math 3-5

Cards (6)

chapter 3 (71)
q: without expanding/factorising, explain why (2x-1)(x-6) and x²+x-6 are not equivalent
_The constant term in (2x-1)(x-6) is 6.
But the constant term in x²+x-6 is -6.
∴ the two expressions are not equivalent
chapter 3 (algebraic identities)
(a+b)² = a² + 2ab + b²
(a-b)² = a² - 2ab + b²
(a+b)(a-b) = a² - b²
chapter 4 (91)
q: n is a positive integer. Explain why 2n is an even number.
_Since 2n÷2=n (which is an integer), then 2n is divisible by 2.
∴ 2n is an even number.
q: explain why the difference between squares of two consecutive even numbers is always a multiple of 4.
_ ... = 4(2n+1), which is a multiple of 4.
{factorise out 4 from end answer!!}
chapter 4 (96)
q: (x+3y)(x-3y)=13
_x-3y=1 --- (1)
x+3y=13 --- (2)
{since 13 is a prime number, it only has 2 factors. since both are positive integers, then x-3y is smaller than x+3y}
chapter 5 (111)
q: explain why 25x²+9=0
_25x²=-9
Since x²≥0 for all real values of x, then 25x²≥0.
Thus 25x² can never be equal to -9
∴ 25x²+9=0 has no real solutions
chapter 5 (5b q13iii)
q: When will the ball be 49m above the ground?
Briefly explain why there are two possible answers.
_ ...
t=1 or t=7
∴ ball will be 49m above the ground again 1s and 7s after the ball reaches maximum height at t=(7+1)/2=4
Graph is symmetrical about the line t=4, which is equidistant from t=1 and t=7. Hence, there are two possible answers.