Free Printable Lower Six Pure Math March Coursework

1.

a)

3x²

b)

x³

c)

6x

d)

3x² + x³

2.

Derive y=3x²-4x+2

a)

6x-6

b)

6x-2

c)

4-6x

d)

6x-4

3.

Differentiate y= 12x^-2

a)

24x^-1

b)

-24x^-3

c)

-24x^-1

d)

6x^-3

4.

Find the derivative of:
f(x) = 7(3x+ 4)⁵

a)

35(3x + 4)⁵

b)

35(3x + 4)⁴

c)

105(3x + 4)⁵

d)

105(3x + 4)⁴

5.

What is the derivative of f?

a)

1/(x - 1)^-1

b)

-1/(x - 1)^-2

c)

-1/(x - 1)

d)

-1/(x - 1)²

6.

What is the derivative of y = 2π?

a)

0

b)

2

c)

-2

d)

None of the above

7.

Calculate the gradient of f(x)=ln(x)+x at x=2/3

a)

0.261

b)

2.5

c)

1.5

d)

-0.405

8.

Find the derivative:
y=5x²e^3x

a)

y'=10xe^3x(2x+3)

b)

y'=5xe^3x(3x+2)

c)

y'=10ex^3x(3x+2)

d)

y'=5xe^3x(2x+3)

9.

Find $\frac{dy}{dx}$ for $y=\frac{3x+2^{ }}{2x+1}$ by using quotient rule.

a)

$-\frac{1}{\left(2x+1\right)^2}$

b)

$\frac{1}{\left(2x+1\right)^2}$

c)

$\left(2x+1\right)^{-2}$

d)

$2x+1$

10.

$If\ y\ =\ \tan\left(x^4\right)\ then\ \frac{\text{d}y}{\text{d}x}=$

a)

$\tan\left(3x^4\right)\$

b)

$\sec\left(x^4\right)\tan\left(x^4\right)$

c)

$\sec^2\left(x^4\right)$

d)

$\sec^2\left(x^4\right).4x^3$

11.

$If\ y\ =\ \sin^5\left(x\right)\ then\ \frac{\text{d}y}{\text{d}x}\ =$

a)

$\cos^5\left(x\right)\$

b)

$5\sin x.\cos x$

c)

$5\cos x$

d)

$5\sin^4x.\ \cos x$

12.

Differentiate ln(secx)

a)

cosec²x

b)

cotxsinx

c)

tanx

d)

sec²x

13.

$\int_{ }^{ }\ \frac{1}{x}+\ \frac{1}{x^2}\ dx$

a)

$x^{-1}\ +\ x^{-2}+\ c$

b)

$x^0\ -\ x^{-1}+\ c$

c)

$\ln x+\ x^{-1}+\ c$

d)

$\ln x-\ x^{-1}+\ c$

14.

$\int\left(6\sqrt{x}-1\right)dx$

a)

$6x^{\frac{3}{2}}+x+C$

b)

$4x^{\frac{3}{2}}-x+C$

c)

$3x^{-\frac{1}{2}}-x+C$

d)

I didn't look at my notes to see how to do this one.

15.

$\int4\sin\left(-x\right)dx$

a)

$4\cos\left(x\right)+C$

b)

$-4\sin\left(-x\right)+C$

c)

$4\cos\left(-x\right)+C$

d)

$-4\cos\left(-x\right)+C$

16.

Integrate $\sqrt{x}$ with respect to x

a)

$x^{\frac{1}{2}}+c$

b)

$\frac{1}{2}x^{-\frac{1}{2}}+\ c$

c)

$\frac{2}{3}x^{\frac{3}{2}}+\ c$

d)

$\frac{3}{2}x^{\frac{3}{2}}+\ c$

17.

∫_₀^²(3x² - 2x)dx ?

a)

8

b)

4

c)

-8

d)

-4

18.

Given that $∫_2^5g(x)dx=-7$ and $\int_5^9\ g\left(x\right)dx=10$

Find the value of $∫_2^9g(x)dx$

a)

-17

b)

3

c)

-3

d)

17

19.

Find the area of the shaded region.

a)

$-2\frac{1}{3}unit^2$

b)

$-4\frac{1}{3}unit^2$

c)

$4\frac{1}{3}unit^2$

d)

$2\ \frac{1}{3}unit^2$

20.

a)

Does not exist

b)

6

c)

4

d)

3

21.

Find the value that makes the function continuous

a)

c=1/3

b)

c=3

c)

c=-3

d)

c=-1/3

22.

Find the limit of the function as x approaches 2⁺.

a)

1

b)

-1

c)

5

d)

DNE

23.

What is the limit of the function as x approaches 1 from the left?

a)

DNE

b)

1

c)

4

d)

-2

24.

What is the limit?

a)

DNE

b)

Infinity

c)

6

d)

12

25.

What is the limit?

a)

DNE

b)

2/3

c)

1/4

d)

∞

Lower Six Pure Math March Coursework

Total questions: 25

Worksheet time: 2hrs 5mins

Similar Resources on Wayground