Grade 12

Calculus

100

Differentiate implicitly: x² + y³ = 5 with respect to x

Dy/dx=-2x\3y²

200

f(x) = e^{x^4}

12x³e^{x^4}

300

f(x) = x⁴+ 2 \cos(x).

4x³ - 2 \sin(x)

400

Determine the intervals where the function

f(x) = -x² + 2x + 3

is increasing and decreasing.

• Increasing: (-\infty, 1)
• Decreasing: (1, \infty)

500

Consider the function defined implicitly by

x² + xy + \sin(xy) = y²+1.

Dy/dx=y/cos((xy)-x)(y-x)/cos(xy))

Calculus

100

Differentiate implicitly:

x³ + 2y² = 10

with respect to x.

Dy/dx=-(3x²)/(2y)

200

Differentiate:f(x)=e^{x^10}

10x⁹ e^{x^10}

300

Differentiate:

f(x) = 2x³ + 3 sin(x)

6x² - 3 \cos(x)

400

Determine the intervals where the function f(x) =-x² + 4x + 1

is increasing and decreasing.

Answer:

• Increasing: (-\infty, 2)
• Decreasing: (2, (infty)

500

Consider the function defined implicitly by

2x² + 2xy + \sin(2xy) = y²+3

Find dy/dx

Dy/dx=y/sin(xy)-2x)(y-2x/sin(xy))

Mathematical Studies

100

5x - 7 = 18

5x = 25

x = 5

200

A car depreciates by 12% per year.

If it was bought for $25,000, what is its value after 1 year?

12\% \text{ of } 25,000 = 3,000

25,000 - 3,000 = 22,000

300

2x² - 3x - 5 = 0

X=10/4=2.5 or or-4/4=-1

400

f(x) = 3x³ - 2x² + 4x - 1

f'(x) = 9x² - 4x + 4

500

2x + 3y = 11

4x - y = 5

x = {13}/{7}, y = {17}/{7}

Mathematical Studies

100

Solve:log10(1000)

=3

200

Find the simple interest on $8,000 at 6% per annum for 3 years.

Interest = $1,440

300

Find the equation of a line with slope 4 passing through (2, 3).

y = 4x - 5

400

Evaluate:

f (6x² - 4x + 3)\,dx

= 2x³ - 2x² + 3x + C

500

A ball is thrown upward with velocity function:

v(t) = 20 - 9.8t

Find the maximum height reached.

Maximum height ≈ 20.4 m