MYP5 Math

Logarithms

100

Evaluate log₉729

3

200

Rewrite the following in the form log(c).

log(3)+log(5)  

log(15)

300

Change the following Logarithm into the base of 10

log₈(500)

log(500) / log(8)

400

Evaluate

log₃(b)⋅log_b(27)

3

500

Find t

−3⋅10^2t=−28

Express this as a logarithm base 10.

log(28/3) / 2

Long division

100

(−18x²−6x+12) / (3x³+9x−1)

What are the degrees of the quotient and the remainder?

Quotient: 0

Remainder: 2

200

(6x⁹ - 5x⁸ - 12x³ + 60) / x⁶

What are the quotient and the remainder?

Quotient: 6x³ - 5x²

Remainder: - 12x³ + 60

300

(x³+5x²−9x+30) / (x+7)

x² - 2 x + 5 - 5/(x + 7)

400

(x³+2x²+x) / (x²+1)

What are the quotient and the remainder?

Quotient: x + 2

Remainder: -2

500

(2x⁴+2x+2x²+7x³+3x−4)  / (x²+3x−1)

2x² + x + 1 + (3 (x - 1))/(x² + 3x - 1)

Synthetic division

100

If I divide a polynomial by (x-1),

When I do synthetic division, what number should I put next to the line?

1

200

(3x³+x²−4x+12) / (x+2)

3x² - 5x + 6

300

(2x³−11x²+25) / (x - 5)

2x² - x - 5

400

(3x³+x−11) / (x+1)

3x²-3x+4 - 15/(x + 1)

500

(16x³ - 2 + 14x - 12x²) ÷ (2x + 1)

8x² -10x +12 - 14/(2x + 1)

Factorization (Factor Theorem)

100

Select all polynomials that are divisible by (x−1).

a) A(x) = 3x3+2x2−x

b) B(x) = 5x3−4x2−x   

c) C(x) = 2x3−3x2+2x−1 

d) D(x) = x3+2x2+3x+2

b , c

200

Find the value of c so that (x−2) is a factor of the polynomial p(x)

p(x) = x³−4x²+3x+c  

c = 2

300

The polynomial p(x)=3x³−20x²+37x−20 has a known factor of (x - 4)

Rewrite p(x) as a product of factors.

p(x) = (x - 4) (x - 1) (3x - 5)

400

Factorize 5x³−9x²−6x+8 

(x - 2) (x + 1) (5x - 4)

500

Factorize x³+3x²−4

(x - 1)(x + 2)²

Calculating exponents

100

What is:

a) 0¹⁸

b) 1³⁵

a) 0

b) 1

200

calculate:

a) 1234⁰

b) 135768749302⁰

a) 1

b) 1

300

Rewrite the expression in the form aⁿ.

a) a⁰*a⁶

b) a⁵*a¹²

a) a⁶

b) a¹⁷

400

a) (10²⋅7⁵)⁵ = ?

b) (x⁴⋅y⁴)³ = ?

 

a) 10¹⁰ * 7²⁵

b) x¹² * y¹²

500

Simplify fully:

(2x⁴*6x²) / 3x³

4x³