $1,440 = $39,120
Factorize 4p3 - p completely
p(2p-1)(2p+1)
= 4p3 - p
= p(4p2 - 1) -> difference of 2 squares
= p(2p-1)(2p+1)
VY = a and VW = b. If S is a midpoint on WY such that WS:SY = 1:2, what is WS?
(a-b)/3
WY = WV + VY = -(VW) + VY = -b + a = a-b
WS:SY = 1:2, so WS = 1/3 of WY = 1/3 (a-b)
List 4 important things to include when we have to sketch a quadratic function (and how to find them)
BONUS POINTS: what is the difference between a maximum point and a maximum value?
Type of curve (min/max): if a is positive or negative
Y-intercept (where the curve cuts the y-axis): the value of c in the function
Roots (where it cuts the x-axis): by solving the function quadratically
Turning point (min/max point): complete the square
The maximum point is the highest point on a curve. The maximum value is the y-value of the maximum point.